Jean-Christophe Baudez
email: jean-christophe.baudez@irstea.fr

Rahul K Gupta
email: rahul.gupta@rmit.edu.au

Nicky Eshtiaghi

Paul Slatter
email: paul.slatter@rmit.edu.au

The viscoelastic behaviour of raw and anaerobic digested sludge: strong similarities with soft-glassy materials

Keywords: Glassy materials, rheology, sewage sludge, soft matter, time-temperature superposition, viscoelasticity

Over the last few decades, municipal and industrial wastewater treatment activities have been confronted with a dramatically increasing flow of sewage sludge. To improve treatment efficiency, process and material parameters are needed but engineers are dealing with vast quantities of fundamentally poorly understood and unpredictable material Thus, accurate prediction of critically important, but analytically elusive process parameters is unattainable and is a matter of grave concern. Because engineers need reliable flow properties to simulate the process, this work is an attempt to approach sludge rheological behaviour with well-known materials which have similar characteristics. Sludge liquid-like behaviour is already well documented so, we have focused mainly on the solid-like behaviour of both raw and digested sludge by performing oscillatory measurements in the linear and non-linear regimes. We have shown that the viscoelastic behaviour of sludge presents strong similarities with soft-glassy materials but differences can be observed between raw and digested sludge. Finally, we confirm that colloidal glasses and emulsions may be used to model the rheological behaviour of raw and anaerobic digested sludge.

Introduction

Sewage sludge production is the residue of wastewater treatment and by definition can't be avoided. In the EU it is produced at more than 30 000 tonnes (dry matter) per day and will increase by at least 10 % in 2020 [START_REF] Eureau | EUREAU POSITION PAPER on how the revision of the Fertiliser Regulation should promote sustainable use of sludge in agriculture[END_REF]. These volumes have to be treated and reused. [START_REF] Slatter | The rheological characterisation of sludges[END_REF][START_REF] Slatter | Sludge pipeline design[END_REF][START_REF] Slatter | Pipeline transport of thickened sludges[END_REF][START_REF] Slatter | The hydraulic transportation of thickened sludges[END_REF][START_REF] Slatter | Pipe flow of highly concentrated sludge[END_REF] has consistently shown that sludge rheology plays a fundamentally important role in analysing the hydrodynamic behaviour of the sludge, as it flows in pipes or in tanks and reactors, such as anaerobic digesters. However, sludge properties continuously evolve due to the ongoing biochemical reactions, and for this reason it cannot be used as a reference material for the design of industrial processes: engineers need reliable and repeatable flow properties to simulate the process. Thus, various researchers attempted to use model fluids instead of sludge, such as kaolin suspension for the yield stress determination [START_REF] Spinosa | A simple method for evaluating sludge yield stress[END_REF], polymeric gels (Legrand et al., 1997), polyvinyl chloride (PVC) suspensions [START_REF] Bongiovanni | Traitement des boues résiduaires par l'association en série d'une déshydratation mécanique et d'un séchage thermique[END_REF], polystyrene latex [START_REF] Sanin | Synthetic sludge: A physical/chemical model in understanding bioflocculation[END_REF], but none of these was particularly successful because each of these model fluids was only representative of a particular application. To model the flow properties of sludge, mainly in its liquid regime, kaolin suspensions are often used (Heritier et al., 2010) because it shows shear-thinning behaviour with a yield stress, modelled with a Herschel-Bulkley model [START_REF] Masalova | Scaling in pipeline flow of kaolin suspensions[END_REF]. Even if this model fluid can be used to simulate high velocity flows, it is not suitable for simulating the liquid-like behaviour at intermediate shear rates, nor the solid-like behaviour at low shear rates, which appears to be crucial in order to avoid -or at least minimize -dead zones in reactors, such as anaerobic digesters or aeration basins.

Because of its fundamental nature, sludge is a very complex mixture of unknown composition and its rheological behaviour is highly dependent of the treatment processes: accurate prediction of critically important, but analytically elusive, process parameters is unattainable and is a matter of grave concern.

For sake of simplicity, in the following we will only distinguish between raw, activated and anaerobically digested sludge, respectively representative of the outlet of sludge treatment when no tertiary treatment is applied and when anaerobic digestion is implemented. Both are temperature-dependent (Dieude-Fauvel et al., 2009;[START_REF] Baudez | The impact of temperature on the rheological behaviour of anaerobic digested sludge[END_REF], present viscoelastic properties at low shear stress and a shear-thinning behaviour at high shear stress [START_REF] Baudez | Physical aging and thixotropy in sludge rheology[END_REF]Coussot, 2001, Baudez et al., 2011), but at intermediate shear stresses, raw sludge is a thixotropic material [START_REF] Tabuteau | A new approach to the thixotropic behaviour of sewage sludge[END_REF][START_REF] Baudez | Physical aging and thixotropy in sludge rheology[END_REF] with ageing effects [START_REF] Baudez | Physical aging and thixotropy in sludge rheology[END_REF] while anaerobic digested sludge highlights shear banding [START_REF] Baudez | The rheological behaviour of digested sludge[END_REF].

