Poppy O'neill

Ludger Fischer

Rémi Revellin

Jocelyn Bonjour
email: jocelyn.bonjour@insa-lyon.fr

Phase change dispersions: a literature review on their thermo-rheological performance for cooling applications

Keywords:

Phase change dispersions are two-phase fluids that consist of a phase change material dispersed in a continuous phase and stabilised with the aid of surfactants. Due to the high thermal storage capacity, on accounts of the latent heat of phase change of the dispersed phase change material, phase change dispersions present as prospective heat transfer fluids in cooling applications.

However, to implement phase change dispersions into cooling systems, for the design of heat exchanger and pipe geometries, detailed fundamental knowledge of the heat transfer and rheological behaviour needs to be understood. Alongside this, limitations encountered such as stability and supercooling need to be addressed. Within this work, a detailed review of the types of dispersion found in literature, their thermophysical, heat transfer and rheological properties are discussed. Current and past methods of improving formulations and overcoming the aforementioned problems are presented. Furthermore, potential figures of merit to evaluate the efficiency of phase change dispersion utilisation are presented and discussed. An outlook to the existing research gap is given.

Nomenclature

Introduction

Cold technologies are essential for a variety of domestic, commercial and industrial applications. They are employed in the preservation of food and medical equipment, comfort cooling in cars, residences and commercial buildings and in the cooling of electronic and industrial equipment. Despite its plethora of usages, the cold energy market is an often over-looked energy-consuming sector. The use of energy for space cooling is the fastest growing area of energy usage in buildings and it has more than tripled between 1990 and 2016 [START_REF] Paris | The future of cooling[END_REF]. Worldwide, almost one fifth of all electricity utilised in buildings is used for cooling [START_REF] Paris | The future of cooling[END_REF]. Current aims to reduce this electrical usage include technologies implemented to increase the coefficient of performance (COP) of cold systems. In recent years, this has involved the incorporation of phase change materials (PCM) into cold systems to act as latent heat stores (LHS) [START_REF] Caliano | Analysis of a phase change material-based unit and of an aluminum foam/phase change material composite-based unit for cold thermal energy storage by numerical simulation[END_REF][START_REF] Yang | Study on the application of latent heat cold storage in a refrigerated warehouse[END_REF][START_REF] Xu | Experimental study on cold storage box with nanocomposite phase change material and vacuum insulation panel[END_REF]. LHS exploits the heat of phase change of materials to store and release significant amounts of energy as a material changes phase. The isothermal nature of phase change allows PCM systems to be fine-tuned to temperature-sensitive applications such as air-conditioning (5 to 15 °C), refrigeration (0 to 4 °C) and freezing (less than 0 °C). However, there are instances where it is much more efficient to use PCM in the form of particles within another fluid. For example, where heat transfer rate is to be maximized, and where it is beneficial to have the PCM in a pumpable form. Using PCM in conjunction with a HTF, generally water, results in a two-phase fluid with a high specific heat capacity [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF].

The high specific heat capacity is due to the fluid not only using the sensible heat, as with a normal HTF, but with the additional latent heat during the phase change process [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF][START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF]. It is expected that because of this, the fluid will have better heat transfer characteristics than for a single-phase HTF, within a limited temperature range around the phase change temperature of the PCM. This is beneficial in a number of applications as improved heat transfer and storage characteristics, such as an increase in the specific heat capacity, allows for a smaller volumetric flow of the HTF to be used. This suggests that less pumping power is required in the system and thus smaller thermal resistances are achieved and therefore higher heat transfer efficiencies [START_REF] Wang | Experimental and simulative investigations on a phase change material nano-emulsion-based liquid cooling thermal management system for a lithium-ion battery pack[END_REF]. Essentially, this could lower the operational and investment costs of the cold-chain network. To date, there are a couple of reported usages of PCD that have been implemented into the cooling network. Fischer et al. [START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF] retrofitted an existing cooling circuit using PCM dispersed in water as the heat transfer fluid (HTF) to isothermally cool a machine spindle. Additionally, Shibutani [START_REF] Shibutani | Pcm-micro capsule slurry thermal storage system for cooling in narita airport[END_REF] installed microencapsulated slurries into a pre-existing chiller unit in Narita Airport in Tokyo and found higher storage densities than using water as the HTF. Despite this, PCD are still to be considered in the developmental stage and are not yet commercialised.

To date, there are four different types of fluid incorporated with PCM: ice slurries, clathrate hydrate slurries, microencapsulated PCM slurries and phase change dispersions (PCD) [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF][START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF]. The first three suffer from high operational costs, associated with shape stabilisation and encapsulation. Additionally, they suffer with problems of stability and consistency during extended cycling periods [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF][START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF]. On the other hand, PCD, or formerly named in literature as phase change emulsions (PCE), are dispersions of two immiscible liquids, stabilised with a surfactant. PCD have simple preparation techniques, smaller thermal resistances (as a result of having no encapsulation shell) and lower production costs [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF][START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF]. PCD can be characterised by the size of the dispersed droplets. Currently, there are three different droplet sizes of the dispersed phase used for cooling purposes; emulsions (1-10 µm), mini-emulsions nm) and micro-emulsions (10-100 nm) [START_REF] Shchukina | Nanoencapsulation of phase change materials for advanced thermal energy storage systems[END_REF]. These sizes are given as reference values and as discussed by Mclements [START_REF] Mcclements | Nanoemulsions versus microemulsions: terminology, differences, and similarities[END_REF], other factors, such as preparation technique and thermodynamic stability should be taken into consideration when assigning categories to emulsion types. Emulsions with droplet sizes above 1 µm are currently the most studied but it is nano-emulsions that show the most promising characteristics such as long-term stability and low viscosities [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF].

So far, the integration of PCD into cooling systems has been limited due to a range of both material and heat transfer limitations. Material properties of the PCM such as supercooling, a phenomenon by which a solution starts crystallising below its freezing point and therefore requires a lower temperature to freeze, significantly limits the application of PCD into cooling systems. Additives, named nucleating agents, are added to dispersions to prevent this from occurring, however their ability to function after multiple cycles and during storage is unknown. Additionally, PCD suffer from instability when cycled due to thinning and disruption of the liquid film between droplets (coalescence), an irreversible process. Furthermore, to ensure the correct design of heat exchangers and systems with PCD, a comprehensive understanding of the heat transfer performance of PCD is required. Whilst for single-phase Newtonian fluids an in depth understanding of heat transfer is known, this is not the case for PCD. Numerical models have been presented [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF][START_REF] Wang | Experimental and simulative investigations on a phase change material nano-emulsion-based liquid cooling thermal management system for a lithium-ion battery pack[END_REF][START_REF] Li | Experimental and numerical studies of a fatty acid based phase change dispersion for enhancing cooling of high voltage electrical devices[END_REF][START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF], but they are yet to be experimentally validated. Despite this, recent literature and reviews have almost predominantly focused on the characterisation and heat transfer properties of microencapsulated phase change material slurries [START_REF] Chai | A review on heat transfer and hydrodynamic characteristics of nano/microencapsulated phase change slurry (n/mpcs) in mini/microchannel heat sinks[END_REF][START_REF] Qiu | Micro-encapsulated phase change material (mpcm) slurries: Characterization and building applications[END_REF][START_REF] Delgado | Review on phase change material emulsions and microencapsulated phase change material slurries: materials, heat transfer studies and applications[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Chen | Preparation and heat transfer characteristics of microencapsulated phase change material slurry: a review[END_REF]. Whilst, there are some reviews which discuss some properties of phase change dispersions [START_REF] Wang | A comprehensive review on phase change material emulsions: Fabrication, characteristics, and heat transfer performance[END_REF][START_REF] Delgado | Review on phase change material emulsions and microencapsulated phase change material slurries: materials, heat transfer studies and applications[END_REF][START_REF] Shao | Review of phase change emulsions (pcmes) and their applications in hvac systems[END_REF], this present review will focus exclusively on the thermophysical properties, heat transfer performance and rheology of PCD. Specifically, this review will focus on PCD made for cooling applications such as: HVAC, which as discussed by Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] requires a PCD with a phase change temperature between 0-20 °C, cooling of machining tools as discussed by Fischer et al. [START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF] with a temperature range of 20-30 °C, refrigeration with a phase change temperature of 0-6 °C and furthermore the cooling of electronic equipment which can require a phase change temperature of up to 50 °C [START_REF] Li | High performance cooling of a hvdc converter using a fatty acid ester-based phase change dispersion in a heat sink with double-layer oblique-crossed ribs[END_REF][START_REF] Fischer | Thermophysical properties of a phase change dispersion for cooling around 50[END_REF].

