Nicolas Lavielle
email: nicolas.lavielle@espci.fr

Daniel Beysens

Anne Mongruel

Memory re-condensation

Keywords: Heterogeneous nucleation, condensation, breath figure, dew pattern, plant nutrition

This paper reveals a phenomenon of memory in dropwise condensation in open air. After a first condensation process and complete evaporation of the condensed droplets, further condensations proceed with droplet nucleating at the very places where former droplets evaporated. The origin of this phenomenon is due to the incorporation of airborn salts during the first droplet condensation and its further concentration during droplet evaporation. Salts act as preferential nucleation sites and humidity sinks. The potential impact of this phenomenon on controlled breath figure patterns and plants metabolism is discussed.

Introduction:

Condensation is used in various industrial applications, such as heat transfer [START_REF] Cho | Nanoengineered Materials for Liquid-Vapour Phase-Change Heat Transfer[END_REF][START_REF] Preston | Heat Transfer Enhancement During Water and Hydrocarbon Condensation on Lubricant Infused Surfaces[END_REF] , desalination [START_REF] Khawaji | Advances in Seawater Desalination Technologies[END_REF] , power generation [START_REF] Zhao | Investigation on the Condensation Behavior of the Trace Element Zinc in (Ar/H2O/HCl/H2S) Gas Mixtures and Its Practical Implications in Gasification-Based Processes for Energy and Power Generation[END_REF] or water harvesting 5,[START_REF] Liu | Water Harvesting from Air: Current Passive Approaches and Outlook[END_REF] . In nature, dew water is a source of fresh water for vegetation [START_REF] Makowski | Effect of Inoculum Concentration, Temperature, Dew Period, and Plant Growth Stage on Disease of Round-Leaved Mallow and Velvetleaf by Colletotrichum Gloeosporioides f. Sp. Malvae[END_REF][START_REF] Hill | The Role of Dew in Negev Desert Plants[END_REF][START_REF] Munné-Bosch | Role of Dew on the Recovery of Water-Stressed Melissa Officinalis L. Plants[END_REF] and consequently for wildlife. Water vapour condensation occurs on a surface when its temperature is below the dew point temperature of the surrounding humid air. In the case of dropwise condensation, droplets are formed in a partial wetting state leading to a pattern of droplets called "breath figure" (BF) [START_REF] Baker | Breath Figures[END_REF][START_REF] Beysens | Growth of Breath Figures[END_REF] . Heterogeneous nucleation preferentially takes place on surface defects where molecules aggregate and forms a liquid cluster. Then, the droplets grow by the direct accretion of pure water molecules through a diffusive boundary layer. Coalescences upon contact with neighbouring drops speed up the growth process [START_REF] Beysens | Dew Nucleation and Growth[END_REF] . When the temperature of the surface becomes larger than the dew point temperature, condensation stops and water evaporates. This cycle is present in nature. At night, the air temperature decreases and its relative humidity increases, which are propitious conditions for dew condensation. In the morning, when the sun rises, the air temperature increases and relative humidity decreases, which leads to the evaporation of the condensed dew droplets. Heterogeneous nucleation is known to take place on surface defects. The control of the nucleation sites and subsequent localization of the droplets is thus difficult to achieve. Patterned surfaces for controlled nucleation have been successfully engineered by considering that heterogeneous nucleation is favoured on hydrophilic surfaces [START_REF] Hou | Recurrent Filmwise and Dropwise Condensation on a Beetle Mimetic Surface[END_REF][START_REF] Bai | Efficient Water Collection on Integrative Bioinspired Surfaces with Star-Shaped Wettability Patterns[END_REF][START_REF] Dai | Hydrophilic Directional Slippery Rough Surfaces for Water Harvesting[END_REF] , soft surfaces [START_REF] Eslami | Thermodynamic Investigation of the Barrier for Heterogeneous Nucleation on a Fluid Surface in Comparison with a Rigid Surface[END_REF][START_REF] Sokuler | The Softer the Better: Fast Condensation on Soft Surfaces[END_REF] or chemical defects [START_REF] Guadarrama-Cetina | Droplet Pattern and Condensation Gradient around a Humidity Sink[END_REF] . Another approach consists in the deposition of a NaCl saturated water droplet or NaCl crystals on a surface prior condensation. It was shown that water preferentially condenses on the salty droplet surrounding by a region of inhibited condensation [START_REF] Guadarrama-Cetina | Droplet Pattern and Condensation Gradient around a Humidity Sink[END_REF] . The same observation was made by using hygroscopic droplets [START_REF] Nath | Duelling Dry Zones around Hygroscopic Droplets[END_REF] .

Here, we propose to investigate another process, herein referred to as the "memory recondensation". After complete evaporation of a first breath figure, and in the absence of any controlled nucleation sites, the new condensed pattern is expected to be totally independent of the former evaporated figure. However, and remarkably, we observe that droplets preferentially condense at the very place where the former droplets were located. This suggests that preferential nucleation sites have been created in relation to the evaporation of the former BF. Surprisingly, this phenomenon has not been studied so far, although indirectly evidenced by Yu et al [START_REF] Yu | Droplet Evaporation during Dropwise Condensation Due to Deposited Volatile Organic Compounds[END_REF] . The potential impacts for plants metabolism and controlled BF patterns are also discussed.

Results and discussion:

Breath figure patterns of re-nucleation

Water condensation was performed on a model surface (silicon wafer) in a mini-climatic chamber equipped with an optical microscope. Condensation was performed for a given time until a first BF of droplets was obtained. Then, the surface was placed outside the chamber to induce a complete and natural evaporation of the water droplets under ambient conditions. Upon total disappearance of the droplets, as verified with microscope, the surface was replaced in the climatic chamber for re-condensation and observed under microscope.

Figure 1abc reports images of different BF obtained after 100, 200 and 300 s of a first condensation on a fresh silicon wafer. The nucleation of droplets preferentially occurs on the surface defects. As time proceeds, droplets grow by direct accretion of water vapour and by coalescences. The smaller droplets in (c) originate from a re-nucleation process in the free space left by coalescence events at large times. They come from the natural evolution of the BF pattern [START_REF] Beysens | Growth of Breath Figures[END_REF] . The lower images (d,e,f) correspond to the initial BF of a second condensation on the surfaces (a,b,c) respectively, after complete evaporation of the former BFs. Note that the patterns (d,e,f) are concerned with the first moments of the second condensation, when the drops are still small and are therefore situated were they have nucleated. At large times, the position of nucleation sites becomes progressively lost because of coalescences. One can observe that the BFs obtained in the first moments of re-condensation in Figure 1(def) seem to follow a specific pattern with well-defined inter-drops characteristic size. Remarkably, the characteristic inter-drop distance is larger when the duration of the first condensation is larger. To quantify this effect, the average distance between the closest neighbour major droplets (<d>) was measured and displayed on images of Figure 1, and the correlation between <d cond. > and <d re-cond. > is reported in Figure S1. The results indicate that the first BF pattern of condensed droplets seems to play a crucial role on the early pattern obtained from re-condensation. For comparison, Figure 2a presents the firstly condensed droplets from a surface washed from condensation history and displays no specific pattern.

To test the robustness of this phenomenon, a set of four experiments was performed. Four given BF obtained from a first condensation, similar to the BF in Figure 1b, were (a) washed under water and dried with compressed air gun, (b) left for natural evaporation in ambient conditions, (c) dried with compressed air gun and (d) left for natural evaporation in ambient conditions and further dried with compressed air gun, respectively. The images of second condensation on these surfaces are displayed in Figure 2. Experiments (a) and (c) give a BF showing no special repartition of nucleation sites (Figures 2a and2c). By contrast, Figure 2b and Figure 2d, presenting the results obtained from experiments (b) and (d) show the same characteristic nucleation pattern, with preferential nucleation sites. This set of experiments thus evidences the key role of natural droplet evaporation on the surfaces and the robustness of the phenomenon under air flow. However, washing with water or direct gun drying cancels memory re-nucleation.

Localisation of re-nucleation sites

In order to establish precisely the relationship between BFs from the first and second condensation, a cycle of first condensation, evaporation and second condensation was performed on a surface placed inside the mini-climatic chamber during the whole process. Continuous observation under the microscope allowed to precisely identify the localization of the droplets. Figure 3a is an image of the droplets formed during the early stage of the second condensation. The localization of their centres is labelled by a red dot and replicated in Figure 3b and3c. Figure 3b is the BF obtained after 100 s of the first condensation. Figure 3c is an image of the BF of Figure 3b under evaporation, just before the droplets disappear. One can observe that in the second condensation, drops nucleate at the place where the droplets from the former condensation were located. The nucleation sites of the second condensation are not situated exactly at the centre of the evaporating droplet. As evaporation proceeds, it can be observed that they are rather situated at the periphery of the droplet. This fact will be discussed below. This experiment thus evidences the direct link between the droplets pattern from condensation and the pattern of preferential second nucleation; it confirms and explains the nucleation patterns found in Figure 1. The fact that, <d re-cond. > is superior to <d cond > in Figure 1a and b could indicate that larger droplets lead to a more efficient second nucleation on their localizations, compared to smaller droplets. In order to further investigate the origin of memory condensation, a 1 µL droplet of diionized (DI) water was deposited on a silicon wafer and left for natural evaporation under ambient conditions. Figure 4a presents the evolution of the evaporation of the water droplet. At 1340 s, the droplet is almost completely evaporated. After a few more seconds, no water is present on the surface. Nevertheless, a persistent dark "stain" is observed later at 2000 s at the place of the evaporated droplet. As one will see later, the deposition of the stain from the water droplet is at the origin of the memory re-condensation phenomenon. Figure 4b reports the condensation pattern obtained in the vicinity of this stain. A large droplet is seen where the stain was located, surrounded by a zone of inhibited condensation. This pattern is characteristic of a droplet pattern around a humidity sink [START_REF] Guadarrama-Cetina | Droplet Pattern and Condensation Gradient around a Humidity Sink[END_REF] .