Raw and digested sludge are mainly composed of water (more than 95%) and the remaining part is made of organic matter and bacteria which tend to aggregate forming flocs. That is the usual 'chemical' definition of sludge: organic flocs suspended in water. However, physically, sludge can also be visualised as interacting particles in a suspending medium: bacteria form extra polymeric substances (EPS), finally presenting a three-dimensional gel-like biofilm matrix [START_REF] Wingender | Microbial extracellulafr polymeric substances[END_REF]. EPS are highly charged polymers that interact with water in a manner similar to gels [START_REF] Keiding | Remember the water : comment on EPS colligative properties[END_REF][START_REF] Sutherland | Exopolysaccharides in biofilms, flocs and related structures[END_REF]. They interact with divalent metal ions to form sludge flocs in both aerobic and anaerobic treatment systems [START_REF] Higgins | Characterisation of extracellular protein and its role in bioflocculation[END_REF]. Flocs in activated sludge usually carry negative charge at neutral pH. It has been found that the extracellular polymeric substances (EPS) contribute to the negative surface charge of the sludge flocs [START_REF] Jia | Extracellular polymers of hydrogen-utilizing methanogenic and sulfate reducing sludges[END_REF][START_REF] Liao | Surface properties of sludge and their role in bioflocculation and settleability[END_REF]. As regards the influence of the anaerobic digestion, [START_REF] Jia | Extracellular polymers of hydrogen-utilizing methanogenic and sulfate reducing sludges[END_REF] also observed that during batch tests both surface charge and EPS content change significantly.

Polysaccharides and proteins were found to be the most significant surface polymers in activated (raw) sludge [START_REF] Forster | Bound water in sewage sludge and its relationship to sludge surfaces and sludge viscosities[END_REF], and the two types of binding mechanisms between water molecules and the EPS structure are considered to be electrostatic and hydrogen bonds [START_REF] Flemming | The forces that keep biofilms together[END_REF].

Digestion leads to the transfer of bigger flocs into smaller ones [START_REF] Mahmoud | Interaction between digestion conditions and sludge physical characteristics and behaviour for anaerobically digested primary sludge[END_REF] and disintegration of the organics brings the solids to a homogeneous grain structure, with an increase of the quantity of colloidal particles (Turovskii and Matai, 2006) and a decrease of EPS [START_REF] Karapangiotis | Extraction and characterisation of extracellular polymers in digested sewage sludge[END_REF]. The anaerobic digestion data showed strong correlations between soluble protein generation and ammonium production [START_REF] Park | The effect of wastewater cations on activated sludge characteristics: effects of aluminum and iron in floc[END_REF]. The most important constituents in digested sludge are proteins and lipopolysaccharides [START_REF] Forster | Bound water in sewage sludge and its relationship to sludge surfaces and sludge viscosities[END_REF], which are amphiphile lipids with both hydrophilic and hydrophobic heads. [START_REF] Novak | Mechanisms of floc destruction during anaerobic and aerobic digestion and the effect on conditioning and dewatering of biosolids[END_REF] found the protein concentration was 3-5 times greater than the polysaccharide concentration in anaerobic systems compared to aerobic ones. They also noticed an increase of monovalent cations.

From a physical point of view, anaerobic digested sludge appears to be a stable suspension with low settling ability (Namer and Ganczarczyk, 1993) and low surface charge [START_REF] Forster | The rheological and physico-chemical characteristics of sewage sludge[END_REF] indicating that interactions are more steric than electrostatic.

Moreover, [START_REF] Mikkelsen | Physico-chemical characteristics of full scale sewage sludges with implications to dewatering[END_REF] showed that the ratio between protein and polysaccharides are more or less of the same order between activated and (mesophilic) digested sludge, but the degree of dispersion is 20 times higher after anaerobic digestion, indicating that sludge structure is strongly affected by anaerobic digestion.

In this paper, we intend to draw parallels between well-known materials and sludge. These wellknown materials could then be used a model fluids to emulate the rheological behaviour of sludge for the investigation and design of treatment technologies. Because the liquid-like behaviour of sludge is well documented, we will intentionally focus on the solid-like behaviour of both raw and digested sludge by performing oscillatory measurements in the linear and non-linear viscoelastic regimes. We show that the viscoelastic behaviour of sludge presents strong similarities with softglassy materials but differences can be observed between raw and digested sludge. Stress and frequency sweeps were conducted at different temperatures to demonstrate that Brownian motion also plays a role in the build-up and break-down of sludge structure. Finally, we demonstrate that colloidal glasses and emulsions may be used to model the rheological behaviour of raw and anaerobic digested sludge.

Materials and methodology

Sludge was obtained from the Mount Martha wastewater treatment plant (Melbourne, Victoria, Australia) at the inlet (called raw sludge in the following) and the outlet (called digested sludge) of the digester number 1. The initial concentration of the raw sludge was found to be 45g.L -1 (this relatively high concentration was obtained after flotation thickening, without chemical conditioning) while the solid concentration of the digested sludge was found to be 18.5g.L -1 . The latter was also gently concentrated to 32g.L -1 (and 42g.L -1 after a second sampling for time sweep experiments) by using a Buchner vacuum. These concentrations were chosen to be representative of thickened sludge which is more often used in digesters. Digested samples were stored at 4°C for 30 days before experiments were conducted to ensure no temporal variability, allowing us to use the same material for several days of testing. This technique was successfully used by [START_REF] Curvers | A centrifugation method for the assessment of low pressure compressibility of particulate suspensions[END_REF].

On the other hand, because of their high degree of fermentation, raw sludge was stored only 5 days before experiments. Although storage implied changes in the composition of the raw sludge, considering the duration of rheological characterisation, especially the frequency sweep, we needed to consider raw sludge as a 'stable' material, from both the biological and chemical points of view during our whole investigation. Because changes are very fast the 72 first hours [START_REF] Baudez | Rheology of aging, concentrated, polymeric suspensions -Application to pasty sewage sludges[END_REF], 5 days appears to be the shortest duration that we could manage with in order to ensure that we dealt with the same material in a short window of 24 hours. Time, stress and frequency sweep measurements were carried out with a stress-controlled DSR200 instrument from Rheometric Scientific, connected to a temperature controlled water bath.