Phase change dispersions

Table 1 The formulation method, components and properties of the PCD discussed in this review, ordered by their relative melting points. It is to be noted that blank spaces were left where the data could not be retrieved. RT6, RT10, RT20 [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] Alcohol ethoxylates (1.5) Paraffin wax (2.5) 5.5, 9.5, 19.9 1-10 um [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF] Tetradecane POE [START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF], POE [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF], POE(20) D-phase method 5.9 [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] RT6 [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] Tween 20, Tween 40 and Tween Graphite nanoparticles (0.25, 0.5, 1, 2, 4) Rotor-stator emulsification 10 1-15 um [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] n-hexadecane [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF][START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] Span 80/Tween 80 D-phase method 15.9 70-750 nm [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] n-hexadecane (10, 20) Span 80/Tween 80 D-phase method 16.2 100-1000 nm [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] n-hexadecane [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] Tween 20/1,3-butandiol [START_REF] Caliano | Analysis of a phase change material-based unit and of an aluminum foam/phase change material composite-based unit for cold thermal energy storage by numerical simulation[END_REF][START_REF] Xu | Experimental study on cold storage box with nanocomposite phase change material and vacuum insulation panel[END_REF][START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF] Rotor-stator emulsification 16.5 200-600 nm [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF] n-hexadecane SDS/Tween 40 Ultrasound disperser/Rotor-stator emulsification 16.5-17.5 1-50 um [START_REF] Morimoto | Heat transfer characteristics of phase change emulsions with solidification of phase change material particles in a circular tube[END_REF] n-hexadecane (10) Tween 60, Tween 80, 1-3-butandiol Rotor-stator emulsification 17 2.2 um [START_REF] Zhang | Evaluation and manipulation of the key emulsification factors toward highly stable pcm-water nano-emulsions for thermal energy storage[END_REF] n-hexadecane (15) Brij L4 (5-15) Hydrophobic SiO2 nanoparticles [START_REF] Mcclements | Nanoemulsions versus microemulsions: terminology, differences, and similarities[END_REF] Low -energy phase inversion emulsification 18 100-1000 nm [START_REF] Abedi | Microfluidic production of size-tunable hexadecane-in-water emulsions: Effect of droplet size on destabilization of two-dimensional emulsions due to partial coalescence[END_REF] n-hexadecane SDS (2) Microfluidic droplet production 18 19-40 um [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF] n-hexadecane POE [START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF], POE [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF], POE(20) D-phase method 18.2 [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] n-hexadecane Tween 20(5)/Tween80(5)//SDS(1) Multi-walled carbon nanotubes (0.05-0.8) Ultrasound probe/Rotor-stator emulsification 18.5 0.1-20 um [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF] n-hexadecane (30) Tween 20, Tween 80, Span 20, Span 80 (5) Hydrophobic SiO2 nanoparticles (2) Phase inversion temperature method 20.2 800-1200 nm [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF] n-heptadecane, RT21HC (2,4,10) SDS (0.25, 0.5, 1.25) n-octacosane, RT55, RT70HC Solvent-assisted method 20.5 100-150 nm [START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF] RT25HC C16/18 ethoxylated alcohols Myristic acid (0.5-5) Rotor-stator emulsification 25 1 um [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] n-octadecane [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF][START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] Span 80/Tween 80 D-phase method 25.5 100-1000 nm [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] n-octadecane [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] Tween 20/1,3-butandiol [START_REF] Caliano | Analysis of a phase change material-based unit and of an aluminum foam/phase change material composite-based unit for cold thermal energy storage by numerical simulation[END_REF][START_REF] Xu | Experimental study on cold storage box with nanocomposite phase change material and vacuum insulation panel[END_REF][START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF] Rotor-stator emulsification 25.5 150-500 nm [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF] n-octadecane (10, 20) SDS [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF] Multi-walled carbon nanotubes, octadecanol (0.1-1.0) Ultrasonic emulsification 26 58-255 nm [START_REF] Wang | Experimental and simulative investigations on a phase change material nano-emulsion-based liquid cooling thermal management system for a lithium-ion battery pack[END_REF] OP28E (10, 20) SDBS (2, 4) 26.2 180-191 nm [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF] n-octadecane POE [START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF], POE [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF], POE(20) D-phase method 27 [START_REF] Hagelstein | Reduction of supercooling in paraffin phase change slurry by polyvinyl alcohol[END_REF] n-octadecane [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] Triton X100, Tween 60, Span 60 (3) Polyvinyl alcohol Rotor-stator emulsification 27.5 2-10 um [START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF] n-eicosane (1-10) 34.7 [START_REF] Ho | Experiments on laminar cooling characteristics of a phase change nanofluid flow through an iso-flux heated circular tube[END_REF] n-eicosane (1,2,5, 10) SLS Ultrasonic emulsification 36.3 50-140 nm [START_REF] Li | Experimental and numerical studies of a fatty acid based phase change dispersion for enhancing cooling of high voltage electrical devices[END_REF] Crodatherm47/Crodatherm 53 [START_REF] Li | Experimental and numerical studies of a fatty acid based phase change dispersion for enhancing cooling of high voltage electrical devices[END_REF] Steareth-100/Steareth-2 (4) Nucleating agent (0.5) Rotor-stator emulsification 49.5 0.1-10 um [START_REF] Puupponen | Preparation of paraffin and fatty acid phase changing nanoemulsions for heat transfer[END_REF] Stearic acid/Myristic acid (1, 3, 5) SDS, Span85 Phase inversion temperature method 53 10-100 nm [START_REF] Sivapalan | Paraffin wax-water nanoemulsion: A superior thermal energy storage medium providing higher rate of thermal energy storage per unit heat exchanger volume than water and paraffin wax[END_REF] Paraffin wax [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Vasile | Experimental study of the heat transfer characteristics of a paraffin-in-water emulsion used as a secondary refrigerant[END_REF] Pluronics P-123 Probe ultrasonication 57.9 200-600 nm [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF] Paraffin [START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF] PVA/PEG-600 (4) Rotor-stator emulsification 59 0.1-60 um [START_REF] Golemanov | Selection of surfactants for stable paraffin-in-water dispersions, undergoing solidliquid transition of the dispersed particles[END_REF] n-hexadecane Brij 35, Brij 52, Brij 58, SDS, Tween [START_REF] Jurkowska | Review on properties of microencapsulated phase change materials slurries (mpcms)[END_REF][START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF][START_REF] Tokiwa | Effect of surface freezing on stability of oil-in-water emulsions[END_REF] Rotor-stator emulsification [START_REF] Kousksou | Crystallization of supercooled pcms inside emulsions: Dsc applications[END_REF] n-hexadecane, n-octadecane Tween 80 High-speed stirring [START_REF] Saarinen | Turbulent heat transfer characteristics in a circular tube and thermal properties of n-decane-in-water nanoemulsion fluids and micelles-in-water fluids[END_REF] n-decane (1, 2, 3, 5) Span 85/Tween 20 (0. As aforementioned, a PCD consists of a dispersed phase which is composed of PCM particles that are stabilised and dispersed in a continuous phase with the aid of surfactants. A diagram of a typical PCD droplet can be seen in Figure 1 and a list of the formulation properties and components of the PCD discussed in this review can be found in Table 1. The most commonly investigated PCDs are oil-in-water, where a hydrophobic PCM is dispersed in a hydrophilic (generally water) continuous phase. In literature, the most commonly reported class of PCM for use in PCD are paraffins, on account of their high latent heats. In Table 2, a list of some of the PCD investigated in literature can be found. Table 2 is ordered based on increasing melting point of the PCD, it also shows (when presented by the author of the study) the thermal conductivity, in both the emulsion form (when the PCM is liquid) and suspension form (when the PCM is solid), the mean particle size of the PCM droplets in the PCD, the viscosity in emulsion and suspension form, and the latent heat capacity of the PCD. The latent heat capacity of a PCD is defined as

: * = (1)
where is the mass fraction of PCM used in the PCD and L is the latent heat of melting. Paraffins however, are derived from non-sustainable oil feed stocks and can be flammable [START_REF] Ravotti | Synthesis and investigation of thermal properties of highly pure carboxylic fatty esters to be used as PCM[END_REF]. In recent years, research has focused on finding more sustainable PCM for PCD. Zhang et al. [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] investigated fatty acids, on accounts of their abundance, low cost, chemical inertness and non-toxicity. Four mixtures of fatty acids and eutectics thereof, were investigated. The thermophysical properties of the fatty acids as PCM can be found in [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF]. From literature studies, 30 wt.% of the dispersed phase is most commonly investigated (see Table 2). Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] studied different weight percentages of paraffin dispersions and found 30 wt.% to be the minimum paraffin content for a specific heat capacity to be twice that of water during melting. However, Fischer et al. [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF] found that 15 wt.% was optimal when considering the capacity rate ratio against the content of dispersed phase, where the capacity rate ratio for a laminar flow regime is defined to be:

= , , (2)
where and are the dynamic viscosities of water and the PCD respectively and , and , are the specific heat capacities of the PCD and water respectively. Figure 2 shows the capacity rate ratio, , against the mass content of the PCM in the PCD, where it can be observed that a maximum is obtained at 15 wt.%.

Physical properties

There are certain criteria that a PCD must fulfil to be considered useful as a HTF. These criteria include [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF][START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF][START_REF] Nižetić | Nano-enhanced phase change materials and fluids in energy applications: A review[END_REF][START_REF] Wang | A comprehensive review on phase change material emulsions: Fabrication, characteristics, and heat transfer performance[END_REF]:

• high specific heat capacity (generally listed as twice that of water for the desired temperature range)

• high latent heat capacity

• high heat transfer rate

• low pressure drop in operation

• high storage stability

• high stability under thermal and mechanical loads during cycling

• high phase change enthalpy

• small degree of supercooling These criteria will be discussed in the following sections of this review.

Stability

PCD should demonstrate long-term stability, both in storage and under shear stress thermal cycling. A dispersion is considered stable if there is no distinct growth in droplet size over continuous cycling or if there is no phase separation during storage of the dispersion [START_REF] Wang | Highly stable graphite nanoparticle-dispersed phase change emulsions with little supercooling and high thermal conductivity for cold energy storage[END_REF][START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF][START_REF] Zhang | Evaluation and manipulation of the key emulsification factors toward highly stable pcm-water nano-emulsions for thermal energy storage[END_REF]. There are currently five known mechanisms by which dispersions can destabilise: creaming, sedimentation, coalescence, Ostwald ripening and phase inversion [START_REF] Wang | A comprehensive review on phase change material emulsions: Fabrication, characteristics, and heat transfer performance[END_REF]. These mechanisms of destabilisation are outlined in Figure 3. Oftentimes, destabilisation mechanisms are accelerated by thermal and mechanical cycling, which is why it is extremely important for researchers to focus on investigating stability over multiple thermal cycles. Within oil-in-water dispersions, the most commonly observed mode of destabilisation is creaming, due to oils (typically paraffins) having lower densities than water [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF][START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF]. Abedi et al. [START_REF] Abedi | Microfluidic production of size-tunable hexadecane-in-water emulsions: Effect of droplet size on destabilization of two-dimensional emulsions due to partial coalescence[END_REF] stated that there are two major shortcomings in studying the stability of dispersions and that is the indirect measurement techniques and polydisperse droplet sizes. To overcome this, Abedi et al. [START_REF] Abedi | Microfluidic production of size-tunable hexadecane-in-water emulsions: Effect of droplet size on destabilization of two-dimensional emulsions due to partial coalescence[END_REF] produced dispersions with controlled and narrow particle size distributions using microfluidics. Zou et al. [START_REF] Zou | Preparation and flow characteristic of a novel phase change fluid for latent heat transfer[END_REF] suggested two methods for overcoming the destabilisation of dispersions, the first is to use an optimal concentration of PCM in the dispersion. High concentrations of PCM have a greater probability for agglomeration or precipitation, but reducing the concentration of PCM significantly will reduce the total heat capacity of the dispersion [START_REF] Zou | Preparation and flow characteristic of a novel phase change fluid for latent heat transfer[END_REF]. The second method proposed by Zou et al. [START_REF] Zou | Preparation and flow characteristic of a novel phase change fluid for latent heat transfer[END_REF] is in accordance with Stokes law.

Stokes law predicts that a stable dispersion will have a high viscosity, small density difference between the two phases and small droplet diameters. From these properties, reducing the droplet size is the most feasible. Zou et al. [START_REF] Zou | Preparation and flow characteristic of a novel phase change fluid for latent heat transfer[END_REF] stated that reducing the droplet size causes a large reduction in the gravitational force in the dispersion, suggesting that the Brownian motion may overcome the gravitational force. It has been suggested that PCD with droplet sizes between 20-500 nm offer high stabilities and have greater longevity [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF][START_REF] Günther | Subcooling in hexadecane emulsions[END_REF]. Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] additionally discovered that creaming can be reduced by decreasing the droplet size of dispersions or increasing the viscosity of the dispersion.