Origin of memory re-condensation

The stain left by the evaporation of water droplets on model silicon wafer surfaces was characterized by scanning electron microscope (SEM) to image the surface morphology and energy dispersive X-ray spectroscopy (EDX) to identify and quantify the chemical elements.

The study was carried out on two different stains for comparison: the first stain was obtained after the evaporation of water droplets deposited outdoor by natural dew, the second stain resulted from the evaporation of a 1µL DI water droplet deposition. Outdoor dew water was harvested on a silicon wafer on the terrace of the laboratory located in Paris downtown. The dew droplets naturally evaporated upon sunrise. The sample was then analysed under SEM coupled with EDX. Figure 5 shows an electron microscope image of a typical stain left by the evaporation of dew water on the silicon surface and an EDX mapping of the chemical elements present on this image with a quantification in atomic percentage. One can observe a circular dark stain in the centre of the image with the presence of crystals inside. The chemical analysis reveals that the main detected chemical elements are Si, Na, K, Cl and C. One can notice that Si is also found on the stain, which was expected because EDX detects surface chemical elements within a thickness of 100 nm. Na, K, Cl are the principal chemical elements of the observed crystals. Carbon element is found to fit the geometry of the dark region of the stain. However, the quantification of C element is not reliable using EDX as the use of the electron beam is known to deposit carbon elements; nevertheless, more carbon is present on the stain than on the neighbouring surface as revealed by the stronger red colour, which corresponds to the stain geometry. The chemical elements (other than Si) are hypothesized to come from the absorption of airborne aerosol in dew water, which are further deposited on the surface by droplets evaporation. Upon evaporation, the droplet increases its concentration in salts until crystallization occurs. Larger droplets can adsorb more aerosols due to their higher exchange surface, which explains why <d re-cond. > can be larger than <d cond > in Figure 1. In order to further characterize the "stain", a 1µL DI water (resistivity of 18.2 MΩ.cm, i.e. close to pure water) droplet was placed on a silicon wafer surface in the laboratory, left for evaporation, and then the surface was analysed by the same method using SEM and EDX. Figure S2 shows the corresponding EDX image. The same crystals and chemical elements are found as in Figure 5 with natural dew water collected outside. The same observations and conclusions can be given. It confirms the hypothesis of airborne aerosol ad/absorption independent from the condensation site, located indoor or outdoor. It is indeed known [START_REF] Beysens | Urban Dew and Rain in Paris, France: Occurrence and Physico-Chemical Characteristics[END_REF] that water condensation in open humid air involves the dissolution of aerosols and absorption of gases. In the experiments described above, the only possible sources of dissolved materials in the absence of chemical reaction with the substrate are the airborne particles and absorbed gases. The deposition of salts on the surface by the evaporation of a BF therefore explains the phenomenon of memory re-condensation as salts are known to act as a humidity sink [START_REF] Guadarrama-Cetina | Droplet Pattern and Condensation Gradient around a Humidity Sink[END_REF] and lead to a specific pattern during re-condensation. This deposition does not occurs at the centre of the evaporating droplet (Figure 3) because the evaporation process involves a random pinning of the contact line on the silicon surface defects. The centre of mass of the droplets thus move during their evaporation. The above findings suggest that memory re-condensation is a phenomenon of preferential condensation observed on any surface subjected to dropwise condensation in open air, when airborne aerosols can be adsorbed at the droplet-air interface. It is characterized by a pattern of nucleated droplets at the very place where, after a first condensation, the original droplet pattern evaporated. Each droplet leaves small salt crystals on the surface, which act as a preferential nucleation site for the next condensation. Condensation of water vapour from natural unfiltered humid air involves the absorption of gases, a fast process, and the dissolution of aerosols [START_REF] Beysens | Urban Dew and Rain in Paris, France: Occurrence and Physico-Chemical Characteristics[END_REF]22 . The absorbed gases are natural or anthropogenic, such as C02, SO2, NO and NO2. The condensing droplets, by growing and sweeping the surface by coalescences, dissolve the aerosols deposited on the substrate. They also incoporate aerosols at the liquid-air interface. These aerosols are mainly salts of sea origin (e.g. NaCl, MgCl2) or from anthropogenic sources (e.g. CaCO 3 , KCl). Other particles, such as carbon diesel particles, may also be incorporated. The chemical analysis in Figures 5 andS2 shows that the main dissolved salt is NaCl, of sea origin. Paris is indeed within 200 km from the Channel and 500 km from the Atlantic Ocean and its climate is Marine West Coast Climate according to the Köppen Classification. The stains left by evaporation of a BF are dependent on the way solubilized or particulate materials are incorporated in the droplet during condensation, and on the thermo-capillary flows and contact line de-pinning arising during droplet evaporation. This complex processes may lead to various deposition patterns [START_REF] Zang | Evaporation of a Droplet: From Physics to Applications[END_REF] , that will in turn impact the re-nucleation patterns. In the present case, dendrite stains such as seen in Figures 5 andS2 are generally observed after the evaporation of a BF condensed on Si wafers. During droplet evaporation, the concentration of dissolved salts increases until reaching the oversaturation of solute, thus leading to crystallization. This process is different from the drying of a droplet containing insoluble particles, leading to a ring deposition pattern [START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF][START_REF] Hu | Effect Reverses Coffee-Ring Depositions[END_REF] . A precise investigation of the crystallization pattern and crystal morphology is, however, out of the scope of the present paper. The chemical nature of the substrate materials will matter to determine the liquid-surface interactions and the values of the contact angles and contact angle hysteresis upon condensation and evaporation. In addition, a chemical reaction with condensed water and/or with the elements in the stain and the substrate may also occur depending on the materials used for the substrate. This reaction could permanently modify the geometrical and chemical properties of the substrate. In the present case, where the stains are mainly composed of Na, K, Cl and C and the substrate is silicon, protected by a surface layer of silicon dioxide, no permanent substrate modification are seen. As a matter of fact, stains can easily be washed away using water or compressed air. Also, one observes the loss of memory at large condensation times, when the drops nucleated on the stains have coalesced with other drops and have moved on the substrate.

Beyond the awareness and knowledge of the existence of the memory re-condensation phenomenon, the results presented here could have applicative impacts in industry and for the understanding of vegetation metabolism. Indeed, the patterning of BFs themselves can be of interest for the precise patterning of polymer films or materials to generate controlled templates by the BF method [START_REF] Muñoz-Bonilla | Towards Hierarchically Ordered Functional Porous Polymeric Surfaces Prepared by the Breath Figures Approach[END_REF][START_REF] Wan | Multiple Interfaces in Self-Assembled Breath Figures[END_REF][START_REF] Zhang | Breath Figure: A Nature-Inspired Preparation Method for Ordered Porous Films[END_REF] . Potential applications are textured surfaces [START_REF] Zhang | Transparent Self-Cleaning Lubricant-Infused Surfaces Made with Large-Area Breath Figure Patterns[END_REF][START_REF] Li | Static and Dynamic Hydrophobic Properties of Honeycomb Structured Films via Breath Figure Method[END_REF] , responsive surfaces [START_REF] De León | Immobilization of Stimuli-Responsive Nanogels onto Honeycomb Porous Surfaces and Controlled Release of Proteins[END_REF] , filtration [START_REF] Yuan | Preparation of Highly Permeable BPPO Microfiltration Membrane with Binary Porous Structures on a Colloidal Crystal Substrate by the Breath Figure Method[END_REF] or catalysis [START_REF] Wan | Patterned Biocatalytic Films via One-Step Self-Assembly[END_REF] . Patterned BFs could also find applications in patterned chemistry for biomedical applications [START_REF] Healy | Kinetics of Bone Cell Organization and Mineralization on Materials with Patterned Surface Chemistry[END_REF][START_REF] Huang | Patterned Porous Silicon Photonic Crystals with Modular Surface Chemistry for Spatial Control of Neural Stem Cell Differentiation[END_REF] , in aqueous media. For the generation of a controlled BF pattern, 0.2µL water droplets were deposited on a silicon wafer surface in the shape of a ring, then condensation was performed post complete evaporation. Figure 6 presents the original deposited "BF" and the corresponding BF of condensation post evaporation. Figure 6 exhibits an efficient controlled patterning of the condensed water droplets. Memory re-nucleation has evidenced the deposition of salts and chemical elements from natural dew water evaporation on a surface, such as Na, Cl, K and C. These elements are adsorbed from air at the air-water interface. Chemical analysis of collected dew water in Paris revealed the presence of numerous ions in its water as well [START_REF] Beysens | Urban Dew and Rain in Paris, France: Occurrence and Physico-Chemical Characteristics[END_REF] . The same phenomenon should be taking place on the leaves of plants when dew forms. Dew is known as an important resource of water for plants [START_REF] Munné-Bosch | Role of Dew on the Recovery of Water-Stressed Melissa Officinalis L. Plants[END_REF] , especially in arid climates or dry soils. It is expected from the above results that dew could also be a vector of macro-nutrients for plants nutrition. Carbon is a nutrient for plants, a major constituent of organic material, involved in enzymatic processes and assimilated by oxidation-reduction reaction [START_REF] Kirkby | Introduction, Definition and Classification of Nutrients[END_REF] . K, Na and Cl are involved in enzymatic reactions, osmotic potential, membrane permeability and electrochemical potentials [START_REF] Kirkby | Introduction, Definition and Classification of Nutrients[END_REF] . K and Cl belong to the top 10 essential elements for plants growth [START_REF] Kirkby | Introduction, Definition and Classification of Nutrients[END_REF][START_REF] Manning | Mineral Sources of Potassium for Plant Nutrition[END_REF] . Uptake of elements from leaves can take place by penetration of the external plant surface through the cuticle or stomata [START_REF] Eichert | Uptake and Release of Elements by Leaves and Other Aerial Plant Parts[END_REF] . Actually, foliar sprays are widely used in agriculture and showed better efficiency than soil fertilization as nutrients are directly delivered to sink organs [START_REF] Eichert | Uptake and Release of Elements by Leaves and Other Aerial Plant Parts[END_REF] . We hypothesize dew to possibly be an additional and unsuspected vesicle of macro-nutrients for plants.