The rheometer was equipped with a cup and bob geometry (inner diameter: 29mm, outer diameter: 32mm, length: 44mm). Temperature varied from 10 to 80°C (high temperatures were applied to highlight thermal phenomena).

To avoid evaporation, sludge was covered with a thin film of known viscosity Newtonian oil: oil and sludge are not miscible, as evidenced by oil removal processes in wastewater treatment plants.

Before each measurement, sludge was strongly pre-sheared at a shear rate of 500s -1 for 5 minutes and then left at rest respectively for 2 minutes for time sweeps, 5 minutes for strain sweeps and 1 hour for frequency sweeps. This procedure allowed us to obtain reproducible results [START_REF] Baudez | The rheological behaviour of digested sludge[END_REF].

Results and discussion

Time sweep

Under constant stress, low enough to be in the linear viscoelastic regime [START_REF] Ayol | Toward efficient sludge processing using novel rheological parameters: dynamic rheological testing[END_REF] and constant frequency, raw sludge aged with a monotonic decrease of the shear strain while the digested sludge reached an equilibrium state after less than 15 minutes (Figure 1). Shear history can be considered as negligible for digested sludge, but not for raw sludge which undergoes an ageing process.

Note that, due to continuous bacterial activity, this ageing process must be considered as a shortterm characteristic: fermentation induces a fluidisation of the material [START_REF] Baudez | Rheology of aging, concentrated, polymeric suspensions -Application to pasty sewage sludges[END_REF] and over long experimental times, under constant stress and constant frequency, the shear strain will increase.

Strain sweep

For both raw and digested sludge, G' is nearly constant at low shear strain, suggesting a linear viscoelastic regime (LVE), in agreement with the results of [START_REF] Ayol | Toward efficient sludge processing using novel rheological parameters: dynamic rheological testing[END_REF]. Then, both moduli become strain dependent with G' decreasing and G'' passing through a peak before decreasing as well (Figure 2). Of further interest is the strain-dependence of G' and G'': when G''>G', they both follow a power-law model (Figure 3), such as:

n n G G 2 ' ' ' - - ∝ ∝ γ γ (1)
This peculiar behaviour is known to be the hallmark of soft-glassy materials [START_REF] Wyss | Mechanics and Microstructures of Concentrated Colloidal Gels[END_REF] and has been noticed for many other systems such as colloidal glasses [START_REF] Mason | Linear viscoelasticity of colloidal hard sphere suspensions near the glass transition[END_REF], emulsions [START_REF] Mason | Osmotic pressure and viscoelastic shear moduli of concentrated emulsions[END_REF] and gels [START_REF] Altmann | Strong through to weak 'sheared' gels[END_REF]. However, while the transition from a solid-like to a liquid-like behaviour is smooth with digested sludge, raw sludge suddenly yields: G' is divided by almost 10 and the strain drops sharply from 5 to 16% when the applied stress changes from 0.43 to 0.46Pa (Figure 2

and insert).

It is also worth noting that the peak in G'' vanishes when the temperature increases (figure 4) and then disappears at very high temperatures for digested sludge while it appears to remain at almost constant amplitude with the raw sludge (figure 5).

At this point, one can conclude that both raw and digested sludge present similarities with softglassy materials, but also some differences:

-digested sludge appears not to be an "out-of-equilibrium" material (at least at the considered concentration) and tends to behave like a simple colloidal suspension; -raw sludge is an out-of-equilibrium material which abruptly yields from a solid-like to a liquid-like behaviour.

These differences may be attributed to the degree of dispersion of digested sludge which is 4 times higher than activated sludge, and the EPS concentration which is 2 times lower for digested sludge: according to Mikkelsen and Keiding (2006), the EPS fraction is the most important parameter with respect to floc structure and the presence of large EPS quantities may increase the interaction via entanglement, which induce relaxation processes [START_REF] Thurston | Shear rate dependence of the viscoelasticity of polymer solutions: theoretical model[END_REF].

In both cases, increase of temperature induces a decrease of rheological characteristics: raw and digested sludge become more and more fluid (Figures 4 and5) and we emphasise a proportionality between water viscosity and the strain at the cross-point where G'=G'' (Figure 6) and above. Because water viscosity follows an Arrhenius law with temperature, we can deduce from Figure 6 that when G''>G', the viscoelastic characteristics follow an Arrhenius law too, with the same activation energy as water viscosity.

These results suggest that the same molecular movements are involved in the temperaturedependence of loss modulus and storage modulus in the liquid-like regime and water viscosity.

However, in the solid-like regime, (G'>G''), both G' and G'' follow a non-Arrhenius Vogel-Tammann-Fulcher (VTF) equation with the temperature (Figure 7) with almost the same 0 T (Table 1):

( )         - ⋅ = 0 exp . ' T T R Ea A G (2)
This relation contains three adjustable parameters, A, Ea and T 0 , with T 0 being the temperature where 'free volume' disappears in many 'free volume' models. The observed deviation from the Arrhenius law in the solid-like regime (G'>G'') is similar to what it is observed with fragile glasses (Kobayashi and Takahashi, 2008): when G'>G'', raw and anaerobic digested sludge can be seen as an amorphous solid; but they behave more like disordered liquids when G''>G'. In the linear regime (shear strain lower than 2%), both raw and digested sludge show a weak power-law dependence (power law index smaller than 0.1) with the frequency (figure 8) with G' and G'' in a nearly constant ratio (#0.15). In the highest frequency range the digested sludge presents a shallow minimum in the G'' curve.