This was also found by Zhang et al. [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF]. The greater stability of more viscous continuous phases was attributed to the retardation of aggregation of the PCM droplets. Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] used Xanthan gum as a thickener and found a reduced creaming destabilisation in their PCD. Despite this, for practical use thickeners cannot be used in industrial or commercial PCD systems due to the increased pumping power needed to pump a more viscous fluid. Abedi et al. [START_REF] Abedi | Microfluidic production of size-tunable hexadecane-in-water emulsions: Effect of droplet size on destabilization of two-dimensional emulsions due to partial coalescence[END_REF] found that dispersions with a smaller droplet size are more stable due to the probability of particle coalescence being reduced. Despite this, smaller droplet sizes are associated with higher PCD viscosities for a given mass or volume of fluid and also an increased supercooling [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF]. It is suggested by the author of this review that a compromise on droplet size should be reached to ensure good stability, low viscosities and lower supercooling degrees. Surfactants are often used to prevent instability in emulsions. From a literature search, it can be found that quite a large range of surfactants have been utilised to prevent destabilisation. Tween variations, which are non-ionic poly-ethoxylated surfactants, are commonly used for oil-in-water dispersions. Golemanov et al. [START_REF] Golemanov | Selection of surfactants for stable paraffin-in-water dispersions, undergoing solidliquid transition of the dispersed particles[END_REF] used a series of Tween surfactants (Tween20, 40, 60 and 80) and compared them to other surfactants. It was concluded that Tween 40 and Tween 60 were the most effective surfactants at stabilising paraffin-in-water dispersions, which was attributed to the fact that their chain length was small enough to allow the formation of dense interfacial layers surrounding the PCM, which were stabilised due to the steric effect [START_REF] Golemanov | Selection of surfactants for stable paraffin-in-water dispersions, undergoing solidliquid transition of the dispersed particles[END_REF]. Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] showed that non-ionic surfactants were better than ionic surfactants for dispersion stability and additionally reducing toxicity. More recently, this was confirmed by Chen and Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF].

Tokiwa et al. [START_REF] Tokiwa | Effect of surface freezing on stability of oil-in-water emulsions[END_REF] found that the concentration of the surfactant is also an important factor when considering PCD stability as the concentration of surfactant needs to be sufficient to ensure the entire surface of the PCM droplets are coated.

To select the appropriate surfactant for a specific system, the Hydrophilic-Lipophilic balance (HLB) should be calculated [START_REF] Fischer | Thermophysical properties of a phase change dispersion for cooling around 50[END_REF]. For oil-in-water emulsions, a HLB of between 8 and 18 has been suggested. For a paraffin-in-water dispersion though, a narrower range of 11.8-12.0 was suggested by Orafidiya and Oladimeji [START_REF] Orafidiya | Determination of the required hlb values of some essential oils[END_REF]. This was also suggested by Xu et al. [START_REF] Xu | Thermal physical properties and key influence factors of phase change emulsion[END_REF] who investigated both the optimal paraffin concentration and surfactant type and concentration for maximum stability of a tetradecane-in-water dispersion. Therefore, to meet the stringent HLB of 12.0, often two or more surfactants are combined. For example, Chen and Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] investigated a dispersion using a combination of Span 80 and Tween 80 in hexadecane and octadecane-in-water dispersions with 1,3-butanediol to reach a HLB of 12.0.

Shao et al. [START_REF] Shao | Development of a novel phase change material emulsion for cooling systems[END_REF] used Brij 52 and Tween 60, with an overall HLB of 12.0, for a paraffin based PCD and the PCD showed good stability. Zhang et al. [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF] further suggested that polymeric surfactants added as co-surfactants to the emulsifier system could increase PCD stability. Co-surfactants can be used to increase the interfacial strength between surfactants and PCM droplets. This method was also tested by Wang et al. [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF] who tested a polymer surfactant mixture of PVA and PEG and found that stable emulsions were created. This was also discovered by Kawanami et al. [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF] who added 1,3 butanediol and ethylene glycol as co-surfactants to increase the stability. Furthermore, the surface charge (Zeta potential) is also an important parameter to consider for a PCD's stability [START_REF] Wiącek | Zeta potential, effective diameter and multimodal size distribution in oil/water emulsion[END_REF]. Measuring the Zeta potential of PCD measures the electrophoretic mobility of the PCM droplets and if the absolute value of the Zeta potential is over 30 mV, there is a strong indication that the electrostatically repulsive charges between the PCM droplets are strong enough to prevent agglomeration and coalescence [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF]. This parameter is controlled by the concentration and type of surfactant used. Pupponen et al. [START_REF] Puupponen | Preparation of paraffin and fatty acid phase changing nanoemulsions for heat transfer[END_REF] investigated the Zeta potentials of different concentrations of two surfactants, individually and as co-surfactants in fatty acid based PCDs. Pupponen et al. [START_REF] Puupponen | Preparation of paraffin and fatty acid phase changing nanoemulsions for heat transfer[END_REF] found that a 1:1 ratio of SDS and Span85 resulted in the highest zeta potential of -78 mV. They also discovered that increasing the ratio of surfactant to dispersed phase increased the Zeta potential and thus the stability against coalescence. Cabaleiro et al. [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF] measured the Zeta potentials of RT21HC in water PCD stabilised with SDS surfactants to be -71 mV. Cabaleiro et al. [START_REF] Cabaleiro | Dynamic viscosity, surface tension and wetting behavior studies of paraffin-in-water nano-emulsions[END_REF] also performed another investigation with RT21HC in water, with varying concentrations of SDS surfactant; 0.25, 0.5 and 1.25 wt.% and it was found that in all cases a Zeta potential of -80 mV was achieved, suggesting that the electrostatic charges were strong enough to prevent coalescence. Jadhav et al. [START_REF] Jadhav | Ultrasound assisted manufacturing of paraffin wax nanoemulsions: Process optimization[END_REF] slowly increased the concentration of the SDS surfactant used in their paraffin wax PCD from 0-10 mg ml -1 and found a corresponding zeta potential drop from -38.1 mV to 38.8 mV. This was attributed to a higher surface charge caused by an increase in the number of surfactant molecules around each paraffin droplet which improved the stability.

Stability during storage

Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] stated that the most important factor to take in consideration when trying to increase PCD stability is PCM concentration. They found that after one month, distinct layering was observed in PCDs containing 16-60 wt.% paraffin, but creaming was not evident in the dispersions with 65-75 wt.% paraffin. However, practically, PCD with such high paraffin concentrations cannot be used in cooling systems as a result of the high viscosity associated with PCD with higher PCM concentrations. Günther et al. [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF] prepared a 30 wt.% hexadecane dispersion and found that creaming occurred in only a few days. Another study performed by Huang et al. [START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] found that after two years of storage, no significant destabilization was observed. Chen and Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] investigated the effect of HLB on the storage stability of their PCD and found that a dispersion with a HLB of 12.0 had a stabilisation period of greater than 210

days, but a dispersion with a HLB of 15.0 began to destabilise after 65 days. Despite this, Shao et al. shao2016 still found that after a storage period of 270 days there was an increased mean droplet size from 3.1 m to 3.4 m which was indicative that coalescence had occurred. Fischer et al. [START_REF] Fischer | Thermophysical properties of a phase change dispersion for cooling around 50[END_REF] showed that when their PCD was below its melting temperature (suspension form), the lifespan was 300 days, and when it was above its melting temperature (emulsion form), the lifespan was 25 days. Cabaleiro et al. [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF] produced PCD with droplet sizes between 90 -120 nm and it was found that after 30 days in storage, the average droplet diameter had not increased, suggesting high stability. This was attributed to the droplets being small enough that Brownian motion ensured that the droplets moved throughout the sample and didn't cream to the top of the sample during storage [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF]. As discussed by Chen and Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF],

who formulated nanoscale PCD, smaller particle sizes tend to improve the stability of dispersions, however they also increase viscosity and degree of supercooling.

Stability during cycling

Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] performed cycling tests on a PCD with 35 wt.% paraffin, 2.5 wt.% surfactant and 2.5 wt.% nucleating agent. The cycling involved a heating/cooling cycle, which was repeated 50 times for 6 days. They found that the particle sizes slightly increased after cycling, and supercooling was observed. It was assumed by the authors that this was due to the nucleation agent separating from the dispersion. It was concluded however, that due to the viscosity remaining the same throughout cycling, that the PCD was stable to mechanical and thermal cycling. This was attributed to the mechanical energy provided in the pumping system preventing creaming from occurring. Another study by Huang et al. [START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] found that dispersions of 30 wt.% RT10 and RT20 respectively also had an increased particle size distribution after thermal-mechanical cycling. Schalbart et al. [START_REF] Schalbart | Formation of tetradecane nanoemulsion by low-energy emulsification methods[END_REF] investigated the preparation methods of dispersions and their effects on stability. It was found that methods, which produced a narrow droplet size distribution, generated dispersions that were stable against creaming for more than 6 months, however during cycling Ostwald ripening was observed which increased the droplet size and decreased the viscosity. Additionally, it has been suggested by Wang et al. [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF] that the addition of co-surfactants ensures good stability of the dispersion. They found that a mass ratio of 50:50 PVA to PEG-600 had good stability after 50 cooling-heating cycles. Although not applied specifically to PCD systems yet, research in emulsion chemistry has found that Pickering emulsions could offer increased stabilisation in PCD. This involves stabilising the surfactants with amphipathic solid nanoparticles [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF][START_REF] Zhang | Evaluation and manipulation of the key emulsification factors toward highly stable pcm-water nano-emulsions for thermal energy storage[END_REF]. More recently however, alternative additives, other than surfactants are being used to safeguard the stability of emulsions and prevent against creaming, for example, Zhang et al. [START_REF] Zhang | Development and characterization of novel and stable silicon nanoparticles-embedded pcm-in-water emulsions for thermal energy storage[END_REF] concluded that the addition of SiO 2 nanoparticles increased the stability of a paraffin-in-water emulsion.

Supercooling

For a material to crystallise, nucleation must occur. However, the process of nucleation has a potential energy barrier, which must be overcome for nucleation and thus crystallisation to initiate. This energy barrier is a function of the radius of a nucleus formed in the solution and it is not until a critical radius is reached that the energy barrier can be overcome and nucleation is initiated [START_REF] Wu | Nucleation kinetics of glycine promoted concentrated potassium carbonate solvents for carbon dioxide absorption[END_REF]. However, if a nucleus is smaller than this critical radius, nucleation will not occur, as the nucleus will collapse. The process of nucleation and supercooling is discussed extensively in PCD with no supercooling, whereby the latent heat is released over a small Δ . The red dashed-line shows a PCD with supercooling, whereby the latent heat is released over a broad temperature range.

[67]. The barrier to nucleation though, can also be overcome through thermal energy fluctuations, which are stochastic events that render nucleation a probabilistic phenomenon [START_REF] Rhafiki | Crystallization of pcms inside an emulsion: Supercooling phenomenon[END_REF]. Because of this, nucleation is highly dependent on temperature. There are two kinds of nucleation, homogeneous and heterogeneous. Homogeneous nucleation occurs in an ideally pure solution, where no external contaminates can act as heterogeneous nucleators. Due to the stochastic nature of homogeneous nucleation, a larger volume of material suggests a higher probability for nucleation to occur.