Methods:

Condensation, DI water droplet deposal and re-nucleation under optical microscope

To generate BFs, condensation was performed for different times (100, 200 and 300s) on silicon wafers (GlobalWafers) in a home-made mini climatic chamber mounted on an optical microscope (Leica DMRXE) equipped with a camera (Imaging Source, DFK 23U445). The mini climatic chamber is composed of: A Peltier thermostat for conductive cooling, on which is placed the samples -A polystyrene cover to hermetically lock the samples with a top opening for a sealed glass slide for optical observation and two side openings for the entrance of saturated humid air -Pump (Rena 101) and tubing are used to inject air in a bath of water in order to re-inject saturated humid air to the two side openings of the sealed mini-chamber. The relative humidity in the mini chamber is 90%. The Peltier element is submitted to a current of 2V and 0.5A (generator, Sodilec SDRI 205) and a flow of cooled water at 10°C (Heto CBN 8-30 and HMT 200) in order to always set the surface temperature of the Peltier at 4°C. The deposition of desired volume of DI water (resistivity of 18.2 MΩ.cm, the value of pure water) on silicon wafer surfaces was performed with a micropipette (VWR) to study re-nucleation after single droplet and ring patterned droplets deposals. Renucleation experiments were performed post complete evaporation of the condensed or deposited droplets. Evaporation took place either outside the mini-climatic chamber in ambient conditions, or inside the mini-climatic chamber (to do not lose the precise localization of evaporating droplets) by the passive increase of the surface temperature to ambient conditions, turning off the Peltier element and opening the mini-climatic chamber. To observe the first re-condensed droplets, the surface of the sample was gently cooled down below the dew point temperature of the lab, without sealing the climatic chamber and without saturated humid air injection; to enable a slow re-nucleation for visualization purpose. Surface temperature of the Peltier is monitored along the experiments using thermocouple sensors and software Picolog. ICCapture software was used for the images sequence acquisition (1 image per second). ImageJ software was used to measure the average distance between the closest neighbour major droplets (<d>).

Characterization of the "stain"

To evaluate the robustness of the stain left by the evaporation of condensed or deposited water droplets, the following scenarios were studied post condensation (for 200s, under the experimental conditions described above) and before re-nucleation: (1) natural evaporation in ambient conditions or (2) washing under water and drying with compressed air gun or (3) drying with compressed air gun or (4) natural evaporation in ambient conditions and further drying with compressed air gun. Two types of stains were analysed under scanning electron microscopy (SEM) coupled to energy dispersive X-ray spectroscopy (EDX): (1) Stain left by natural dew evaporation on silicon wafer and (2) stain left by 1µL DI water deposal and evaporation on silicon wafer in laboratory. Natural dew was obtained in a morning of march when meteorological conditions were met to form dew, on the roof of the Institut de Physique du Globe de Paris; equipped with a weather station (temperature, relative humidity and wind force/direction sensors) (Davis). SEM and EDX were performed with a SEM Quattro (Thermofisher) under a voltage of 15 kV and intensity of 0.22 nA; the samples were placed 10 mm below the source of the electron beam. SEM was used to characterize the morphology of the stain. For EDX, X-ray emission spectra were integrated to identify and quantify (in atomic percentage) the present chemical elements on the studied surface and chemical mapping was generated to localize the detected elements.

Supporting information

-Experimental conditions to obtain memory re-condensation -Morphological and chemical analysis of the stain left by the evaporation of a DI water droplet at the origin of the phenomenon of memory re-condensation.

Figure 1 :

 1 Figure 1: Re-nucleation patterns: Microscope pictures of different BFs obtained after (a) 100, (b) 200 and (c) 300 s of water vapour first condensation. The BFs were then left for natural evaporation under ambient conditions until complete disappearance. The renucleation pattern obtained from the former BFs (a, b, c) are shown in (d, e, f) respectively. The distance <d> is the average distance between the closest neighbour major droplets. (The scale bar applies to all images).

Figure 2 :

 2 Figure 2: Experimental conditions for memory re-condensation: Optical microscope images of the re-nucleation pattern obtained on a surface after a first condensation BF (obtained after 200s of condensation) submitted to: (a) washing under water and drying with compressed air gun, (b) natural evaporation in ambient conditions, (c) drying with compressed air gun and (d) natural evaporation in ambient conditions and further drying with compressed air gun.

Figure 3 :

 3 Figure 3: Localization of re-nucleation sites: (a) Optical microscopy image of the first droplets obtained from re-nucleation. The position of the centre of each major droplet is marked by a red dot and transferred to images (b) and (c). (b) Original BF after 100 s of condensation. Evaporation starts after that time. (c) BF of (b), just before complete droplets evaporation.

Figure 4 :

 4 Figure 4: Condensation pattern on silicon wafer after the evaporation of a water droplet: (a) Optical microscopy images of the time evolution of the evaporation of 1 µL ultrapure deionized water droplet on silicon wafer evidencing the deposition of a persistent stain after complete droplet evaporation (middle of the interrupted white square). (b) BF of condensation around the stain (middle of the interrupted white square), which acts as a site of preferential condensation or humidity sink with a region of inhibited condensation.

Figure 5 :

 5 Figure 5: Origin of memory re-condensation: Scanning electron microscope (SEM) image of a typical "stain" left by the evaporation of natural dew water droplets and energy dispersive X-ray spectroscopy (EDX) mapping of the SEM image for the identification and quantification (in atomic %) of the chemical elements comprising the stain.

Figure 6 :

 6 Figure 6: Controlled re-condensation pattern: (a) Deposition of 0.2µL water droplets as a ring pattern. (b) BF of condensation post complete evaporation of droplets from a).

Acknowledgements

This project received the support from the METAWATER Project (No. ANR-20-CE08-0023 META-WATER).

Conflict of Interest

The authors declare no conflict of interest.


Joachim Trosseille
email: joachim.trosseille@espci.fr

Anne Mongruel

Laurent Royon

Daniel Beysens

Radiative cooling for dew condensation

Keywords: Dew, Condensation, Radiative cooling, Emissivity, Infrared

We describe a radiative cooling chamber which reproduces in the laboratory radiative cooling and subsequent dew formation. Based on radiative exchange with a cold source (at a temperature of nearly -80 • C), which acts as a cold black body, cooling power of at least 50 W.m -2 is achieved. Radiative exchange is quantitively estimated. This original device permits to study under controlled air temperature and humidity the formation of dew on any system (material, biological) for which contact cooling is inefficient, and in particular investigate the influence of radiative and wetting surface properties on dew yield. It is applicable to the study of dew itself and its effects on plants and small animals, as well as dew atmospheric chemistry, and more generally of any natural radiative cooling application.

Introduction

Atmospheric humidity can be condensed in the form of dew on a surface radiatively cooled below the air dew point temperature. The dew point defines the temperature at which air is saturated with water vapor, i.e water vapor contained in air is at saturation pressure. Radiative cooling of the surface is obtained overnight by a deficit between the emitted radiation from the surface and the radiation coming from the atmosphere. In the context of global warming and decrease of pure water resources, dew water can be seen as a non-conventional source of water, giving an appreciable amount of good quality water to population and animals living in places where water is lacking. Dew can have a positive role for plants, bringing nocturnal moisture, especially in arid areas or during droughts (but also a negative action, favouring the development of fungal diseases). Dew also takes part in the chemistry of atmosphere, for instance in the nitrites oxides diurnal (and nocturnal) cycle. For a general review, see [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF][START_REF] Beysens | Dew Water[END_REF].