In the non-linear regime (shear strain higher than 10%), digested sludge exhibits a plateau for G' at intermediate frequencies and a localized minimum for G'' (Figure 9) while raw sludge exhibits a plateau for both G' and G'' (data not shown). At lower frequencies, for both sludges, the loss modulus varies linearly with the frequency while the storage modulus follows a power-law with a power-law index higher than 1 which also increases with the temperature, at least for the digested sludge (figure 9-10):

( )

ω ω ∝ > ∝ ' ' , 1 ' G n G n (3)
Moreover, the linearity between frequency and loss modulus at low frequencies suggests similarities of the behaviour at all temperatures investigated in this work. Unfortunately, as previously mentioned such an assumption cannot be verified with raw sludge which is a highly fermentable and continuously changing material: frequency sweep experiments are time consuming and as the temperature increases, fermentation kinetics also increase. Consequently in such a case it is simply not possible to assume constant material properties throughout the experiment. However, with digested sludge, we can make this assumption and by horizontally shifting the frequency-dependence curves we obtain a master curve (Figure 11) for digested sludge samples at two different concentrations Surprisingly, the horizontal shift factor presents a linear relationship with the water viscosity for the lower concentration (Figure 12) but not for the higher concentration, indicating that thermal agitation cannot be considered as a key factor when the concentration increases. Consequently, other interactions can no longer be neglected, such as hydrophobic or electrostatic forces [START_REF] Mikkelsen | Physico-chemical characteristics of full scale sewage sludges with implications to dewatering[END_REF].

Table 2 summarizes the main characteristics of the raw and digested sludge, including results get from the literature. First of all, anaerobic digestion not only modifies sludge composition but also its rheological behaviour. Consequently, these changes have to be taken into account in the flow behaviour analysis of material being digested in order to improve mixing and homogenisation.

If we try to establish a parallel with well-known materials, these features (of raw and digested sludge) are similar to those found in the literature regarding the viscoelastic behaviour of softglassy materials (Chen et al., 2010). However, soft-glassy materials encompass many materials such as pastes, foams, emulsions, colloids, etc. with their own specific characteristics. Looking at the ageing process; emulsions [START_REF] Mason | Linear viscoelasticity of colloidal hard sphere suspensions near the glass transition[END_REF] or paints [START_REF] Baldewa | Thixotropy and physical aging in acrylic emulsion paint[END_REF] could be seen as a convenient model for digested sludge. This assumption can be strengthened with the fact that, according to the literature [START_REF] Forster | Bound water in sewage sludge and its relationship to sludge surfaces and sludge viscosities[END_REF], digested sludge is composed mainly of protein and lipopolysaccharides which can be seen as amphiphile materials. Besides, raw sludge highlights a more complex behaviour, with ageing and abrupt yielding, but also with temperature dependence, which is reminiscent of (thixotropic) colloidal gels [START_REF] Joshi | Rheological behaviour of aqueous suspensions of laponite: New insights into the ageing phenomena[END_REF]. This last assumption is in agreement with the work of [START_REF] Legrand | Deswelling and flocculation of gel networks: Application to sludge dewatering[END_REF] and [START_REF] Dursun | Toward the conceptual and quantitative understanding of biosolids conditioning: the gel approach[END_REF] who considered that the gel approach is a pertinent conceptual model for sludge structure.

Even if these assumptions still have to be clearly established, it may signify that during anaerobic digestion sludge evolves from a colloidal gel-like material to an emulsion-like material, and we may have to deal with a mix of emulsion-like and gel-like materials within reactors. Such a complexity may induce a very complex rheological behaviour in terms of mixing and homogenisation (industrial digesters are bigger than 10.000m 3 ).

Thus, further work has to be done by comparing all the rheological characteristics of digested and raw sludge with emulsion or paint and with colloidal gels over a broader range of concentrations; but also by looking at the rheological behaviour of sludge during anaerobic digestion, when all the highlighted characteristics coexist.

Conclusion

The viscoelastic behaviour of raw and anaerobically digested sludge was analysed using oscillatory measurements. We found that both materials present strong similarities with soft-glassy materials: the storage modulus decreases monotonically with the shear strain, while the loss modulus passes through a maximum before decreasing. In the liquid-like regime, when G'<G'', both moduli followed a power-law dependency against frequency. Increase of temperature also induced a fluidisation of sludge, with a decrease of rheological characteristics according to both Arrhenius and VTF laws. However, raw and digested sludge have different structure and dominant interactions: also -the ageing process only occurs with raw sludge, not with digested sludge.

In the range of concentrations tested, both sludges are temperature dependent and this behaviour appears to be highly dependent of thermal agitation, with some linear relationship between rheological characteristics and temperature-water viscosity variations.

We have shown that colloidal gels and emulsion can model the rheological behaviour of respectively raw and digested sludge. Thus, this paper opens a new insight into sludge management by empowering engineers to model digested sludge with emulsions and raw sludge with colloidal gels. However, more work has to be done, by comparing all the rheological characteristics of digested and raw sludge with emulsion or paint and with colloidal gels over a broader range of concentrations.

ACKNOWLEDGMENT

The authors gratefully acknowledge Irstea, Melbourne Water and South East Water (Ltd.) as well as the Research and Innovation Office of RMIT University for providing support for Dr Jean-Christophe Baudez's visit to pursue this research. ) when a constant shear stress is applied, respectively equal to 1Pa and 0.65Pa. The insert shows the strain evolution of digested sludge over longer time at a smaller shear stress (0.3Pa) and evidences that shear strain is remaining constant.

Figure 1 :

 1 Figure 1: Time evolution of the shear strain in the linear viscoelastic regime for both digested (at 42 g.L -1 ) and raw sludge (at 45 g.L -1

Figure 2 :

 2 Figure 2: Evolution of storage and loss moduli during stress sweep. The insert shows the stressstrain relationship and the abrupt yielding of raw sludge compared to anaerobic sludge.