However, within a dispersion, the PCM volume is dramatically reduced compared to a bulk solution, hence reducing the likelihood of homogeneous nucleation occurring, resulting in large supercooling degrees. This is particularly obvious in the case of nano-sized emulsions, whereby in the small and isolated droplets, the probability of their being an external contaminant is lower, and thus crystallisation proceeds via homogeneous nucleation [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF].

It is well observed that large degrees of supercooling limit the applications of PCD in cooling systems as the latent heat contributing to the large heat capacities of dispersions is released over a broad temperature range, rather than being released as a sharp peak over a narrow temperature range, this is outlined in Figure 4. Figure 4 shows an example of a typical DSC curve for crystallisation of two different PCD, one of the curves represents an "ideal" PCD with little to no supercooling, and the other curve represents a PCD with a large supercooling degree. Within PCD, there tends to be large degrees of supercooling, over a broad temperature range, as a result of the different crystallisation temperatures of different PCM droplets within the PCD (as a result of different particle size distributions and local droplet temperatures). A narrow crystallisation temperature of PCM within the PCD is essential for PCD acting as HTF for temperature stability and for applications which require isothermal conditions. Large degrees of supercooling also suggest that the PCM within the PCD crystallises at lower temperatures, meaning a lower temperature from the chiller is required to crystallise the PCM which increases the energy consumption of PCD systems and reduces their efficiency [START_REF] Zhang | Fabrication of a novel nano phase change material emulsion with low supercooling and enhanced thermal conductivity[END_REF]. Methods to combat supercooling have been the centre of PCM and PCD research for quite some time.

Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF][START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] performed a two part investigation on supercooling in tetradecane and hexadecane dispersions.

Effect of droplet size

Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] discovered that a 30 wt.% tetradecane-in-water emulsion with a droplet diameter of 1-10 µm had a supercooling degree of 7 K. Large supercooling degrees were also found by Günther et al. [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF], Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF], Hagelstein and Gschwander [START_REF] Hagelstein | Reduction of supercooling in paraffin phase change slurry by polyvinyl alcohol[END_REF] and Wang et al. [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF]. To investigate the claim that particle size influences the degree of supercooling, Günther et al. [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF] prepared dispersions with droplet sizes ranging from 0.2 to 20 µm using different methods, ultrasound and different frequencies. For the smaller droplet sizes, supercooling on the scale of 15 K was observed, and for the larger particle sizes a supercooling of 5 K was observed. Figure 5 shows the nucleation Nucleation temperature for hexadecane PCD with varying hexadecane droplet diameters, which were prepared with different methods, ultrasound (US), homogenisier at 24,000 rpm and 9,000 rpm from [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF] temperature against droplet diameter for PCD with different production methods and surfactants used. From Figure 5, it is evident that the larger the droplet size, the higher the nucleation temperature and thus the lower the supercooling degree

Effect of surfactant used

Günther et al. [START_REF] Günther | Subcooling in hexadecane emulsions[END_REF] concluded that interfacial phenomena between the surfactant and the PCM has an effect on the initiation of crystallisation due to surfactants having a large impact on the thermal properties of the dispersion.

Functionalising the surfactant ensures that each dispersed particle contains a nucleation seed, therefore suggesting that each individual dispersed particle should crystallise. Hagelstein and Gschwander [START_REF] Hagelstein | Reduction of supercooling in paraffin phase change slurry by polyvinyl alcohol[END_REF] used PVA as a surfactant to reduce the supercooling of hexadecane dispersions from 12 K to 2 K. Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] also found that using hexadecanol, as a co-surfactant, reduced supercooling by 3 K compared to when just Tween 20 was used. Hexadecanol was also used by Zhang et al. [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] as a co-surfactant in a capric acid/lauric acid in water dispersion, and here it was found that the supercooling degree was reduced from 20 K to 10 K.

Effect of additives

Additives are often added to PCD to induce heterogeneous nucleation. Huang et al. [START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] added a paraffin with a phase change temperature of 50 (which is a paraffin with a higher melting point than the PCMs used in the PCD)

to the dispersion as a nucleating agent. Adding a higher melting point paraffin was also found to be effective by Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF]. Zhang et al. [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] used multi-wall carbon nano-tube (MWCNT) particles that resulted in the supercooling being reduced by 46% from 6.4 to 3.5 K. Fischer et al. [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF] investigated varying amounts of Myristic acid in a RT25HC-in-water dispersion and found that increasing the amount of Myristic acid in the PCD decreased the degree of supercooling. Furthermore, a time-cycling dependency has been observed on the efficacy of nucleating agents, whereby after a certain amount of thermo-mechanical cycles the nucleating agents stops or reduces its impact on the crystallisation temperature [START_REF] Fischer | Thermophysical properties of a phase change dispersion for cooling around 50[END_REF]. It is therefore suggested that these cycling effects of nucleating agents and efficacy in reducing supercooling is researched more in depth.

Heat Capacity

Utilising PCD as a HTF requires an increase in the total heat capacity compared to the specific heat of water at the desired application temperature. When comparing the total heat capacity of a PCD with water, the applied temperature range (around the phase change temperature) needs also to be considered on an application by application basis, depending on the operational conditions. When considering PCD, the total heat capacity of the PCD is defined as [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF]:

, , = (1 -) , + , Δ (3)
and is it generally calculated over a 6 K temperature difference around the melting point of the PCM within the PCD as found with DSC analysis (unless otherwise stated) [START_REF] Höhne | Differential scanning calorimetry[END_REF]. Generally, the c , is higher for PCD than for water as a result of the increase in the specific heat capacity during the phase change of the PCM. In fact, it is the increased total heat capacities of PCD over single-phase HTF which stands as the basis for the development of PCD. Chen and

Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] concluded in their study that due to the high total heat capacity of their PCD, the dispersion was particularly attractive for practical applications such as cooling and air-conditioning. This is because, as found in a study by Lu

and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF], that amongst other parameters, the total heat capacity was found to have a great influence on the heat transfer of the PCD. To increase the total heat capacity, increasing the mass content of PCM within the dispersion is effective. Sivapalan et al. [START_REF] Sivapalan | Paraffin wax-water nanoemulsion: A superior thermal energy storage medium providing higher rate of thermal energy storage per unit heat exchanger volume than water and paraffin wax[END_REF] found that a 10 wt.%, 20 wt.% and 33 wt.% paraffin wax PCD possessed a total heat capacity which was 7, 31 and 43% higher than water respectively. Huang et al. [START_REF] Huang | Experimental study on heat capacity of paraffin/water phase change emulsion[END_REF] investigated a PCD composition of 50 wt.% and 30 wt.% of RT10 which had total heat capacities which were 2.7 and 2.0 times higher than water respectively for the applied range of 5-11 °C, i.e a 6 K temperature range. In another investigation, Huang et al. [START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] found that their Cryosol 6, Cryosol 10 and Cryosol 20 PCDs had a latent heat capacity that was 3 times, 2 times and 1.8 times higher than that of water respectively, also in a 6 K temperature range. Despite this, increasing the mass fraction of PCM decreases the thermal conductivity of the PCD and increases the viscosity, and thus when creating a PCD all parameters discussed in this review must be balanced and analysed using figures of merit, which is discussed further in section 5.

Thermal conductivity

Currently, one of the major drawbacks of dispersions is that paraffins have low thermal conductivities therefore dispersions in general have lower thermal conductivities than traditional single phase HTF. Shao et al. [START_REF] Shao | Development of a novel phase change material emulsion for cooling systems[END_REF] measured the thermal conductivity of a 25 wt.% RT10 in water PCD to be 30% less than water at the same temperature. Whilst an increase in thermal conductivity is not necessary in terms of heat transfer into the dispersed particles to melt them (due to their small size), it is important in terms of the overall heat transfer mechanism within PCD. Currently, this is unknown and therefore represents a major research gap in the study of PCD. It has also been stated that the thermal conductivity of PCD varies non-linearly with the size of the PCM droplets, concentration of PCM, fluid properties and temperature, making correlations for describing the thermal conductivity difficult to produce [START_REF] Kousksou | Crystallization of supercooled pcms inside emulsions: Dsc applications[END_REF]. Yu et al. [START_REF] Yu | Comparative review of turbulent heat transfer of nanofluids[END_REF] explained that the thermal conductivity of dispersions depends not only on the concentration of the PCM within the dispersion but is a complex mixture of: the particle size and distribution, the particle shapes and orientations, the Brownian motion of the droplets, the aggregation of the droplets, the dispersions continuous phases's interfacial layer, additives, pH and temperature. This section will further explore the effects of different parameters on a dispersion's thermal conductivity.

Effect of PCM concentration

Effect of phase change

The operational temperature of the PCD has an influence on the thermal conductivity for example, Wang et al. [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF] found that for a 20 wt.% dispersion, the thermal conductivity at 30 °C was 0.49 W m -1 K -1 and at 60 °C was 0.61 W m -1 K -1 . However, phase change has a significant impact, after the PCD melts, there is a sharp decrease in the thermal conductivity due to the decreased thermal conductivity of liquids compared to solids. Chen and Zhang [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF] found a large decrease in the thermal conductivity at the melting temperature, due to the PCM changing phase from a solid to a liquid. It has also been suggested that the thermal conductivities of dispersions have been overestimated

during melting, due to the large amount of heat absorbed by the dispersion under isothermal conditions [START_REF] Xu | Thermal physical properties and key influence factors of phase change emulsion[END_REF]. Figure 6 shows the significant decrease in the thermal conductivity during melting of two different dispersions prepared in [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF].

Effect of droplet size

Additionally, experimental work by Liu et al. [START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF] highlighted that the thermal conductivity of paraffin-in-water dispersions vary with the PCM droplet size and that the thermal conductivity can be increased by reducing the droplet size. However, it should be noted that droplet size should be chosen when taking into consideration other factors such as supercooling, stability and viscosity.

Effect of additives

Current methods to increase the thermal conductivity of dispersions involve the addition of nanoparticles. For example, Zou et al. [START_REF] Zou | Preparation and flow characteristic of a novel phase change fluid for latent heat transfer[END_REF] investigated adding 1 wt.% of aluminium nanoparticles into a paraffin emulsion and found a 30% increase in the thermal conductivity, so that the thermal conductivity almost rivalled that of pure water. Ho and Gao [START_REF] Ho | Preparation and thermophysical properties of nanoparticle-in-paraffin emulsion as phase change material[END_REF] added 5 and 10 wt.% of Al 2 3 nanoparticles which showed a 2 and 6% increase in the thermal conductivity of the PCD compared to without the nanoparticles. At 60 °C, an increase in 17% of the thermal conductivity was achieved, which was suggested by the authors to be due to the enhanced Brownian motion with the addition of the nanoparticles in the base fluid having a much lower viscosity at increased temperatures [START_REF] Ho | Preparation and thermophysical properties of nanoparticle-in-paraffin emulsion as phase change material[END_REF]. However, it has been noted that the addition of nanoparticles adds extra cost and reduces the fraction of paraffin used (and thus the total heat capacity) and as a result have been rendered unsuitable for use in most dispersion systems. Ho and Gao [START_REF] Ho | Preparation and thermophysical properties of nanoparticle-in-paraffin emulsion as phase change material[END_REF] found that by adding 10 wt.% of Al 2 O 3 , that the latent heat of fusion decreased from 243 kJ kg -1 (with no nanoparticles) to 212 kJ kg -1 .