Regarding the typical value of radiative loss for nocturnal conditions where dew forms (≈ 60 W.m -2 ), the upper thermodynamic limit of dew yield is around 0.7 litre/m 2 /night [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF][START_REF] Beysens | Dew Water[END_REF][START_REF] Monteith | Principles of Environmental Physics: Plants, Animals, and the Atmosphere[END_REF][START_REF] Nilsson | Condensation of water by radiative cooling[END_REF].

On natural surfaces, dew always occurs as dropwise condensation, following different stages from the heterogeneous nucleation of a single droplet, its growth by incorporation of water vapor molecules and its interactions with neighboring droplets by coalescences [START_REF] Beysens | Dew Water[END_REF]. Dew collection is achieved passively by gravity provided that water droplets have reached a typical size enabling them to easily slide down the surface to be collected at the surface lower edge. The quest for enhancing and controlling droplet shedding has motivated a considerable amount of experimental investigations focusing on the wetting properties of the surfaces, with the development of complex hierarchical micro-structures often inspired by natural surfaces [START_REF] Beysens | Dew Water[END_REF]. However, all these laboratory experiments are performed by conductive (contact) cooling of thin objects (sheets, plates, wafers ...). In this arrangement, the bottom surface of the object is in thermal contact with a cooling device (e.g. a Peltier stage). For given thermal losses, decreasing the temperature of the upper surface of the object below the dew point temperature is a process that is thus limited by the thermal resistance of the object (the ratio of its thickness to its surface area and thermal conductivity). In outdoor devices, the dew collector is usually isolated from below and its upper surface is cooled by radiative deficit with the atmosphere. Hence, the upper surface temperature does not depend on the thermal conductivity of the dew collector, but on its surface emissivity and on the heat exchange coefficient with the surrounding air. For such reason, radiative cooling proves more efficient for objects with high thermal resistance to heat conduction. This includes complex 3D geometries such as plant leaves, cactus spines, insect shells, spider nets, etc ... Outdoor experiments on radiative cooling surfaces for dew collection have been widely performed since the 90's [START_REF] Nilsson | Condensation of water by radiative cooling[END_REF][START_REF] Clus | Dew, fog and rain water collectors in a village of s-morocco (idouakssou)[END_REF][START_REF] Beysens | Urban dew and rain in paris, france : Occurence and physico-chemical characteristics[END_REF][START_REF] Sharan | Dew plant for bottling water[END_REF]. Here, we aim to develop their indoor counterpart, with the idea of getting rid of the outdoor disadvantages (weather variations, duration and cost of experiments). To our knowledge, indoor radiative devices have received very little attention, except more than 50 years ago and nearly exclusively from biologists. Several prototypes have been developed in order to simulate the effect of radiative dew or frost on various plants (fruits, eucalyptus leaves, strawberry leaves, potatoes ...). Pioneering works used a nitrogen atmosphere in a chamber [START_REF] Scott | Use of liquid nitrogen in a winterhardiness test chamber for fruit trees[END_REF], or boiling nitrogen pulverized on a surface [START_REF] Aston | Radiation exchange in controlling leaf temperature[END_REF][START_REF] Aston | Frost room design for radiation frost studies in eucalyptus[END_REF][START_REF] Gill | Design and Performance of a Portable Frost Chamber for the Investigation of Hardiness of Strawberries[END_REF]. Several chambers were developed thereafter on the same concept, but using refrigeration devices [START_REF] Clifford | The construction and operation of a dew-simulation chamber[END_REF]. Moreover, precautions were taken to separate the cold source from the rest of the chamber by films transparent to infrared radiation, and to prevent water condensation on those films [START_REF] Pescod | A method of forming dew on plants under controlled conditions[END_REF][START_REF] Went | The Effect of Dew on Plant Water Balance in Citrullus vulgaris and Cucumis melo[END_REF][START_REF] Marcellos | A plant freezing chamber with radiative and convective energy exchange[END_REF][START_REF] Flura | Mise au point de chambres de refroidissement pour l'étude de la gélivité des bourgeons. application au cas de la vigne[END_REF][START_REF] Fuller | A chamber for the simulation of radiation freezing of plants[END_REF]. More recently, a dew simulation chamber (Mercia Scientific, UK), based on the prototype of [START_REF] Clifford | The construction and operation of a dew-simulation chamber[END_REF] was used to quantify the amount of dew formed on artificial sea-grass [START_REF] Kotzen | Innovation and evolution of forms and materials for maximising dew collection[END_REF]. In all the above-mentioned radiative chambers, no quantitative evaluation has been carried out of their performances in terms of homogeneity and radiative cooling power. Note that an indoor device has been reported very recently in a study with radiative cooling power similar to what is found under outdoor conditions [START_REF] Zhou | A polydimethylsiloxane-coated metal structure for all-day radiative cooling[END_REF]. However this device, designed only for daytime cooling, does not provide the humid air conditions needed to generate condensation.

It is thus the aim of this article to present an original device developed to reproduce the phenomenon of radiative dew in the laboratory and to obtain quantitative data on the dynamic of the physical process. Based on radiative exchange with a cold source, cooling power of at least 50 W.m -2 is achieved in order to reproduce the main features of natural dew formation under controlled conditions. It permits to study, among other phenomena, the influence of radiative and wetting properties of surfaces on dew harvesting in a controlled humidity and temperature environment.

Materials and method

The experimental setup needs to meet some basic requirements in order to simulate natural dew. First, the condensation surface (also denoted as "dew collector") has to be exposed to an exclusively radiative thermal deficit. In addition, the condensation surface has to be surrounded by humid air with controlled temperature and relative humidity. A high content of water vapor in the air is needed to reproduce the nocturnal air conditions. Finally, in order to collect quantitative data, it is necessary to measure the temperature of air and dew collector, together with the mass of condensed water. Figure 1 shows a schematic view of the experimental setup designed to meet the above specifications.

The device consists in a cylindrical chamber (4) with 10 cm height and 8 cm internal diameter. Cooling is performed by a cold source (1) at a temperature of 194.7 K located under the setup. The dew collector (2) is placed on a sample holder (3), positioned inside the cylindrical chamber (4) and resting on a balance [START_REF] Clus | Dew, fog and rain water collectors in a village of s-morocco (idouakssou)[END_REF]. Humid air is injected from the top of the chamber, and evacuated at the bottom. The flux is measured and controlled by the flowmeter [START_REF] Aston | Frost room design for radiation frost studies in eucalyptus[END_REF]. Radiative heat exchange between the dew collector and the cold source is performed by reflection on mirrors [START_REF] Sharan | Dew plant for bottling water[END_REF]. The chamber (4) is separated from the cold source [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF] by an IR transparent double windows [START_REF] Beysens | Urban dew and rain in paris, france : Occurence and physico-chemical characteristics[END_REF]. Condensation inside the chamber is observed with optical cameras through two PMMA (plexiglas) windows ( 8) and [START_REF] Aston | Radiation exchange in controlling leaf temperature[END_REF]. Alternatively, window [START_REF] Scott | Use of liquid nitrogen in a winterhardiness test chamber for fruit trees[END_REF] on top of the chamber can be replaced by an IR temperature sensor to monitor the surface temperature of the object (2). Three thermocouples (T1, T2, T3) measure the temperature of incoming air, mirrors and double IR window, respectively,

Cold source

We use solid carbon dioxide CO 2 ("dry ice") as a cold source [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF]. Dry ice pellets are cylinders about 1 cm thick and 1 to 5 cm long, stored in a styrofoam box. The temperature of dry ice in equilibrium with its vapour at atmospheric pressure is of 194.7 K, ensuring a constant temperature of the cold source. No liquid carbon dioxide is formed during the sublimation process thereby simplifying its use. The sublimation rate is low but a refill of the vessel every hours is necessary to maintain a stabilized radiative heat flux. When exposed to room humid air, dry ice pellets are covered by a layer of frozen water forming ice crystals, which may modify the surface temperature. Despite of this layer, no significant modification of the radiative cooling power was observed.

Ice water emissivity being approximately ε g ≈ 0.98 [START_REF] Hori | In-situ measured spectral directional emissivity of snow and ice in the 8-14 µm atmospheric window[END_REF] and the presence of water crystals suggesting a diffuse emission of infrared light, the cold source can thus be considered as a black body. Finally, the density of CO 2 in its gazeous form at 194.7 K is larger than the air density, making cold CO 2 vapour flowing downward, therefore not disturbing the window (6) situated above the cold source.

Humidity control

The setup is designed to alternatively work in a "dry air" or in a "humid air" modes. The "dry air" mode actually means that air is at room relative humidity (RH), generally on order 50 % (RH is the ratio of ambient vapour pressure to the saturation pressure at ambient temperature). In this mode, the valve V 1 is in open position and let ambient air go directly to the chamber (see fig. 1). In the "humid air" mode, the valve V 1 is closed and the air passes through a bubbler at room temperature, which increases its relative humidity.