Figure 3 :

 3 Figure 3: strain dependence of elastic (G') and loss (G'') moduli, at 25°C and 1Hz, for the digested sludge concentration of 3.2%. The insert represents the strain dependence of G' and G'' for the raw sludge in the liquid-like regime.

Figure 4 :Figure 5 :

 45 Figure 4: Strain sweep, at 0.2Hz, for a digested sludge concentration of 3.2%

Figure 6 :

 6 Figure 6: Water viscosity and strain for which G'=G'' at 0.2Hz for the digested sludge (at 3.2%) and 0.5Hz for the raw sludge at the 5 temperatures considered (10, 25, 40, 60°C).

Figure 7 :

 7 Figure 7: G' and G'' both follow a non-Arrhenius law. Model parameters for the 3.2% sludge submitted to a constant shear stress equivalent to a 2% shear strain at 0.2Hz are respectively A=12.94Pa, Ea/R=50.43°C and T 0 =98.40°C for G', A=1.61Pa, Ea/R=13.77°C and T 0 =97.91°C for G''.

Figure 8 :

 8 Figure 8: Frequency sweep in the LVE regime for both sludges. The slight increase of G' and G'' for the raw sludge may be attributed to ageing process

Figure 10 :

 10 Figure 10: Frequency-dependence of the digested sludge at 40°C

Figure 12 :

 12 Figure 12: Horizontal shift factor against water viscosity for the 1.85% and 3.2% sludge. The solid line represents a linear model.

Table 1 : Parameters of Equation (2) for the raw and digested sludge (at 3.2%) submitted to a constant shear stress respectively equivalent to a 1 and 2% shear strain.

 1

	G'	G''

Table 2 : main characteristics of both raw and digested sludge. The symbol * indicates results coming from the literature and cited in the introduction.

 2


J C Baudez

P Slatter

N Eshtiaghi

The impact of temperature on the rheological behaviour of anaerobic digested sludge

Keywords: Digested sludge, Rheology, Structural change, Temperature, Thermal agitation, Viscosity, Yield stress

The rheological properties of municipal anaerobic digested sludge rheology are temperature dependent. In this paper, we show that both solid and liquid characteristics decrease with temperature. We also show that the yield stress and the high shear (Bingham) viscosity are the two key parameters determining the rheological behaviour. By normalising the shear stress with the yield stress and the shear rate with the yield stress divided by the Bingham viscosity, a master curve was obtained, independent of both temperature and concentration. We also show that the rheological behaviour is irreversibly altered by the thermal history. Dissolution of some of the solids may cause a decrease of the yield stress and an increase of the Bingham viscosity. This result suggests that the usual laws used to describe the thermal evolution of the rheological behaviour of fluids are no longer valid with anaerobic digested sludge. Finally, the impact of temperature and thermal history have to be taken into account for the design of engineering hydrodynamic processes such as mixing and pumping.

Introduction

Anaerobic digestion is one of the most important processes for reducing sludge volume by reducing of about 30% of the organic load (part of the solid organic matter is converted into gas) and for producing biogas. To be efficient, anaerobic digestion needs to satisfy at least three conditions: (i) controlled temperature, between 35 and 37°C for mesophilic processes or between 55 and 58°C for thermophilic processes, (ii) homogeneous mixing conditions and (iii) no dramatic variation in organic load. To control temperature, biogas is partly used for heating large digesters through heat exchangers installed in recirculation loops [START_REF] Gerardi | Effect on premixing raw and digested sludge on high-rate digestion[END_REF]. If possible sludge also has to be initially pre-heated to the appropriate temperature and raw sludge is sometimes mixed with digested sludge before entering the digester (Keeper, 1959). In other cases, the digester mixing system ensures that the cold, newly introduced sludge, is mixed with the warm older solids and the bacteria. Finally, the entire digester volume needs to be turned over once every 3-4 hours using pumps and recirculation loops. It is imperative that digester design take into account the energy requirements needed to maintain these essential operating conditions, such as the power consumption of pumps and mixing systems, which are directly related to the sludge rheology [START_REF] Baudez | The rheological behaviour of digested sludge[END_REF].

Because flow velocities within the digester and the recirculation loops are not of the same order of magnitude, a better understanding of the rheological properties of digested sludge over a wide shear rate range would provide a sound basis for the efficient design of digesters. Monteiro (1997) showed that anaerobic digested sludge rheology can be described using the Herschel-Bulkley model, for which the rheological characteristics decreased with the degree of fermentation. More recently, Baudez et al. (2011a) highlighted a more complex behaviour with shear banding at low shear rates and a viscosity plateau at very high shear rates. However, these studies did not focus on the temperature dependence of the rheology of digested sludge, which would fundamentally affect the flow properties and consequent operating conditions of the digester.

Since the pioneering work of Manoliadis and Bishop (1984) who pointed out a decrease of rheological characteristics similar to what is usually observed with Newtonian fluids, there is very little literature on the impact of temperature on municipal sludge rheology. In a recent paper, [START_REF] Baudez | Digested sludge rheology: similarities with soft glassy materials[END_REF] showed that the decrease of viscoelastic properties is proportional to the decrease of water viscosity with increase in temperature, suggesting thermal motion may be the key factor, in agreement with what was observed by Manoliadis and Bishop (ibid.) while Dieude-Fauvel et al. (2009) considered a VTF model (Vogel-Tamman-Fulcher) on secondary sludge.

However, because municipal sludge in mainly composed of water, mineral particles and organic matter (polymeric and dissolved), one can imagine that the temperature dependence of sludge would be similar to what it is observed with mineral suspensions and organic polymers. If there is a general agreement in polymer science to consider that temperature decreases rheological characteristics, de [START_REF] De Kretser | The effect of temperature on the yield stress of mineral suspensions[END_REF] showed that the solid characteristics of mineral suspensions can increase with an increase of temperature while liquid characteristics decrease.