Calculating the thermal conductivity of PCD

Due to the different components in PCD having different thermal conductivities, equations have been produced from researchers to quantify the effective thermal conductivities of PCD for different mass fractions of PCM used. The effective thermal conductivity is most often calculated by modified versions of the first-order approximation Maxwell equation [START_REF] Maxwell | Electricity and magnetism[END_REF]:

= + 2 + 2( - ) ) + 2 -2( - ) ) (4)
where , , are the thermal conductivities of the dispersion, PCM and water respectively and is the particle volume fraction. The Maxwell equation is an empirical equation based on the effective medium theory.

It has been suggested by Cabaleiro et al. [START_REF] Cabaleiro | Development of paraffinic phase change material nanoemulsions for thermal energy storage and transport in low-temperature applications[END_REF] that the Maxwell equation does not take into account scale-related phenomena, for nano-sized PCM droplets which include; interfacial resistance, Brownian motion, droplet-continuous phase interactions or the flow of the droplets.

Kawanami et al. [START_REF] Kawanami | Thermophysical properties and thermal characteristics of phase change emulsion for thermal energy storage media[END_REF] used the Hamilton and Crosser equation to evaluate the thermal conductivity [START_REF] Hamilton | Thermal conductivity of heterogeneous two-component systems[END_REF]:

= ( + ( -1) -( -1) ( - ) ( + ( -1) + ( - )) (5)
where = 3/ and is a sphericity factor, which was assumed to be 1. Within literature, it has been noted that an increase of thermal conductivity exists in oil-in-water dispersions and that this increase, alongside droplet size has not been considered in current equations for calculating the effective thermal conductivities of PCD [START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF]. However, Liu

where describes the thermal inertia in short-time responses, is the delayed time caused by heat transport mechanisms in micro-scale, S is the time derivative, is the heat flux and is the thermal diffusivity. When / > 1 the governing equation of the dual-phase-lag heat conduction is hyperbolic and therefore is transported by thermal waves.

When / < 1 the thermal conductivity is dominated by non-Fourier heat conduction and when / = 0, the governing equation is the classical diffusion equation employing Fourier's law. Liu et al. [START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF] found all their investigated dispersions had / between 0.1 and 0.3 suggesting that a diffusion-dominated non-Fourier heat conduction could exist in oil-in-water emulsions. Further investigation into this for other dispersions is suggested by the authors.

Rheology and viscosity

It is important to investigate the rheology of dispersion systems as viscosity influences the heat transfer, stability and pumping power requirements of dispersions [START_REF] Fischer | Phase change dispersion properties, modeling apparent heat capacity[END_REF]. Delgado et al. [START_REF] Delgado | Experimental analysis of a low cost phase change material emulsion for its use as thermal storage system[END_REF] showed that due to the high viscosity of their 60 wt.% paraffin in water dispersion, the natural convective heat transfer was highly reduced. Additionally, Chen et al.

[27] found that PCD had higher viscosities than water, which led to drastic increases in the required pumping power in their feasibility studies. Increased viscosities of PCD has also shown to increase the pressure drop in comparison to water [START_REF] Chen | Preparation and characterization of nano-sized phase change emulsions as thermal energy storage and transport media[END_REF][START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF]. Wang et al. [START_REF] Wang | Preparation of phase change material emulsions with good stability and little supercooling by using a mixed polymeric emulsifier for thermal energy storage[END_REF] found that although the PCD had double the storage capacity of water, due to the higher viscosity and thus higher pressure drop of the PCD, the power consumption for the PCD system was found to be higher than for water. This increase in viscosity was originally attributed to solely the weight percentage of PCM employed, with an increasing concentration of PCM leading to an increased viscosity. For example, Ho et al. [START_REF] Ho | Experiments on laminar cooling characteristics of a phase change nanofluid flow through an iso-flux heated circular tube[END_REF] investigated 1-10 wt.% n-Eicosane-in-water dispersions and reported pressure drops which were up to 200% for 10 wt.% compared to 1 wt.% highlighting the dependency of the pressure drop and viscosity on the concentration of the dispersed phase.

However, more recently it has been suggested that the temperature the PCD is operated at and the concentration of surfactant are two other important factors [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF][START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF]. These results are promising as it is suggests that PCD can be fine-tuned to create compromised rheological properties whereby optimising the composition of the PCD allows for smaller viscosities and pressure drops whilst still retaining high heat transfer properties and stabilities. The majority of the dispersions tested in literature show extremely high viscosities compared to water, for example, Inaba and Morita [START_REF] Inaba | Flow and cold heat-storage characteristics of phase-change emulsion in a coiled double-tube heat exchanger[END_REF] produced a 5 wt.% and 40 wt.% tetradecane-in-water emulsion and found the dispersions had viscosities of 31.1 mPa⋅s and 2.5 Pa⋅s, which are 1167 and 21 times higher than the viscosity of water respectively. Additionally, Zhao

and Shi [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF] found dispersions of 16 wt.% and 50 wt.% tetradecane-in-water had apparent viscosities of 24.5 mPa⋅s and 150 mPa⋅s which is 16 and 100 times the apparent viscosity of water respectively. Shao et al. [START_REF] Shao | Development of a novel phase change material emulsion for cooling systems[END_REF] also observed a viscosity for a 30 wt.% paraffin-in-water dispersion, which was 13 times higher than that of water. The high viscosities of these dispersions render them unviable for HVAC and cooling applications due to the increase in the pump energy consumption. Additionally, this causes a switch from the turbulent to laminar flow regime resulting in a decreased heat transfer coefficient. However, more recently, Chen et al. [START_REF] Chen | Experimental research on laminar flow performance of phase change emulsion[END_REF] prepared a PCD with 30 wt.% paraffin and found a viscosity of 8.46 mPa⋅s which is only 5.6 times higher than water.

Effect of PCM concentration

One of the most well-known and investigated factors in the viscosity of dispersions is the concentration of the dispersed phase [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF][START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF]. Within literature, there are two competing notions concerning the influence of concentration and shear rate on the rheological properties of fluids. To determine whether a fluid exhibits Newtonian or non-Newtonian behaviour, one examines the relationship between the shear stress and shear rate that is usually presented using the Ostwald formula [START_REF] Ostwald | The theory of solutions[END_REF]:

= ̇ ( -1) (8)
where is the fluid behaviour index and describes the degree of non-Newtonian behaviour exhibited and is the consistency index, where the larger the value of , the more viscous the fluid is. A value of = 1 indicates Newtonian behaviour, > 1 shear-thickening behaviour and < 1 shear-thinning behaviour. Morimoto and Kumano [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] defined experimentally and found that after melting the dispersions displayed Newtonian behaviour with = 0.95, which was attributed to the liquid state of the particles becoming more deformable which created a more Newtonian behaviour.

The first competing notion in literature, is that at and below a 30 wt.% of dispersed phase, PCD demonstrate Newtonian behaviour, and above this concentration non-Newtonian behaviour is observed [START_REF] Xu | Thermal physical properties and key influence factors of phase change emulsion[END_REF]. Vasile et al. [START_REF] Vasile | Experimental study of the heat transfer characteristics of a paraffin-in-water emulsion used as a secondary refrigerant[END_REF] investigated the rheology of a 30 wt.% paraffin-in-water emulsion and found that the emulsion exhibited Newtonian behaviour with measurements performed on a rheometer in both the cone and plate geometry. Morimoto et al. [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] discovered that dispersions with 10-30 wt.% paraffin were considered to be Newtonian, whereas a dispersion containing 40 wt.% paraffin was considered non-Newtonian. This was attributed to higher concentrations of dispersed phase having a greater probability of generating aggregation-type structures, which cause more non-Newtonian behaviours. Chen et al. [START_REF] Chen | Experimental research on laminar flow performance of phase change emulsion[END_REF] also found that the friction factor of the 30 wt.% conformed to the classical formula of [START_REF] Chen | Experimental research on laminar flow performance of phase change emulsion[END_REF]:

= 64 (9)
for laminar flow in circular pipes which confirmed its Newtonian behaviour. Conversely, the second notion is that all concentrations of paraffins show non-Newtonian behaviour. Huang et al. [START_REF] Huang | An experimental study on rheological behaviors of paraffin/water phase change emulsion[END_REF] investigated a larger range of paraffin concentrations, 15-75 wt.% and discovered that they all exhibited non-Newtonian behaviour and that the degree of non-Newtonian behaviour and viscosity dramatically increased once the paraffin concentration surpassed 50 wt.%.

In another investigation by Huang et al. [START_REF] Huang | Low temperature paraffin phase change emulsions[END_REF] dispersions containing RT10 with weight percentages of 15 to 50% all exhibited non-Newtonian behaviour. Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] also found that non-Newtonian behaviour was observed for a dispersion of 30 wt.% RT6 and a dispersions of 6 wt.% RT25. The conflict in these findings can be attributed to other factors that contribute to the rheology of dispersions such as surfactant type and concentration, temperature and shear rate.

Effect of surfactant choice

The role the surfactant plays in influencing the viscosity of PCD is attributed to the micelle structure, which is formed by the surfactant interface. This indicates that the viscosity is dependent on both the surfactant type and their respective concentrations. Zhang et al. [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] investigated the effects of three commonly used surfactants, SDS, Tween 80 and Tween 20 on the viscosity of a 30 wt.% hexadecane dispersion. It was concluded that there was great variation in the viscosities by just changing the type of surfactant used. Zhao and Shi [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF] built on the idea of the surfactant influence by investigating the effect of the surfactant concentration on the viscosity. The surfactant concentration was varied from 2.6 to 4.7 wt.% and a corresponding dynamic viscosity change of 0.00055 Pa⋅s to 0.00294 Pa⋅s was observed at 20 °C. This can be explained by recognising that as the surfactant concentration increases, there will be an increased attraction strength of the surfactant monolayer. This increased attraction requires more energy to be transported than a smaller attraction strength, thus increasing the viscosity [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF]. It is suggested by the authors that due to the complex surfactant system now employed in dispersions, as seen in the previous section, with co-surfactants and using a variety of surfactants mixed together that rheological properties are properly understood and tested for multi-component dispersion compositions.