An adjustable valve V 2 situated in the flowmeter at the outlet of the pump controls the flow rate. An air flow rate value of Q =1.46 ×10 -5 m 3 .s -1 is used in all the experiments, corresponding to a mean air flow velocity around the sample holder (3) of V = Q/(S 0 -S s ) = 3.4 mm.s -1 , S 0 being the internal section of the chamber (4) and S s the section of the sample holder. The RH value inside the chamber cannot be directly measured because of possible IR exchange between the RH sensor and the cold source. Instead we use the fact that no condensation occurs on the mirrors, meaning that their temperature T 2 is larger than the dew point temperature T d corresponding to a humid air temperature of T a . From the expression of T d (RH, T a ) [START_REF] Lawrence | The relationship between relative humidity and the dewpoint temperature in moist air : a simple conversion and applications[END_REF] we get the maximum possible value of the relative humidity RH inside the chamber. Typical values of RH ≈ 95 % are obtained with T a = 298.3 K and T 2 = 297.5 K (see section 3.2). The fact that RH is close to 100 % is corroborated by the determination of the injected mass of water in air measured by weighing the bubbler during a typical experiment. This high value of relative humidity is selected in order to reduce the duration of the experiments. In fact, as can be seen in Supplementary Informations, experiments performed at a lower humidity ratio (89 %) show a lower condensation rate. Although the dew point temperature T d is close to the temperature of the air at this humidity level (T a -T d = 0.85 K) it is well known that dropwise condensation needs supersaturation to form, corresponding to at least several degrees below the dew point temperature (see e.g. [START_REF] Anand | How droplets nucleate and grow on liquids andliquid impregnated surfaces[END_REF]).

The needed temperature drop is provided to the sample (Fig. 7) through the radiative exchange with the cold source which is the only heat sink of the system.

As a matter of fact, no condensation is observed on the mirrors nor on the transparent window, a phenomenon which would have shut down the radiative transfer, whereas thermocouples measure temperature close to T d as can be seen in Fig. 7. Note that high relative humidity has usually a detrimental effect on radiative cooling, but it does not impact the radiative cooling in our system considering the small size of the device [START_REF] Minkina | Atmospheric transmission coefficient modelling in the infrared for thermovision measurements[END_REF][START_REF] Wiecek | Thermovision in infrared -basics and applications[END_REF]. In the latter references are estimated the transmission decrease in the atmospheric window; for a typical experimental path length of 20 cm (density-length product m w = 4.4 × 10 -4 g.cm -2 , see [START_REF] Bliss | Atmospheric radiation near the surface of the ground : a summary for engineers[END_REF]), it leads to an attenuation of about 4 x 10 -4 , i.e. negligible.

Radiative heat exchanges

The cold source (simulating the nocturnal sky) is situated below the dew collector. In order to perform radiative exchange above the sample, mirrors have been positioned inside the chamber and around the dew collector and its holder. Their role is to connect radiations emitted from the dew collector and the cold source. Figure 2 shows the shape of the mirrors and their dimensions.

Mirrors are composed of 1 mm thick Mylar sheet on which is stuck a laminated aluminum sheet on the inside face. The low emissivity of aluminum foil (ε alu ≈ 0.04, normal emissivity between 4.5 and 40 µm [START_REF] Gustavsen | Spectral emissivity of anodized aluminium and the thermal transmittance of aluminium window frames[END_REF]) makes the mirrors highly reflective to mid-infrared radiations.

The sample holder (3) supporting the dew collector is positioned at the center of the chamber, and thus experiences radiative heat exchanges with the cold source by its lower and side surfaces. For that reason, care must be taken to prevent it from becoming cooler than the dew collector. In that case, an undesirable conductive cooling of the dew collector by the sample holder would take place. A careful design of the sample holder is thus a key step for the control of the radiative exchanges. Figure 2 shows the sample holder and its dimensions. It is composed of a cylinder of 15 mm height and 15 mm radius made with a thermal insulating material (natural cork). On top of the holder lies a circular plate of aluminum of the same radius and of 1 mm thickness. The cork thermal conductivity measured by the hot plate method [START_REF] Salmon | Thermal conductivity of insulations using guarded hot plates, including recent developments and sources of reference materials[END_REF] is

λ c = 0.057 W.m -1 .K -1 .
The aluminum plate insures a perfectly plane top surface with a large thermal conductivity (λ a ≈ 240 W.m -1 .K -1 ) [START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF]. An additional thermal resistance between the aluminum plate and the cork participates in the insulation of the top face. Finally, the cork cylinder and the aluminum plate are folded together into an aluminum sheet of low emissivity, in order to minimize the radiative exchanges between the bottom surface of the sample holder and the cold source.

In order to validate the design of the radiative chamber, we have performed a modelling of thermal exchanges between the dew collector (2) and the rest of the chamber. The aim of the modelling is to calculate the incoming radiative heat flux on dew collector (2) and on sample holder (3), and to study the influence of radiative properties of these surfaces. The model is based on some hypothesis : i) The double window is a single transmittive interface ; ii) IR emissions are isotropic ; iii) Reflections are diffusive ; iv) Surfaces are homogeneous and isothermal grey bodies (except surface 3 whose transmitive properties are wavelength dependent) and v) Air is a totally transparent media. We recall that in a N faces enclosure, for isotropic emissions and diffuse reflections, the radiosity of face i is the radiative heat flux leaving face i and composed of the radiation emitted by the surface itself and the radiation coming from other faces and reflected by face i. Radiosity J i of face i is thus expressed as

J i = ϕ e i + ρ i N j=1 F ij J j (1)
with ρ i the reflection coefficient of surface i and F ij the view factor between i and j, that is the fraction of heat flux emitted by j and intercepted by i. ϕ e i is the heat flux density emitted and/or transmitted by surface i.

Solving equation 1 for all surfaces of the enclosure (see Appendix A for details) then lead to the expression of the incoming heat flux density as

ϕ i i = N j=1 F ij J j (2)
Of particular interest are the following expressions for the incoming heat flux density on the different faces (5 : bottom),(7 : top) and (11 : side) of the sample holder (see Appendix A. for schematic).

Table 1 shows the resulting numerical values of the incoming heat flux for the lower (5), upper [START_REF] Sharan | Dew plant for bottling water[END_REF] and lateral [START_REF] Gill | Design and Performance of a Portable Frost Chamber for the Investigation of Hardiness of Strawberries[END_REF] From the knowledge of the incoming heat flux densities the distribution of temperature in the bulk of the sample holder ( 3) is simulated to confirm that the conductive flux is directed towards its upper suface (2), i.e that this later surface is not conductively cooled. For that we solve the stationary energy equation ∆T = 0 in 2D axisymmetric coordinates as shown in Figure 3 :

ϕ i 5 (W.m -2 ) ϕ i 7 (W.m -2 ) ϕ i 11 (W.m -2 ) Case 1 (ε 5 =0.
1 r ∂ ∂r r ∂T ∂r + ∂ 2 T ∂z 2 = 0 (3)
with following boundary conditions on the three faces ( 5), ( 7) and [START_REF] Gill | Design and Performance of a Portable Frost Chamber for the Investigation of Hardiness of Strawberries[END_REF] :

-λ l ∇T = h i (T -T a ) -ε i ϕ i i + ε i σT 4 (4)
with λ l the bulk material thermal conductivity, σ the Stefan-Boltzmann constant, T the local temperature, T a the air temperature and ϕ i i the incident radiative heat flux density incoming on surface i of emissivity ε i . The convection coefficient h i applied to surface i is calculated from natural convection correlations : [START_REF] Radziemska | Heat transfer by natural convection from an isothermal downward-facing round plate in unlimited space[END_REF] and [START_REF] Churchill | Correlating equations for laminar and turbulent free convection from a vertical plate[END_REF]. Note that expression (4) is only valid in the "dry" mode. In order to take into account the latent heat of condensation, the term a w L(p v (T a ) -p s (T )) has to be added to Eq. 4, with a w the water vapor transfer coefficient, L the latent heat of condensation of water, p v (T a ) the partial pressure of water vapor at temperature T a and p s (T ) the saturation pressure of water vapor at temperature T [START_REF] Beysens | Dew Water[END_REF]. Figure 3 shows the results of the simulation with and without condensation, for air temperature T a = 298.3 K (see section 3) and with emissivity of the upper support surface varying from 0.04 to 1.

h 5 ≃ 4.4 W.m -2 .K -1 [29], h 7 ≃ 4.8 W.m -2 .K -1
h 11 ≃ 6.3 W.m -2 .K -1
From table 1 and figure 3 it can be seen that 1) condensation on the sample holder can slightly modify the incoming radiative heat flux and that 2) heat is transferred from the lower face of the sample holder to its upper face, indicating that the cooling of the upper face is only due to radiative exchanges.

IR transparent double-window

To separate the humid air from the cold source, an IR transparent doublewindow [START_REF] Beysens | Urban dew and rain in paris, france : Occurence and physico-chemical characteristics[END_REF] in Fig. 1 is used to close the chamber while permitting a radiative heat transfer with the cold source. The double-window is composed of two parallel polypropylene films of 15 µm thickness and 8 cm diameter, and separated from each other by 13 mm. The upper film closes the chamber. The films are not perfectly transparent to infrared radiations and are also radiatively cooled by the cold source, which can lead to some condensation on the upper film inside the chamber. Water being opaque to IR light, it decreases the transmission coefficient of the film and hinders radiative exchange. To avoid such a condensation, a second film is placed below the first film and an air stream (from the room) is blown in the gap between films to warm up the upper film.