In this paper, we revisit the temperature dependence of digested sludge, both in the liquid and the solid regimes and we propose that thermal motion has the most important impact. We also show that it is not the only mechanism impacting sludge rheology. Similarities between the rheological behaviour of digested sludge at different temperatures were found, but temperature also irreversibly modified sludge structure. After being heated and cooled down, digested sludge showed a lower yield stress but a higher consistency index than the initial material, at the same temperature. Apart from the fundamental contribution this makes to understanding sludge behaviour, such behaviour has to be taken into account for the practical design and operation of anaerobic digesters, especially heat exchangers and pipe flow.

Material and methods

Anaerobic digested sludge was sampled at the Mount Martha waste water treatment plant (Melbourne, Victoria, Australia) at the outlet of the mesophilic anaerobic digester number 1. Its initial solids concentration was at 18.5 g.L -1 and was also gently concentrated to 25.5, 32.5 and 49 g.L -1 by using a Buchner vacuum. To reach these concentrations, sludge was basically poured into a cylinder onto a filter paper and vacuum suction was applied at the pressure of -0.5 bars. During all the filtration process, sludge was softly mixed to let the solid particles in suspension, avoiding clogging of the filter paper. Solid concentration was determined by drying the sludge at 105°C for 24 hours.

Because fermentation alters sludge rheological characteristics mainly in the first 10 days of storage [START_REF] Baudez | Rheology of aging, concentrated, polymeric suspensions -Application to pasty sewage sludges[END_REF], and although anaerobic digestion is a stabilization process, our samples were stored at 4°C for 30 days before experiments, to ensure no temporal variability, allowing us to use the same material over several days. This technique was successfully used by [START_REF] Curvers | A centrifugation method for the assessment of low pressure compressibility of particulate suspensions[END_REF].

Rheological measurements were performed with a stress-controlled DSR200 from Rheometric Scientific, connected to a temperature controlled water bath. The rheometer was equipped with a cup and bob geometry (inner diameter: 29 mm, outer diameter: 32 mm, length: 44 mm). In order to highlight its impact on the rheological behaviour of digested sludge, temperature was varied from 10 to 80°C using a temperature controlled water bath. To avoid evaporation, sludge was covered with a thin film of Newtonian oil (oil and sludge are not miscible, as evidenced by oil removal processes in wastewater treatment plants).

Before each measurement, the sludge was presheared for 10 minutes at a shear rate of 1000 s -1 then left at rest for 10 minutes before each measurement. With such a procedure, measurements were repeatable and reproducible [START_REF] Baudez | Rheology of aging, concentrated, polymeric suspensions -Application to pasty sewage sludges[END_REF]Baudez et al., 2011a).

Because of shear banding, direct determination of the yield stress has to be conducted with caution in the sense that the data we could consider as the yield stress would be basically the stress at which shear localisation occurs. Thus, we focused our measurements on (i) the solid characteristics by applying a linear ramp of increasing shear stress as long as the strain remained limited and (ii) the liquid characteristics by applying decreasing stress ramps, starting from a high stress corresponding to a shear rate of approximately 1000s -1 or lower for the less concentrated sludge (to avoid turbulent conditions).

The solid characteristics were only determined on the most concentrated sludge and below 60°C because at 80°C the measured values were too low to be considered consistent, with respect to the rheometer characteristics.

It must be noted that what will be called yield stress in the following should be seen as the extrapolation of the flow curve towards zero shear rate: it basically represents the limit below which there is no steady state flow.

Lastly, all the data fits shown in this paper were obtained using Excel software and its solver macro based on the "least squares" difference between model and experiment.

Definition of the general behaviour of anaerobic digested sludge

The following results will be interpreted according to the behaviour of digested sludge determined by Baudez et al. (2011a):

-a linear viscoelastic behaviour in the solid regime, well represented by a generalised Kelvin-Voigt model, with a wide relaxation times spectrum modelled by a stretched exponential:

( ) ( ) ( ) ( ) m t G t λ τ γ - - ⋅ ⋅ = exp 1 1 (1)
where γ represents the strain, τ the stress and µ λ

G =
with G (representative of the purely elastic spring) and µ (representative of the purely viscous damper) the usual parameters of a Kelvin-Voigt model.

-a shear-thinning behaviour with a constant high-shear viscosity in the liquid regime, well represented by a Herschel-Bulkley model coupled with a Bingham model (Baudez et al., 2011a):

n c c c n c c n c c n c K K K         ⋅ = ⋅ = Γ Γ + Γ ⋅ + = ⇔ ⋅ + ⋅ + = ⇔ ⋅ + ⋅ + = 0 0 0 0 , 1 1 α τ τ ξ γ τ α ξ τ τ γ τ α γ τ τ τ γ α γ τ τ
τ represents the extrapolated limit below which there is no steady-state flow (improperly named yield stress in the following), K the consistency index, 0 α the high shear viscosity rate (named Bingham viscosity in the following) and n the power-law index. Note that such a dimensionless form was previously used by Coussot (1995) with mineral suspensions. It comes from from the identical shape of the flow curves. Thus, it is natural to scale the shear stress by the yield stress, such that all curves go through the same point

. This means we probably smooth the solid interactions since represents the strength of particle interactions 'at rest'. In parallel it is necessary to scale the shear rate by a factor also related to viscous dissipation. This may be done by assuming that for high shear rates the energy dissipation resulting from interactions between solid particles becomes negligible compared to hydrodynamic dissipation. Under these conditions, like Coussot (1995) did for mineral suspensions, it is natural to use a dimensionless number, Γ defined as

γ τ µ & ⋅ = Γ c
where µ is the viscosity of the equivalent suspension of force-free particles in water. Following the work of Quemada (1998), we assumed that at high shear particles are independent of each others, so 0 α µ = .