Effect of temperature

Lu and Tassou [START_REF] Lu | Experimental study of the thermal characteristics of phase change slurries for active cooling[END_REF] discovered that the viscosity of their PCD was heavily dependent on the temperature, where a decrease in temperature led to an increase in viscosity until the crystallisation temperature was reached. This was attributed to the presence of surfactants, as the liquid paraffin droplets remain smooth and flexible until their crystallisation point and therefore make little contribution to the friction. This was also confirmed by Huang et al. [START_REF] Huang | Evaluation of paraffin/water emulsion as a phase change slurry for cooling applications[END_REF] who discovered that the viscosity of all the tested dispersions increased with the increasing frozen fraction of the RT10 paraffin in the dispersion, therefore as the temperature decreased the viscosity increased. This has been attributed to the fact that solid particles are less likely to deform under shear stress like liquid droplets, therefore increasing the viscosity. The variation of the viscosity with temperature was also found to be reduced for dispersions with lower paraffin concentrations, caused by the difference in water content [START_REF] Vasile | Experimental study of the heat transfer characteristics of a paraffin-in-water emulsion used as a secondary refrigerant[END_REF]. Chen et al. [START_REF] Chen | Experimental research on laminar flow performance of phase change emulsion[END_REF] revealed that viscosities decrease with an increase in temperature, and the larger the mass fraction of the PCD, the quicker this effect is observed. For example, at 0 °C the viscosity of a 30 wt.% hexadecane dispersion was 42 mPa•s and at 30 °C was 17 mPa•s, whereas the 10 wt.% hexadecane dispersion had a viscosity of 4 mPa•s at 0 °C and 2 mPa•s at 30 °C . The temperature dependency of viscosity is due to the tendency of droplets to aggregate at lower temperatures, as explained by Zhang et al [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF]. Zhang et al. [START_REF] Zhang | PCM in water emulsions: Supercooling reduction effects of nano-additives, viscosity effects of surfactants and stability[END_REF] performed further experimentation on a capric/lauric acid-in-water dispersion and found that the cohesion of PCM droplets influenced the viscosity. This was attributed to temperature increases causing an increased distance between the PCM droplets thus reducing the attractive forces holding them together. In turn, this reduces the shear stress by deformation and therefore a reduced viscosity is shown

Physical properties summary

It is evident to see that all the aforementioned physical properties of PCD; stability (during cycling and storage), degree of supercooling, heat capacity, thermal conductivity and viscosity are influenced by the formulation and physical and operational parameters and conditions used when creating and testing PCD. These parameters include the concentration of PCM used, the effect of temperature, the effect of PCM droplet size and the effect of chemical additives. It is important to understand the dual-nature that some of these parameters and conditions have on the physical properties of PCD for future optimisation of PCD formulations and to glean information on how these parameters can be balanced to create a HTF which fulfils the requirements outlined in Section 3. Additionally, the hysteresis between the cooling and heating cycles of such behaviour is poorly reported, and the authors believe a thorough investigation into the thermal cycling of all physical properties should be conducted.

Heat transfer

Unlike microencapsulated phase change slurries, limited investigations, both experimentally and numerically have been performed on PCD. Experimental studies for PCD as potential HTF are essential as they not only have the potential to demonstrate the benefits of using PCD, but also they help to understand the heat transfer processes and mechanisms that occur in PCD. Ultimately, this allows predictive correlations to be produced for heat exchanger design and optimisation. The phase change process of PCD occurs over a temperature range where the PCD has a much higher specific heat capacity (during phase change) than a single-phase fluid. This means that a PCD has a much larger ability to transport heat. Zhao and Shi [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF] provide a theoretical analysis of this and found that convective heat transfer can be increased if the flow rate of the fluid is increased, the temperature gradient is increased and certain material properties, such as the specific heat is increased.

This section on heat transfer will be separated into the different operational parameters that can be controlled when performing experiments with PCD. Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] explained the physical reason for the influence of physical operational parameters on the melting heat transfer performance of PCD. The author stated that during melting, a liquid layer of melting PCM droplets near the tube wall impedes the heat transfer from the wall to the bulk of the fluid. This effectively reduces the heat transfer from the wall to the bulk, and certain operational parameters such as the flow rate, imposed temperature or heat flux at the wall and mass concentration of PCM effect the rate at which this liquid layer develops. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF]. This is discussed further in section 4.1.

Furthermore, for implementation of PCD into industrial and commercial systems, a complete understanding of both the melting and crystallisation heat transfer behaviour is required to understand the complete cycle of PCD.

Therefore, in this section the effect of the operational parameters are further split into melting and crystallisation experiments. Additionally, forced convection is more highly studied than natural convection, due to the usefulness of forced convection in temperature stability and refrigeration applications and this is the focus of this review. Despite this, natural convection is still the focus of a few research articles, where the motivation is energy storage owing to the latent heat of phase change for PCD [START_REF] Delgado | Experimental analysis of a low cost phase change material emulsion for its use as thermal storage system[END_REF][START_REF] Inaba | Natural convection heat transfer of microemulsion phase-change-material slurry in rectangular cavities heated from below and cooled from above[END_REF].

Melting

Generally, authors focus their heat transfer experiments on the melting behaviour of PCD because during crystallisation the supercooling phenomena makes the heat transfer behaviour difficult to predict.

Effect of the wall heat flux

Morimoto and Kumano [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] found that a higher applied wall heat flux decreased the local heat transfer coefficient due to a faster melting PCD. Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] explained this by stating that the mass fraction of un-melted PCM is larger at lower heating powers at the same axial location as higher heating powers and therefore the liquid layer of melted PCM, which usually hinders heat transfer develops slower at lower heat fluxes. Ho et al. [START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF] varied the heat flux in their divergent mini-channels and found that with PCD, when the wall heat flux was decreased that the dimensionless wall temperature would also decrease, suggesting a greater degree of melting. However, Ho et al. [START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF] discovered that the heat flux had a minor effect on the average Nusselt number ( ). Morimoto and Kumano [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] showed that the enhancement ratio of (of the PCD to the base fluid) was decreased as the wall heat flux was increased. This was most likely due to the latent heat absorption decreasing as the wall heat flux increased. This effect was shown through the following relation for the modified specific heat capacity ( * ) inside the thermal boundary layer MORIMOTO2018:

* ≈ + ( -) (10)
where L is the latent heat of melting for the PCD, is the wall temperature and is the bulk inlet flow temperature.

From Equation 10 when a low heat flux is applied, almost all the heat is allocated to the latent heat of the PCM because the temperature difference between the main flow and the wall temperature is relatively small. On the other hand, when a relatively high wall heat flux is applied, the heat is transferred under the form of sensible heat because the wall temperature is relatively high and the temperature of the PCD increases even though the PCM particles are melting.

This was also validated with numerical results [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF].

Effect of the mass flow rate

It is important to note that in all experimental and numerical investigations on the heat transfer of PCD, the flow regime is always described as turbulent or laminar, which is a classification generally attributed to single-phase fluids, such as water. However, for PCD, laminar and turbulent flow regimes are more difficult to define without a set of standard PCD formulations (including set droplet sizes and PCM concentrations) and there is little discussion on the validity of describing PCD as flowing in the turbulent or laminar flow regime, especially when they have a non-Newtonian behaviour: the laminar turbulent transition of such fluids remains a non fully solved scientific issue.

Ho et al. [START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF] found that when a higher mass flow rate was used, the dimensionless wall temperature increased because the effective heat exchange duration between the PCD and the wall was too short. However, this occurs at a critical Reynolds number ( ) and generally, an increase in number in the turbulent flow regime increases the heat transfer behaviour. Ho et al. [START_REF] Ho | Thermal performance of phase change nano-emulsion in a rectangular minichannel with wall conduction effect[END_REF] found that an increase in number increased the average due to thinning of the thermal boundary layer resulting in an increased heat transfer rate. Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] also stated that an increase in increased the local heat transfer coefficients due to greater thinning of the thermal boundary layer. Morimoto

and Kumano [START_REF] Takashi | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 2. turbulent flow[END_REF] suggested that the thermal boundary layer development was suppressed largely at higher flow rates, attributing to higher heat transfer coefficients. Despite this, Roy and Avanic [START_REF] Roy | Laminar forced convection heat transfer with phase change material suspensions[END_REF] numerically found that in the laminar flow regime, the dimensionless wall temperature was independent of the used for their octadecane-in-water PCD.

This is what is observed for single-phase fluids, such as water and further indicates the need for more research in attributing PCD to the turbulent or laminar flow regime. Saarinen et al. [START_REF] Saarinen | Turbulent heat transfer characteristics in a circular tube and thermal properties of n-decane-in-water nanoemulsion fluids and micelles-in-water fluids[END_REF] discovered similar results in the turbulent regime where for = 2300-6000, enhancement did not increase a great deal. However, at = 7000, the highest enhancements of 13-15% were obtained. Additionally, the same results could be seen for the convective heat transfer coefficients. Therefore, = 7000 was classified as a critical by the authors [START_REF] Saarinen | Turbulent heat transfer characteristics in a circular tube and thermal properties of n-decane-in-water nanoemulsion fluids and micelles-in-water fluids[END_REF].

Effect of the PCM concentration

Cho et al. [START_REF] Cho | A novel concept for heat transfer fluids used in district cooling systems[END_REF] numerically investigated a PCD in a mini-channel and found that increasing the concentration of the PCM in the PCD decreased the wall temperature increase along the channel compared to the base fluid. Cho et al. [START_REF] Cho | A novel concept for heat transfer fluids used in district cooling systems[END_REF] attributed this to an increased melting time of the PCM when the concentration of the PCM is higher. Furthermore, Morimoto and Kumano [START_REF] Morimoto | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 1. laminar flow[END_REF] numerically investigated the heat transfer behaviour of a PCD, in laminar flow, and found that the numerically obtained agreed with the experimentally obtained results for 20 and 30 wt.% PCM based PCD.

However, the numerical model showed much lower values for Nusselt at 10 wt.% than the experimental results, they concluded that heat transfer promotion mechanisms occurred in PCD with low PCM concentrations. Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] found that the local heat transfer coefficient increased with the mass concentration of PCM used whereby the local heat transfer coefficient of a 20 wt.% PCM dispersion was found to be 1.4 times higher than a 10 wt.% PCM dispersion at the same Reynolds. Overall, despite the increase in the heat transfer performance with an increase in the concentration of PCM (at the same ), a compromise of the mass fractions of PCM used in PCD needs to found by weighing up the increase in thermal performance and the additional increase in viscosity and pumping power required. This is discussed further in section 5.

Other notable effects

Wen and Ding [START_REF] Wen | Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions[END_REF] numerically found that during melting, a non-uniform particle size distribution resulted in higher Nusselt numbers because of particle migration and Brownian motion. During melting, Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] found that although the development of the thermal boundary layer is faster in smaller tubes than in larger tubes that the Nusselt number increased in smaller tubes. This was attributed to greater particle-wall interactions in smaller tubes.