The radiative properties of the polypropylene films are measured in the wavelength range [2.5 -25] µm by infrared spectroscopy in the direction normal to the film. The radiative properties of the double window composed of the two films are calculated from the properties of each single film and the analysis of the reflections between the two films [START_REF] Huetz-Aubert | Rayonnement thermique des matériaux semi-transparents[END_REF]. Figure 4 shows the spectral transmission coefficient of single and double films. Considering an incident flux corresponding to a black body at T ≃ 195 K (i.e. the temperature of the cold source), the integration of the transmission coefficient in the range [2.5 -25] µm gives τ = 0.92 for a single film and τ = 0.86 for the double-window.

Measurements

Visualization of the condensation process is performed by two cameras (DFK 23U445 from TheImagingSource), at 30 fps and with a 1280×960 px CCD sensor.

With camera Cam1, the condensation rate on the upper surface of the sample is determined by a visual method described in [START_REF] Trosseille | Roughnessenhanced collection of condensed droplets[END_REF]. The method is based on the recognition of the contour of each individual droplets, giving access to their radius. Knowing the droplets contact angle on the surface, the volume of each droplet is calculated, and hence the total volume of condensed water on the surface is obtained as a function of time.

The sample holder is resting, with the help of an arm, on a balance [START_REF] Clus | Dew, fog and rain water collectors in a village of s-morocco (idouakssou)[END_REF] positioned outside the chamber. The balance (Sartorius ENTRIS, interfaced with MATLAB) thus measures the total mass of water condensed on the sample holder with a precision of ± 1 mg and 1 measurement per second. Note that condensation occurs not only on the sample surface ( 2), but also on the lateral surface of the sample holder.

An IR thermometer can be introduced inside the chamber replacing window (8) by a supporting device. The IR thermometer is a Omega OS-Mini 802 sensor with variable emissivity. It has a precision of ±1 K, a repeatability of ±0.5 K and works in the range [START_REF] Scott | Use of liquid nitrogen in a winterhardiness test chamber for fruit trees[END_REF][START_REF] Aston | Radiation exchange in controlling leaf temperature[END_REF][START_REF] Aston | Frost room design for radiation frost studies in eucalyptus[END_REF][START_REF] Gill | Design and Performance of a Portable Frost Chamber for the Investigation of Hardiness of Strawberries[END_REF][START_REF] Clifford | The construction and operation of a dew-simulation chamber[END_REF][START_REF] Pescod | A method of forming dew on plants under controlled conditions[END_REF][START_REF] Went | The Effect of Dew on Plant Water Balance in Citrullus vulgaris and Cucumis melo[END_REF] µm. Thermocouples are located at the entrance of the chamber (T1), on mirrors (T2) and on the IR transparent window (T3). They are K-type with a precision of 20 mK and are connected to an acquisition device giving one measurement per second. The use of thermocouples to measure air temperature has to be avoided because the thermocouple can be affected by radiative exchanges. Air temperature inside the chamber is calculated as the mean between inlet air temperature (T1) and mirrors temperature (T2) as

T air = (T 1 + T 2)/2, giving typically T 1 -T 2 ≈ 2 K.
The incoming radiative heat flux density on the upper surface of dew collector (2) is measured using a sensor (Captec) giving a voltage U s as a function of the net radiative heat flux density exchanged between the sensor and the environment. Its sensitivity is K = 0.517 µV.W -1 .m -2 . An integrated thermocouple gives the temperature of the sensor, T s . Knowing U s , K and T s , and considering the sensor as a black body (constructor specification), the value of the incident radiative heat flux density is obtained from

ϕ i = U s K + σT 4 s ( 5
)
where σ is the Stefan-Bolztmann constant.

Experimental procedure. To ensure the reproductibility of the results, it is important to go through the following steps. The room thermal stability has to be close to ±0.1 K. When the room temperature and relative humidity are stabilized, dry ice is inserted in the device, and air stream is sent between the two polypropylene films. The air pump is switched on in "dry air" mode and the flow rate is adjusted to the value 1.46 ×10 -5 m 3 .s -1 with valve V2. The sample surface and sample holder, cleaned with ethanol before use, are inserted in the chamber. Once the thermal equilibrium is reached, the dry ice reservoir is refilled every hour to compensate the volume reduction due to sublimation.

Data collection begins at the time t = 0 s defined when switching the air circuit to "humid air" mode. It is necessary to readjust the flow rate with V2 as it slightly decreases when passing through the bubbler. Experiment usually ends after ≈ 10000 s but can be extended if needed.

Experimental results

Radiative versus conductive cooling

This section presents a qualitative experiment which demonstrates the ability of the radiative cooling chamber to achieve water condensation on objects of high thermal resistance. We use as dew collector (2) a small block of PMMA of 10 × 13 × 8 mm 3 with thermal conductivity λ pmma = 0.19 W.m -1 .K -1 [START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF] and mid-IR emissivity ε pmma > 0.95 [START_REF] Linteris | Absorption and reflection of infrared radiation by polymers in fire-like environments[END_REF]. The block of PMMA is stuck with thermal grease on the sample holder (3) to insure thermal contact. The temperature of the inlet air is T 1 = 295 K and its relative humidity RH = 95 %.

In a first experiment, the cold source (1) of the device is used to radiatively cool the piece of PMMA. Figure 5a shows the distribution of condensed droplets on PMMA surface. Droplets are uniformly distributed all over the surface, excepted at the base where no condensation occurs, and at the vertical and upper edges where droplets grow faster than in the middle. Note that one has to be careful when relating the size distribution of the droplets to the temperature field, as a complex interplay with edge effects occurs. Edge effect are present at the periphery (resp. at the base) of the block where the drops capture more (resp. less) moisture than in the middle of the surface [START_REF] Medici | Edge effects on water droplet condensation[END_REF]. However, in the center of the block, far from the edges, one can determine isolines of drops of the same size, as represented by white lines in figure 5a. The stationary 3D heat equation was solved in the block to obtain a qualitative appreciation of the

λ l =λ pmma , h 3 =5.9 W.m -2 .K -1 , ε i =ε pmma , ϕ i =355 W.m -2 )
and for the vertical faces of the block (face 2 in the insert :

λ l =λ pmma , h 2 =6.4 W.m -2 .K -1 , ε i =ε pmma , ϕ i =355 W.m -2
). The value of ϕ i is calculated from equation A.3b. A positive conductive heat flux of 15 W.m -2 was used as boundary condition for the bottom face of the block (face 1 in the insert), in order to get the temperature T b =289.8 K. From the comparison of isolines in drop size and in temperature we see that there is a gradient in drop size in the center of the block which has the same shape and direction than the simulated thermal gradient. We can infer from these observations that the surface, when cooled by radiation deficit, exhibits higher condensation yield towards the top of the block (and near boundaries thanks to the addition of edge effects).

In a second experiment, the cold source ( 1) is removed and the bottom face of the sample holder ( 3) is in contact with a Peltier cooling stage, whose temperature is homogenized by a thick electrolytic copper plate (env. 5 mm).

The power of the Peltier is adjusted such as the temperature of the top face of the holder surface is the same as in the first experiment, i.e. T b = 289.8 K.

Figure 5b shows that the distribution of condensed drops on the PMMA surface is very different from the first experiment. In this case of conductive cooling, were used for the boundary conditions of the horizontal top face 3 resp. vertical faces 2 of the block. The comparison of the isolines confirms that the block is cooled by conduction. Moreover it shows that a thermal gradient is created from the base to the top of the PMMA block such as its upper edge, acting as a thermal fin, is heated by air convection and is not sufficiently cold to insure droplet condensation. Note that the isotherm corresponding to the condensation limit does not equal the dew point temperature of T d = 294.2 K, consequently with the supersaturation associated with heterogeneous nucleation.

To further illustrate the potentialities of the device for cooling complex 3D surfaces, Figures 5c and5d show that condensation successfully proceeds on dew collectors (2) of complicated 3D shapes, such as a cactus spine and a spider.

For these structures, cooling by thermal contact is inefficient. As an example, a simplified calculation of the temperature distribution in an infinite circular thermal fin of radius r f = 100 µm with thermal conductivity

λ f ≈ 0.2 W.m -1 .K -1
(wood conductivity [START_REF] Suleiman | Thermal conductivity and diffusivity of wood[END_REF]) can be made. With a base temperature T 0 = 22 • C in a surrounding air at T a = 25.1 • C (temperatures for a classical experiment, see sec. 3.2.2), the convection coefficient for free convection around the fin is esti-

mated to be h f ≈ 500 W.m -2 .K -1 [37]. The temperature distribution T = f (x)
along the fin can be expressed as θ(x)/θ 0 = exp(-mx) with θ(x) = T (x) -T a , θ 0 = T 0 -T a and m 2 = 2h f /λ f r f [START_REF] Bergman | Fundamentals of Heat and Mass Transfer[END_REF]. Condensation conditions are met in the fin while T (x) < T d , or x < x d . Solving the previous equation then lead to x d ≈ 0.15 mm. This calculation shows that thermal conditions needed for condensation wouldn't be met in the cactus spine if just cooled by conduction.