Results and discussion

The impact of temperature on the solid characteristics First focusing on increasing shear stress sweep, the model defined by Eq (1) is accurate at low shear stress (fig. 1), and the higher the temperature, the higher the shear strain at a given shear stress (fig. 1). Only the elasticity appears to change significantly with the temperature (Table 1), and its changes with temperature are proportional to those of water viscosity (Fig. 2), indicating that there are probably the same molecular movements which are involved in both water viscosity and elastic coefficient changes with the temperature. The constant value of the parameter λ also indicated that both the elastic and viscous characteristics of the Kelvin-Voigt model follow the same relationship regarding temperature., mainly caused by thermal agitation (due to the proportionality with water viscosities).

The impact of temperature on the liquid characteristics

The same temperature evolutions are observed with the flow curves, in the liquid regime (fig. 3):

the higher the temperature, the higher the shear rate (and so, the lower the apparent viscosity) at a given shear stress. Sludge becomes less and less viscous as the temperature increases.

In the dimensionless form of ( 2), all the flow curves resolve to a single master curve, independent of both temperature and concentration (fig. 4), indicating that the (extrapolated) yield stress and the Bingham viscosity are the two key parameters to characterise the flowing behaviour of digested sludge. Note that the consistency index K appears to be proportional to c τ (data not shown) but at this stage, we have no explanation for that.

Moreover, in the temperature range of [10-60°C], both the yield stress (fig. 5) and the Bingham viscosity decreased, this latter followed a linear relationship with water viscosity (fig. 6), meaning thermal agitation also had a major influence in the change of the liquid characteristics. Surprisingly, the temperature changes of c τ are not proportional to the water viscosity changes, which could have been expected because of the impact of temperature on the elasticity. This probably comes from the determination of c τ which is not a 'real' rheological characteristic but rather a fitting parameter (due to shear banding, c τ cannot be measured directly).

Following the results of Rodd et al. ( 2001), [START_REF] Baudez | Physical aging and thixotropy in sludge rheology[END_REF] and Baudez et al. (2011a), the yield stress and the Bingham viscosity can be expressed as follows:

( ) m c a 0 φ φ τ - ⋅ = (3) ( ) φ β µ α ⋅ ⋅ = exp 0 0 (4)
where 0 φ is the lowest concentration below which there is no yield stress (also called gel point in polymer science), m is a parameter which can be related to the fractal dimension of sludge flocs (Pignon et al., 1996), 0 µ is the viscosity of the liquid medium, and a and β are model parameters.

From the fitted values of c τ and 0 α (see appendix for all the rheological values), we have determined the numerical values for the parameters of ( 3) and ( 4): 0 µ and β of ( 4) and a and m of (3) decreased when the temperature increased while 0 φ increased (fig. 7 andtable 2)). Assuming that m reflects the fractal dimension of the flocs (Pignon et al., 1996), its decrease means that the flocs became less dense and compact [START_REF] Li | Fractal geometry of particle aggregates generated in water and wastewater treatment processes[END_REF]. From a more fundamental perspective, this also means that if flocs are seen as spherical agglomerates of particles, the decrease in fractal dimension implies that (i) floc surface remained constant while the number of voids increased or (ii) floc surface increased. In both cases, it would mean that sludge structure is modified when the temperature increases..

The impact of thermal history

If sludge is heated and cooled before measurement, its rheological behaviour is irreversibly altered compared to its initial behaviour with no such thermal history (fig. 8): the hotter the preheat, the smaller the yield stress and the higher the Bingham viscosity (fig. 9), the consistency being almost constant. This result strengthened the assumption we previously made and it also indicated that the structural changes induced by an increase of temperature are globally irreversible.

At this time, it must be strongly emphasised that our initial anaerobic digested sludge was picked up at the outlet of a mesophilic digester which runs between 35 and 38ºC. So our results obtained at the temperature below the digester operating temperature were already influenced by the previous thermal history of the sludge. That's may explain why the variation of the rheological characteristics are weak below 40ºC and also why there is no significant change in fig. 6 between 25 and 40ºC: in this range, the yield stress and the water viscosity appear to be proportional (data not shown), suggesting that (i) thermal fluctuation is the main factor responsible of the yield stress decrease below 40ºC and (ii) the alteration of the composition with the temperature is irreversible.

However, by reducing shear rate and shear stress to dimensionless form as proposed in Eq(2), a master curve was also obtained (fig. 10), indicating that ultimately the yield stress and the Bingham viscosity can again be considered as the two key parameters which drive the rheological behaviour of anaerobic digested sludge and its (physical) evolution with temperature.

As suggested above, thermal history apparently irreversibly modified the structural characteristics of the sludge, because of the change of the rheological characteristics, but did not change the total solid concentration. Indeed, we did not find significant changes in the total solid concentration regarding temperature history, which is quite logical in the sense that water content determination imply to heat sludge at a higher temperature that we did. So, assuming the total solids concentration was kept constant by preheating the sludge, from Eq (4), we can deduce the increase of Bingham viscosity originates only from an increase in 0 µ (since β decreases with temperature) and in parallel, the yield stress decreases.

Keeping in mind that the fractal dimension of the flocs decrease with the temperature, if the viscosity of the medium increased while the yield stress decreased, it implies that there is a transfer from solids constituents to dissolved constituents, the total solids concentration being constant. This assumption has to be confirmed, by measuring the liquor viscosity before and after heating. However such a result was already reported by Appel et al. (2010) who pointed out that temperature increase promoted dissolution of the main organic (proteins, carbohydrates and volatile fatty acids) and inorganic (heavy metals, S and P) sludge constituents. Paul et al. (2006) suggested a preferential dissolution of proteins over carbohydrates by measuring COD released after thermal treatment of digested sludge.