Crystallisation

To date, very few studies have been performed examining the heat transfer behaviour during crystallisation. As aforementioned, the supercooling makes analysis and creating correlations more difficult.

Effect of the flow regime

Morimoto et al. [START_REF] Morimoto | Heat transfer characteristics of phase change emulsions with solidification of phase change material particles in a circular tube[END_REF] found that a turbulent flow regime caused an increase in the heat transfer promotion effect.

Despite Roy and Avanic [START_REF] Roy | Laminar forced convection heat transfer with phase change material suspensions[END_REF] finding that during melting the heat transfer coefficient was independent of the Reynolds number in laminar flow, Vasile et al. [START_REF] Vasile | Experimental study of the heat transfer characteristics of a paraffin-in-water emulsion used as a secondary refrigerant[END_REF] discovered that the average heat transfer coefficient increased as the increase in a laminar flow regime for crystallisation.

Effect of the PCM concentration

Zhao and Shi [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF] discovered that in a coiled circular tube that increased as the mass fraction of the PCM was increased. Inaba and Morita [START_REF] Inaba | Flow and cold heat-storage characteristics of phase-change emulsion in a coiled double-tube heat exchanger[END_REF] experimentally investigated a tetradecane-in-water PCD in a double-tube coiled heat exchanger and showed that an increase in the concentration of the PCM in the PCD led to an increase in the .

Other notable effects

Alongside the main operational parameters, several other parameters have been noticed to affect the heat transfer behaviour of PCD. Inaba and Morita [START_REF] Inaba | Flow and cold heat-storage characteristics of phase-change emulsion in a coiled double-tube heat exchanger[END_REF] stated that a decrease in the temperature difference between the PCD and the fluid cooling it down increases the heat transfer performance of the PCD. Zhao and Shi [START_REF] Zhao | Experimental investigations of flow resistance and convection heat transfer and prediction of cold heat-storage characteristics for a phase-change emulsion in a coiled circular tube[END_REF] found that the Nusselt number for the solid dispersed phase (after phase change) was larger than for the liquid dispersed phase (before phase change). The two explanations which were presented are, firstly that the emulsion becomes a solid-liquid two phase fluid when the emulsion temperature falls below the freezing point and the mixing and disturbing effects caused by small particles improve the convective heat transfer in the thermal boundary layer. Secondly, the emulsion's effective thermal conductivity has a somewhat higher value when the dispersed phase becomes solid particles. Inaba and Morita [START_REF] Inaba | Flow and cold heat-storage characteristics of phase-change emulsion in a coiled double-tube heat exchanger[END_REF] also found that for the solidified PCM a larger Nusselt enhancement was obtained due to the higher thermal conductivities in the solid phase. Morimoto et al. [START_REF] Morimoto | Heat transfer characteristics of phase change emulsions with solidification of phase change material particles in a circular tube[END_REF] investigated two different PCD with different surfactants, they plotted the Nusselt number for each PCD versus the dimensionless cooling distance alongside the Dittus-Boelter equation (from [START_REF] Morimoto | Heat transfer characteristics of phase change emulsions with solidification of phase change material particles in a circular tube[END_REF] for a single-phase fluid, as shown in Figure 7. From Figure 7, the initiation of solidification time is different for each different surfactant used and the deviation between the empirical equation for a single-phase fluid and the Nusselt number's experimentally observed are greater for the PCD with Tween 60 surfactant than Tween 80 surfactant. This deviation suggests that surfactants can also play a role in the heat transfer performance of PCD during crystallisation and this is something which needs to be further researched.

Heat transfer summary

Overall, the lack of experiments, both numerically and experimentally can be seen for crystallisation of PCD. This creates a problem because in all usages of PCD, knowledge of the full melting-crystallisation cycle is needed to design

Figures of merit

To choose the appropriate PCD for a specific application, the heat transfer capabilities of the dispersion compared to its base fluid or the standard HTF must be calculated. The figures of merit found in literature are colour coded with the respective operational parameters that they take into consideration in Figure 8. for comparison omits the increase in pumping power required with a more viscous PCD which is pumped at a higher flow velocity to reach the same as the less viscous base fluid. However, under the constant flow velocity comparison criterion, the flow velocity effect, which is inherently present under the constant comparison criterion, is eliminated.

A PCD with the same velocity (or mass flow) as the base fluid will have a larger specific heat capacity flow due to the available latent heat [START_REF] Yu | Comparative review of turbulent heat transfer of nanofluids[END_REF]. Temperature increase will be lower and driving temperature difference higher, which results in larger heat transfers even though the heat transfer coefficient might be smaller. Even though the pumping power for PCD is higher than for the base fluid, it has been found that in many applications the pumping power difference between a PCD and its base fluid is small at the same flow velocity. Furthermore, the constant pumping power comparison, which compares the heat transfer under the condition that the PCD and base fluid require the same amount of pumping power suggests that the flow velocity for the more viscous PCD is slightly lower than for the base fluid [START_REF] Yu | Comparative review of turbulent heat transfer of nanofluids[END_REF]. However, the constant pumping power comparison criteria represents the most explicit choice of criteria and should be used when the relevant information is known.

Nusselt number based figures of merit

is a dimensionless form of the heat transfer coefficient that should be used to depict the convective heat transfer performance of HTF. Bonjour et al. [START_REF] Bonjour | Theoretical evaluation of the use of phase change material emulsions and figures of merit[END_REF] used the Colborn Factor ( ), to assess the heat transfer versus the necessary pressure drop for a specific flow where is defined as follows:

= 1 3 (11)
It is useful because it shows the dependency of heat exchange on and therefore the optimal surface depends on the of interest and thus the Colburn Factor. can be interpreted as the ratio between the convective heat transfer (including advection and diffusion) to the conductive heat transfer within a fluid. is useful in defining the heat transfer mechanisms which occur in the PCD.

Heat transfer coefficient based figures of merit

Oftentimes the figure of merit of comparing heat transfer coefficients, is referred to the heat transfer effectiveness and is defined as the ratio of the convective heat transfer coefficient for the PCD relative to the convective heat transfer coefficient of the base fluid as below [START_REF] Wen | Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions[END_REF][START_REF] Ho | Performance of a compact, spiral coil heat exchanger[END_REF]:

= ℎ ℎ (12)
where ℎ and ℎ are the heat transfer coefficients for the PCD and the base fluid (water) respectively at the same mass flow rate. From this, an enhanced heat transfer ability of the PCD is observed when > 1. Memon et al. [START_REF] Memon | Investigation of the thermal performance of salt hydrate phase change of nanoparticle slurry flow in a microchannel[END_REF] investigated different PCD by using the heat transfer effectiveness ratio, and found that the maximum ratio was reached when all the particles of the PCM were melted inside the dispersion. It was further concluded that this ratio could be further enhanced by minimising the sensible heat region at the inlet of the flow channel, which would allow the remaining length of the channel to be represented by the latent heat effect. In turn, this would permit a lower temperature increase along the channel and a greater temperature control within the channel. This can be shown non-dimensionally in the form of the Stefan number ( ), which represents the ratio of the sensible heat to latent heat as shown in Equation 13.

= Δ (13)
for the boundary condition of constant wall temperature or defined as [START_REF] Li | Experimental and numerical studies of a fatty acid based phase change dispersion for enhancing cooling of high voltage electrical devices[END_REF]:

= ( ∕ ) (14)
For the boundary condition of constant wall heat flux. The Stefan number has been used in some investigations to determine the melting time. Morimoto et al. [START_REF] Takashi | Flow and heat transfer characteristics of phase change emulsions in a circular tube: Part 2. turbulent flow[END_REF] used a modified Stefan number and discovered that the Nusselt number increases when the modified Stefan number decreased meaning that the Nusselt number was found to increase when the heat allocated to the latent heat of phase change increased. Ma et al. [START_REF] Ma | Experimental study of the hydraulic and thermal performances of nano-sized phase change emulsion in horizontal mini-tubes[END_REF] also used the Stefan number to investigate the optimal heat input to use to obtain the best heat transfer performance of their PCD.

Ho et al. [START_REF] Ho | Performance of a compact, spiral coil heat exchanger[END_REF] went further and discussed the dependence of on and found a critical velocity to enhance .

At extremely high , the sensible heat dominates over the latent heat of the PCD due to the particles only partially melting due to higher flow velocity, whereas at slightly lower , the PCM particles within the slurry have more time to absorb the surrounding heat and are therefore more likely to fully melt. It is suspected by Memon et al. [START_REF] Memon | Investigation of the thermal performance of salt hydrate phase change of nanoparticle slurry flow in a microchannel[END_REF] that the maximum value of the effectiveness ratio is obtained when the sensible region at the inlet is minimised, and that the peak in effectiveness ratio is when the flow through the length of the channel is dominated by latent heat of phase change of the PCM. Further investigation into this by use of is recommended by the author for future research.

Pumping power based figures of merit

Whilst an increase in the heat transfer coefficient is advantageous for PCD, an increase in the pumping power is detrimental for their use as HTF. As a result of this, the two quantities can be combined to form a new figure of merit which shows the ratio of the heat transfer coefficient increase to the pumping power enhancement and is defined as [START_REF] Yu | Comparative review of turbulent heat transfer of nanofluids[END_REF]:

= ℎ ∕ℎ ∕ (15)
If this figure of merit is utilised under the constant pumping power comparison criterion, then it reduces to the ratio of heat transfer coefficients between the PCD and the base fluid, see Equation 12. When the figure of merit is higher, it is indicative that there is a greater heat transfer increase when using the PCD than pumping power penalty.

Memon et al. [START_REF] Memon | Investigation of the thermal performance of salt hydrate phase change of nanoparticle slurry flow in a microchannel[END_REF] defined a figure of merit based on the pumping power and heat transfer named Merit number ( ). It uses a measure of the irreversibility of the heat transfer and frictional losses due to the addition of the PCM particles within a fluid. Subsequently, it represents the ratio of the enhancement in heat transfer due to PCM addition to the total of the heat transfer to the top wall of the channel and the irreversibility. is defined as:

= + ′ (16)
where is the rate of increase of heat absorption in the dispersion due to the addition of the PCM, is the heat transfer rate of the bulk fluid to the wall and ′ is the rate of irreversibility the definitions of both can be found in [START_REF] Memon | Investigation of the thermal performance of salt hydrate phase change of nanoparticle slurry flow in a microchannel[END_REF].

The irreversibility depends on the volumetric entropy generation rate which is defined in [START_REF] Yeh | Thermal management of microelectronic equipment: Heat transfer theory, analysis methods, and design practices. asme press book series on electronic packaging[END_REF]. It is expected that at higher heat flux to mass ratios, the lower concentration of dispersions will show higher values, this is suspected because the heat transfer enhancement is smaller than the increase in irreversibility, due to higher pressure-drops and viscosities.