Further investigations on the thermal aspects of radiative condensation on cactus spines would nevertheless be interesting. Finally for the spider example, the fact that bigger drops are situated on top of it suggests, as well as figure 5.a, that a thermal gradient is present from the top to the bottom of the spider, inconsistent with conductive cooling. During the condensation experiment, room air is maintained at temperature T ext = 299.2 K and relative humidity RH = 45 %. Figure 6 shows that the temperature of incoming air, mirrors and IR transparent double-window are stable during the experiments, except for small oscillations due to the control of ambient room temperature. Under these conditions, air inside the chamber is at the temperature T air = (T 1 + T 2 )/2 = 298.3 K and relative humidity RH = 95 %.

Radiative cooling of model surfaces

Radiative deficit

The incident radiative heat flux density onto the composite surface C1 is measured with a flux sensor placed on the composite surface C1, measuring a voltage that is converted into a heat flux through Eq.5. Figure 7 shows the values of temperatures measured by thermocouples T 1 , T 2 and T 3 as well as the temperature of the flux sensor T s , just after the latter is inserted into the device.

The evolution of the measured voltage U s is also plotted.

In the steady state without condensation, this flux has value ϕ i C1 = 368.3 ± 0.3 W.m -2 . It is interesting to note that this experimental value compares well with the corresponding value obtained by the numerical modelling of the thermal exchanges (see ϕ i 7 in case 1 of table 1), as well as the temperature of the sensor positioned on the top surface [START_REF] Sharan | Dew plant for bottling water[END_REF] of the sample holder which corroborates the temperature found by numerical simulation (see figure 3). These measurements thus validate the fact that the cooling of the upper surface of the sample holder, and by extension the sample itself, is only radiative.

The radiative deficit applied to the surface of the C1 composite can be written as

ϕ rad = ε C1 ϕ i C1 -ε C1 σ(T 0 c ) 4 (6)
T 0 c is the temperature of the C1 surface in steady state without condensation (for t < 0s in the experiment). With T 0 c = 22 • C (from figure 8) and ε C1 = 0.96, one get ϕ rad = -59.5 W.m -2 . This radiative deficit is close to the natural radiative deficit from atmosphere under conditions of dew formation, which ranges from ∼ 60 W.m -2 to 100 W.m -2 [START_REF] Beysens | Dew Water[END_REF][START_REF] Zhao | Radiative sky cooling : Fundamental principles, materials and applications[END_REF]. It is also comparable to the cooling power of other dew chambers where values of -71.9 W.m -2 [10] and -67.7 W.m -2 [START_REF] Went | The Effect of Dew on Plant Water Balance in Citrullus vulgaris and Cucumis melo[END_REF] have been reported. visual method (see section 2.5 and [START_REF] Trosseille | Roughnessenhanced collection of condensed droplets[END_REF]). Figure 9 shows the growth dynamics of droplets on the C1 surface. The evolution is linear, with a steady condensation rate ṁ = 1.0 × 10 -5 g.s -1 .

Condensation rate

The evolution of mass as indicated by the balance during the experiment is depicted in Figure 8 as Curve C. The evolution of weighed mass is concerned with the total mass condensed on the whole surface exposed to condensation, i.e. not only the C1 surface but also the lateral and bottom surfaces of the sample holder [START_REF] Monteith | Principles of Environmental Physics: Plants, Animals, and the Atmosphere[END_REF]. The weighed mass increases non-linearly until time t d ≈ 2500 s, after which the condensation rate reaches a steady state, yielding a constant rate 3) the delayed condensation on the lateral surface of (3), due to its lower emissivity and hence higher temperature, as compared to the C1 surface. Note that the IR measurement of the surface temperature and the droplets visualization cannot be simultaneously performed, thus two condensation experiments had to be carried out to obtain figure 8, the reproductibility being ensured by the monitoring of temperatures in the radiative chamber and in the room. However, a slight difference in the weighed mass is observed, due to the presence of the camera or the IR thermocouple, which have a small but noticeable impact on the thermal conditions of the device. The mean of the two experiments is thus plotted with the associated uncertainty as represented by the grey zone.

The insert in Figure 8 presents the evolution of the condensed-water volume per unit surface (in mm or L.m -2 ) as obtained by dividing the condensed mass by the density of water ( ∼ = 1000 kg.m -3 at 295.6 K) and by the area of the surface exposed to condensation. The data of curve B are concerned with the C1 top surface of sample holder (3), of area 707 mm 2 . We thus obtain curve B' with a constant rate ḣ = 1.4 ×10 -5 mm.s -1 . For the data of curve C, the condensation occurs on top, bottom and lateral surfaces of the sample holder (3), corresponding to a total area of 4×707 mm 2 . We thus obtain curve C', which is situated below curve B' at any given time. After 2500 s, curve C' becomes almost parallel to curve B', with a steady condensation rate characterized by a constant slope Ḣ = 1.6 × 10 -5 mm.s -1 , close to ḣ. Note that during a 10 hours experiment, a total condensed-water volume of v ∼ = 0.5 L.m -2 would be obtained. As a comparison outdoor dew yield (for one night) is reported to range from 0.12 L.m -2 [START_REF] Beysens | Application of passive radiative cooling for dew condensation[END_REF] in Ajaccio (France) to 0.6 L.m -2 [START_REF] Sharan | Dew plant for bottling water[END_REF] in Kothara (India). Our experiment thus produces an amount of dew comparable to natural dew condensation. To our knowledge the only quantitative study in terms of condensation rate in indoor experiments were performed by Went in 1978 [START_REF] Went | The Effect of Dew on Plant Water Balance in Citrullus vulgaris and Cucumis melo[END_REF] on watermelon leaves. Went found an artificial dew yield of about 2.6 × 10 -6 mm.s -1 , corresponding to 0.11 L.m -2 for a 12h night duration.

When comparing the curves B' and C', it has to be stressed that despite the fact that they are concerned with surfaces of different emissivities, the condensation rate obtained in steady state is nearly the same. This suggests that the emissivity of the surface has a strong influence on the onset of condensation and on the transient regime, but its influence reduces as more and more water droplets of high emissivity cover the surface.

The effect of the surface emissivity on the condensation rate can be further studied using composites C1, C2 and C3 as dew collector (2). C2 and C3 surfaces have the same contact angle with water, but quite different emissivities (0.88 and 0.05 respectively). The evolution of the mass of water weighed by the balance during a condensation experiment is shown in Figure 10.

The evolution curves exhibit a transient non-linear evolution followed by a linear evolution. The transient regime is longer for the low emissivity C3 surface (lag time of t 0 3 ∼ = 2200 s) than for the high emissivity C1 and C2 surfaces (t 0 1 ∼ = 1100 s and t 0 2 ∼ = 1600 s). In the linear (steady state) regime, the curves are nearly parallel, with similar rates of condensation Ṁ1 = 4.55×10 -5 g.s -1 , Ṁ2 = 3.95 × 10 -5 g.s -1 and Ṁ3 = 4.13 × 10 -5 g.s -1 , respectively. A first conclusion to be drawn from these experiments is that the difference in emissivity leads to a significant difference in accumulated dew yield at a given time (see Figure 10).

A second conclusion is that the limiting effect of a low emissivity of the surface disappears progressively as condensation proceeds and water droplets of high emissivity (≃ 0.95 [START_REF] Downing | Optical constants of water in the infrared[END_REF]) are covering the surface. For high values of substrate emissivity the condensation rate seems to be independent of the contact angle of water on the substrate. Further experiments need to be performed on low emissive substrates in order to probe the influence of the contact angle, which determines the surface coverage of water [START_REF] Zhao | From Droplet Growth to Film Growth on a Heterogeneous Surface: Condensation Associated with a Wettability Gradient[END_REF] and thus the effective emissivity of a condensing surface.

Conclusion

We have shown that quantitative data of water condensation (dew) can be obtained in the laboratory by radiative cooling of surfaces. The device developed in this study provides radiative deficit and condensation rates comparable to those observed for natural (outdoor) dew. The device is thus applicable to the quantitative study of dew itself and its effects on plants and small animals, density emitted and/or transmitted by surface i and calculated as

ϕ e i = ε i M • (T i ) + τ i ϕ i i (A.1)
with ε i the emissivity of surface i, τ i the transmission coefficient of surface i, ϕ i i the heat flux density incident to surface i and coming from an adjacent enclosure, M • (T i ) the black body emittance at temperature T i . The incoming table 1 for different sets of emissivities.

10 Figure 1 :

 101 Figure 1: Schematics of the experimental setup (not at scale). 1: Cold source ; 2: Dew collector ; 3: Sample holder ; 4: Cylindrical chamber ; 5: Balance ; 6: IR transparent window ; 7: Mirrors ; 8 and 9: Visualization windows ; 10: Flowmeter ; arrows: Direction of air flow. Interrupted line: Axis of revolution.