Because material composition changed with temperature, it is then quite impossible to define temperature evolution laws with consistent physical meaning for parameters from Eqns (3) and ( 4):

it would be fundamentally inaccurate to consider constant activation energies, as the composition is changing with temperature.

Conclusion

The impact of temperature on the rheological behaviour of digested sludge has been investigated.

Sludge became progressively more fluid when the temperature was increased, but by normalising the shear stress with the yield stress and the shear rate with the yield stress divided by the Bingham viscosity, a master curve was obtained. Both yield stress and Bingham viscosity decreased with increasing temperature, indicating that thermal agitation had a major influence.

However, it is not the only parameter influencing the fluidisation of sludge: thermal history also played an important role.

If sludge was preheated and cooled before experiment, the initial yield stress decreased while initial Bingham viscosity increased: this may result from a conversion of solid to dissolved constituents, a process which is partially irreversible. Thus, the usual laws used to model temperature dependence would be no longer valid because such laws can only be used when the composition remains constant. This point cannot be asserted in the case of anaerobic digestion sludge as our results suggest that the sludge composition may be altered by temperature. In order to confirm this assumption, further work is needed to measure liquor viscosity by filtering sludge at different temperatures. The apparatus to enable such an experiment is under construction.

Such behaviour has to be taken into account in the hydrodynamic modelling of industrial flow processes in which temperature is modified, such as in recirculation loops through sludge heaters,

where head loss determination can be significantly affected.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Viscoelatic behaviour of the 4.8% sludge. at 25 and 60ºC. The dotted lines represent the fit of the generalised Kelvin-Voigt model Equation (1)

Figure 4 :Figure 5 :

 45 Figure 4: Dimensionless flow curves of the digested sludge at different solids concentration and temperature. The dotted line represents the model of Equation (2) with the following parameters: 3 . 0 , 57 . 4 = = n ξ

Figure 6 :

 6 Figure 6: Thermal evolution of the Bingham viscosity of the digested sludge at different concentrations plotted against the viscosity of water at the same temperatures.

Figure 7 :

 7 Figure 7: Evolution of the parameters of Equation (3) with temperature.

Figure 8 :

 8 Figure 8: Flow curve of the 3.2% digested sludge at 25°C after being heated to 40. 60 and 80°C.

Figure 9 :Figure 10 :

 910 Figure 9: Evolution of the parameters of Equation (2) for the 3.2% sludge at 25°C with respect to its thermal history

Table 1 : Values of the viscoelastic parameters given by Eq (1) at different temperatures.

 1

		10°C	25°C	40°C	60°C
	G/100 [Pa]	0.559	0.385	0.263	0.167
	λ [t -n ]	1.488	1.489	1.489	1.499
	n [1]	0.416	0.421	0.374	0.479

Table 2 : Values of parameters of (3) and (4) at different temperatures.

 2

		10°C	25°C	40°C	60°C
	0 φ [%]	0.787	0.792	0.825	0.948
	a [Pa]	0.0855	0.0817	0.0803	0.0654
	m [1]	2.482	2.366	2.352	2.153
	0 µ [mPa.s]	1.826	1792	1.777	1.762
	β [1]	0.6935	0.605	0.517	0.426

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	n	0.308	0.308	0.308	0.308
	α 0	0.012	0.009	0.008	0.006
			32.5 g.L -1
	rheological behaviour. Wat. Sci. Tech., 36 (11): 61-67 τ c 0.711 0.711	0.606	0.376
	Paul, E., Camacho, P., Lefebvre, D., Ginestet, P., 2006. Organic matter release in low temperature K 0.976 0.905 0.770 0.499
	thermal treatment of biological sludge for reduction of excess sludge production. Water Science n 0.308 0.308 0.308 0.308
	and Technology, 54 (5), pp. 59-68 α 0 0.016	0.013	0.011	0.008
	Pignon F, Piau JM, Magnin A., 1996. Structure and pertinent length scale of a discotic clay gel. 49.0 g.L -1
	Phys. Rev. Lett. 76, 4857-4860 τ c 2.844	2.300	2.175	1.255
	Quemada, D., 1998. Rheological modelling of complex fluids. The concept of effective volume
	K	3.686	2.769	2.327	1.383
	fraction revisited. The European Physics Journal AP, 1, 119-127.
	n	0.308	0.308	0.308	0.308
	Rodd, A. B., Cooper-White, J. J., Dunstan, D. E. and Boger, D. V., 2001. Polymer concentration
	α 0	0.054	0.035	0.022	0.014
	dependence of the gel point for chemically modified biopolymer networks using small amplitude
	oscillatory rheometry. Polymer, 42 8: 3923-3928.
	Slatter P. T. 2011, The Engineering Hydrodynamics Of Viscoplastic Suspensions. J. Particulate
	Science and Technology, 29: 2, 139-150.
	Appendix : numerical values of rheological characteristics allowing us to plot the master curve Captions
		10°C	25°C	40°C	60°C
			18.5 g.L -1
	τ c	0.100	0.092	0.088	0.052
	K	0.194	0.169	0.148	0.097
	n	0.308	0.308	0.308	0.308
	α 0	0.007	0.005	0.004	0.003
			25.5 g.L -1
	τ c	0.335	0.293	0.201	0.146
	K	0.531	0.436	0.331	0.240

& & & &(2) where c

Acknowledgements

The authors gratefully acknowledge Irstea, Melbourne Water and South East Water (Ltd.) as well as the Research and Innovation Office of RMIT University for providing support for Dr Jean-Christophe Baudez's visit to pursue this research