Heat capacity based figures of merit

In laminar flow regimes, Prasher et al. [START_REF] Prasher | Measurements of nanofluid viscosity and its implications for thermal applications[END_REF] suggested the following F.O.M. ratio [START_REF] Prasher | Measurements of nanofluid viscosity and its implications for thermal applications[END_REF]:

= - - (17)
where it was stated that for < 4 , the PCD is considered better in terms of the heat transfer compared to the base fluid (water). Fischer et al. [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF] also investigated this figure of merit, and named it the heat capacity rate ratio, . This can be seen in Equation 2. The derivation for can be seen in [START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF]. It was discussed that cannot be applied directly to turbulent flow. This is because the derivation of this equation involves calculating the pressure drop in the pipe, and then equating the pressure drop of water and PCD. This is possible in laminar flow, however due to the exponent in the pressure drop calculation in a pipe for turbulent flow this cannot be equated.

Figures of merit summary

Overall, the heat transfer and rheological performance of new HTF need to be compared to the heat transfer performance of existing HTF. For choosing an appropriate HTF, the three main parameters which need to be considered are the heat transfer coefficient, the pressure drop and the capacity flow rate. As discussed in Sections 3 and 4, there are many factors which need to be considered when formulating and using PCD as an enhanced HTF. Figures of merit aim

to quantify these parameters and allow a direct comparison between different HTF on their performance for specific applications under certain comparison criteria.

Conclusions and Future directions

This review has focused on and highlighted the types of PCD that have been investigated in the literature, alongside their thermophysical, rheological and heat transfer properties. It clearly demonstrates that the increased heat capacities shown by dispersions renders them strong candidates for HTF. The thermophysical properties of paraffins as phase change material in dispersions are widely reported for a broad temperature range within the cooling domain;

however, low thermal conductivities indicate that other classes of materials should be investigated to increase the heat transfer capabilities. Currently, the application of PCD into systems for cooling has been limited on accounts of large degrees of supercooling of dispersions because of their microscopic geometries and stability observed both in storage and during cycling. Additionally, from this review, it has been highlighted that out of the functional latent heat transfer fluids developed, phase change dispersions are the least investigated, particularly in terms of heat transfer and the mechanisms of heat transfer. Whilst numerical models have been developed in both laminar and turbulent flow, experimental validation is still required. It has been suggested that for PCD to become prevalent as heat transfer fluids, a more comprehensive understanding and validation of their heat transfer performance is required. This is in order to design correct heat exchangers and optimise the cooling system geometries. Additionally, the heat transfer performance of PCD undergoing crystallisation needs more attention that melting due to the lack of studies performed during solidification. On top of this, an effective model to describe the rheology of dispersions should be generated as currently literature offers conflicting experimental results, most likely due to different test set-ups and data collection methods. Furthermore, this review highlights the need to be careful in designing PCD for cooling applications, due to the positive and negatives effects each parameter can have on the PCD as a fluid overall. An overview of the different formulation properties and controlled parameters; PCM concentration, surfactant system, temperature, droplet size, chemical additives, wall heat flux and mass flow rate on the PCD properties and behaviour; stability, supercooling, heat capacity, thermal conductivity, viscosity and heat transfer performance are given in Table 3.

Whilst the current standard PCM used in PCD is paraffins, as can be seen by Tables 1 and2, the global standards for improving sustainability amongst energy solutions will encourage researchers to investigate bio-based PCM for use in PCD, such as fatty acids and esters. New PCMs will require new literature in terms of formulation such as;

effective surfactant systems and nucleating agents. One of the main future directions of the formulation of PCD, will be more attention given to the finding of novel and efficient nucleating agents, and testing whether these nucleating agents hold up over thermo-mechanical cycling and storage. Particularly, the use of surfactants to initiate nucleation (reduce supercooling) will be a future direction of PCD formulation research. Once a greater understanding of the interfacial tension, and crystallisation kinetics of phase change dispersions has been achieved, and more research has been performed, carefully selecting surfactant systems to induce nucleation will become more commonplace when formulating PCD. Additionally, this balance between choosing the appropriate surfactant system for stability and for inducing nucleation will have to also be investigated. Furthermore, once supercooling has been successfully reduced within phase change dispersions, more attention should be geared towards investigating the heat transfer behaviour of PCD during crystallisation and the author's believe that as more PCD are pushed into the developmental stage, that more research will focus on crystallisation as a complete understanding of the heating-melting cycle will need to be considered for implementation into cooling systems.

Figure 1 :

 1 Figure 1: A dispersed particle within a PCD showing the PCM, surfactant layer and the continuous phase. The figure was adapated from Fischer et al. [8].

Figure 2 :

 2 Figure 2: Heat capacity rate ratio, , for a laminar flow in a pipe versus mass content of PCM within the PCD, , based on Equation2. For each assumed temperature difference, Δ , (1, 3 and 5 K), the two curves of the same colour show the upper and lower limits of . The two limits are calculated from:± Δ , where Δ = 1, 3, 5. The figure was adapted from Fischer et al.[START_REF] Fischer | Investigation of heat transfer in phase change dispersions (PCD)[END_REF]

Figure 3 :

 3 Figure 3: Schematic showing a stable emulsion alongside the destabilisation mechanisms.

Figure 4 :

 4 Figure 4: Example of a DSC curve showing the crystallisation curves of two PCD, the solid black line shows an "ideal"PCD with no supercooling, whereby the latent heat is released over a small Δ . The red dashed-line shows a PCD with supercooling, whereby the latent heat is released over a broad temperature range.

Figure 5 :

 5 Figure5: Nucleation temperature for hexadecane PCD with varying hexadecane droplet diameters, which were prepared with different methods, ultrasound (US), homogenisier at 24,000 rpm and 9,000 rpm from[START_REF] Günther | Subcooling in hexadecane emulsions[END_REF]

Figure 6 :

 6 Figure 6: Variation of the thermal conductivity of (a) a hexadecane-based PCD and (b) an octadecane-based PCD at different temperatures and weight percentages of the dispersed PCM. Figure was adapated from Chen et al. [5].

  et al.[START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF] proposed a new semi-empirical equation of the effective thermal conductivity, which takes into account the droplet size of the PCM[START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF]: conditions: 20 °C ≤ T ≤ 70 °C, 0.5% ≤ ≤ 4.0,%, 0.5 µm < d < 0.9 µm where is the reference temperature of 20 °C. Liu et al.[START_REF] Liu | Non-fourier heat conduction in oil-in-water emulsions[END_REF] investigated the dual-phase-lag heat conduction which combines the microstructural effects occuring between PCM droplets into delayed temporal responses into the macroscopic formulation of the entire PCD. The dual-phase lag heat conduction was quantified based on the time lag ratio suggested by Kang et al.[START_REF] Kang | A method for predicting thermal waves in dual-phase-lag heat conduction[END_REF]:

Figure 7 :

 7 Figure 7: The local Nusselt number versus the dimensionless distance from inlet and the empirical correlation for singlephase fluid for (a) a PCD with Tween 80 as the surfactant and for (b) a PCD with Tween 60 as the surfactant. Figure was adapted from Morimoto et al. [15].

  Figures of merits aim to characterise this comparison andcomparison criteria are used to set the conditions under which the figure of merit comparison takes place. Additionally, an important aspect of experimental research into PCD is to produce predictive equations for heat transfer coefficients, which eventually permits the effective design of heat exchangers and pipe geometries. For these equations to be applied to real applications, non-dimensional parameters are used to represent heat transfer coefficients, thermophysical properties and geometric configurations. For heat transfer fluids, the most commonly used dimensionless numbers are Nusselt, Prandlt ( ) and Reynolds. When choosing an appropriate PCD, there are three main parameters, which are of the upmost importance; these are highlighted at each point of the triangle in Figure8. Firstly, the heat transfer coefficient, ℎ, this is a direct measurement of the heat transfer performance of a fluid and is thus vital in the generation of a figure of merit for PCD performance characterisation. Secondly, the pressure drop, Δ , which increases due to the increased viscosity of the phase change of the PCD and impairs the applicability of PCD. Finally, the capacity flow rate, which is taken into account because of the increase in specific heat capacity of the PCD during phase change.

Figure 8 :

 8 Figure 8: A depiction of the three key parameters for PCD comparison and their respective figures of merit

Table 2

 2

also highlights a range of commercial PCM, which have also been investigated for use as PCD. Due to the distinctive melting points of paraffins, and because of the high cost for pure paraffins, many commercial PCM paraffins are blends of different paraffins to obtain the desired application temperatures.

Table 2

 2 PCD listed in literature alongside the PCM used in the formulation, ordered on increasing melting temperatures with some relevant thermophysical properties.

	P. O'Neill et al.: Preprint submitted to Elsevier	Tetradecane Tetradecane	4.6 4.8	30 20			51 0.2		7.5 4.2	73 43	[27] [28]
		n-alkanes	5	30	0.38			7.3	5.5	60	[50]
		Tetradecane	5.9	10			0.5			19.3	[14]
		Tetradecane	6	40			17			66.3	[51]
		RT6	6.1	30		0.48		10	25	40	[30]
		RT6	8	30			0.5	20	20	75	[29]
		RT10	8.2	25	0.4		4		21	41	[31]
		RT10	9	30			5			43	[32]
		RT10	9.3	30			5			36	[24]
		n-alkanes	9.5	50			2	24.3	22.3	78.9	[52]
		RT10	9.7	30		0.46				38	[30]
		RT10	10	30			0.5	40	20	50	[29]
		Hexadecane	16.5	10			100				[53]
		Hexadecane	17.5	10	0.56	0.54	0.2	2.9	1.7	22.9	[15]
		Hexadecane	17.5	20	0.52	0.48	0.3		4.1	45.8	[15]
		Hexadecane	17.5	30	0.49	0.47	0.3		16.5	68.7	[15]
		Hexadecane	18.2	10			0.5				[14]
		Hexadecane	19.4	50			1.8		45	73.4	[40]
		RT20	22	30			0.5	80	20	44	[32]
		RT25HC	23	26			1			41	[8]
		Octadecane/Hexadecane (50:50)	24	16	0.52	0.48	0.3	4.4	3.1	24	[54]
		Octadecane	27	10	0.5	0.45	0.5				[14]
		Octadecane	27.2	10	0.56	0.54	0.18	3.4	1.8	24.3	[15]
		Octadecane	27.2	20	0.52	0.48	0.2		4.1	48.6	[15]
		Octadecane	27.2	30	0.49	0.41	0.23			72.9	[15]

PCM

Melting Temperature (℃) wt.% suspension (W m -1 K -1) emulsion (W m -1 K -1) Mean Particle size ( m) suspension (mPa s) emulsion (mPa s) Latent heat capacity (J -1 ) [Ref]

Short Title of the Article Table 3 Overview of the formulation properties and controlled parameters on the thermophysical and heat transfer behaviour of PCD During crystallisation, an increase in the mass flow rate was found to increase the Nu. However, during melting a critical Reynolds was found. When a Reynolds above the critical value was found a high Nusselt enhancement was obtained.