Figure 2 :

 2 Figure 2: Top : Schematics of the mirrors (7), the colored zones corresponds to the openings to the outside. The interrupted line shows the axis of revolution. Bottom : Schematics of the sample holder (3). The interrupted line shows the axis of revolution.

  faces of the sample holder for three different configurations. Case 1 (ε 5 = 0.04, ε 7 = 0.95, ε 11 = 0.04) corresponds to a highly emissive sample collector. Case 2 (ε 5 = 0.04, ε 7 = 0.04, ε 11 = 0.04) corresponds to a low emissive sample collector. Case 3 (ε 5 = 0.04, ε 7 = 0.95, ε 11 = 0.95) corresponds to the upper and side faces of the sample holder wetted by condensed water, their emissivity being modified by the presence of drops.

Figure 3 :Figure 4 :

 34 Figure 3: Numerical simulation of temperature distribution inside the support. Temperature scale is in K. A: Case 2, ε 5 = 0.04, ε 7 = 0.04, ε 11 = 0.04 ; B: Same as case 1 but with sample of lower emissivity, ε 5 = 0.04, ε 7 = 0.7, ε 11 = 0.04 ; C: Same as case 1 but with sample of higher emissivity, ε 5 = 0.04, ε 7 = 1, ε 11 = 0.04 ; D: Case 3, ε 5 = 0.04, ε 7 = 0.95, ε 11 = 0.95 (condensation). Ta = 298.3 K. Side view of the sample support. h j : Convection coefficient applied to face j ; ϕ i j : Incident radiative heat flux density to face j ; ϕ e j : Radiative heat flux density emitted by the surface j. λc : Cork conductivity.

Figure 5 :

 5 Figure 5: Top : PMMA block (10 × 13 × 8 mm 3 ) cooled by radiation (a) and conduction (b) from its base (temperature T b ), t=5830 s after the begining of condensation with chamber conditions : T 1 = 295 K , RH=95 %, T b = 289.8 K. Bottom : condensation obtained by radiative cooling on cactus spines (c) and a spider (d). Inserts in a) and b) : simulated temperature distribution (see text for simulation details)

  the thermal conditions necessary to condensation are met only in the middle part of the PMMA surface, where droplets are larger than droplets situated at the edges of the block. Indeed, condensation at the base is prevented in the same way as with radiative cooling. However, no condensation occurs at the upper edge of the block and on lateral edges. As well as for the first experiment, the heat equation were solved inside the PMMA block. The result is plotted in the insert of figure5b. A conductive heat flux of -110 W.m -2 were used as boundary condition of the bottom face of the block (face 1 in the insert), consequently with a base temperature of T b =289.8 K. A convective heat flux with coefficient of respectively h 3 =5.9 W.m -2 .K -1 and h 2 =6.4 W.m -2 .K -1

  This section presents quantitative results for radiative condensation obtained on planar model surfaces. The condensation surface (2) is a circular thin sheet of 30 mm diameter made of a composite material specially designed to control the emissivity and contact angle with water. Three composites of different emissivity and water contact angle were designed. Composite 1 (C1) is composed of a foil of laminated aluminum, and two foils of poly-vinyl chloride (PVC) of 250 µm and 140 µm thickness on top of it, leading to an overall emissivity ε C1 = 0.96, and a contact angle with water θ C1 = 84.6 • ± 3.6 • . Composite 2 (C2) is composed of a foil of laminated aluminum, a foil of PVC of 250 µm thickness and a foil of Polyethylene of 6 µm thickness on top of it, leading to an emissivity ε C2 = 0.88. Composite 3 (C3) is composed of a foil of laminated aluminum, and a foil of Polyethylene (PE) of 6 µm thickness on top of it, leading to an emissivity ε C3 = 0.05. The contact angle with water of C2 and C3 is the same, θ C2 = θ C3 = 65.9 • ± 3.6 • . The values of the emissivity have been obtained from the comparison between the luminance of the composite, measured by an IR camera (FLIR), and the luminance of a material of known emissivity (PVC, ε = 0.96) at the same temperature. The measured emissivities are total emissivities integrated over the spectral range [7.5 -14] µm, corresponding to the range of the IR camera, and in the direction normal to the surface.

Figure 6 :

 6 Figure 6: Temperature evolution of incoming air (T 1 ), mirrors (T 2 ), and IR transparent window (T 3 ) during a condensation experiment. See Figure 1 for location of the thermocouples.

1 Figure 7 :

 17 Figure 7: Temperatures of T 1 : incoming air, T 2 : mirrors, T 3 :IR transparent window and Ts : sensor, during a radiative heat flux measurement. Us : voltage measured by the radiative heat flux sensor.

Figure 8

 8 Figure 8 presents data collected during a condensation experiment using the composite C1 as dew collector (2). Curve A depicts the temperature T s of an IR thermocouple sensor focused on the C1 surface, showing two regimes. A first regime occurs between t 0 and t c , where the temperature of the sensor increases rapidly from T 0 c = 22 • C at the begining of the experiment, without condensation, and a second regime after time t c where temperature progressively decreases until a constant value T ∞ c = 22.4 • C, indicating the steady state of condensation. Curve B depicts the evolution of the water-condensed mass on the C1 surface, as measured by the

Figure 8 :

 8 Figure 8: Experiments with Composite 1 (C1) with Ta = 25.1 • C (298.3 K) and RH = 95 %. Curve A: Temperature T S of an IR thermocouple sensor focused on the C1 surface : T 0 c = 22 • C at the beginning of the experiment, without condensation, T ∞ c = 22.4 • C in steady state of condensation. Curve B: Mass of droplets condensed on the C1 surface with a condensation rate ṁ = 1 × 10 -5 g.s -1 , measured with the visualization method. Curve C : Mass of droplets condensed on the surface {C1 + lateral surface+ bottom surface} with a condensation rate Ṁ = 4.55 × 10 -5 g.s -1 measured with the balance. The grey zone around C represents the uncertainty due to the presence of the camera or IR thermocouple (see text). Curves B' and C' : same as B and C but the condensed mass has been converted in volume per unit surface, yielding ḣ = 1.4 × 10 -5 mm.s -1 (C1) and Ḣ = 1.6 × 10 -5 mm.s -1 (C1 + lateral and bottom surface). t 0 , tc, t d : times related to condensation regimes (see text).

Figure 9 :

 9 Figure 9: Visualization of the evolution of condensation obtained by radiative cooling on the surface C1 with Ta = 298.3 K and RH = 95 %. Size of the pictures : 6.1 x 4.6 mm 2 .

Figure 10 :

 10 Figure 10: Evolution of the mass weighed by the balance during the condensation obtained by radiative cooling of surfaces (2) of different emissivities and contact angle : Surface C1 (ε C1 = 0.96, θ C1 =84.6 • ), Surface C2 (ε C2 = 0.88, θ C2 =65.9 • ), Surface C3 (ε C3 = 0.05, θ C3 =65.9 • ). Chamber conditions are Ta =298.3 K and RH = 95 %.

Figure A. 11 :

 11 Figure A.11: Different parts involved in the radiative heat transfer (schematics). 1: Cold source ; 2: External environment ; 3: Double window ; 4: Mirrors ; 5: Lower face of the support ; 6: Virtual boundary ; 7: Upper face of the support ; 8: Mirrors ; 9: External environment ; 10: Mirrors ; 11: Lateral face of the support ; 12: Mirrors ; 13: Virtual boundary.

Table 1 :

 1 Incoming radiative flux densities on the three faces of the sample holder : (5) Lower

	04, ε 7 =0.95, ε 11 =0.04)	316.4	365.1	347.2
	Case 2 (ε 5 =0.04, ε 7 =0.04, ε 11 =0.04)	314.9	350.8	339.1
	Case 3 (ε 5 =0.04, ε 7 =0.95, ε 11 =0.95)	319.2	377.3	362.0

face ;

[START_REF] Sharan | Dew plant for bottling water[END_REF]

Upper face ;

[START_REF] Gill | Design and Performance of a Portable Frost Chamber for the Investigation of Hardiness of Strawberries[END_REF]

lateral face, for different values of the faces emissivities.

Acknowledgements

We thank the Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie de Sorbonne Université (UMR 7590-Sorbonne Université-CNRS-MNHN/IRD) for the spectroscopy measurements. This work was support by a PhD grant from the French Ministère de l'Enseignement Supérieur et de la Recherche.

as well as dew atmospheric chemistry, and more generally of any natural radiative cooling applications. Of particular interest is its ability to radiatively cool surfaces of various complicated shapes, for which contact cooling is inefficient.

Moreover, systematic studies concerning surfaces with different radiative and wetting properties can be carried out, helping to design optimal surfaces before field tests. The limitations of the device are, firstly, its relatively small size, which can nevertheless be easily improved by rescaling the setup. Secondly, the weighing system, which is inherently exposed to the cold source radiations, also collects dew water during experiment and imposes comparative studies.

Finally, the angular distribution of the incoming radiation on the sample is different from the atmosphere distribution. A larger device could be useful to control the angular distribution. Also, further experiments with a fine control of humidity would allow to explicitly link the condensation rate and the supersaturation inside the device. The results obtained with surfaces of contrasted emissivities raise an interesting question, that is to quantify the evolution of the effective emissivity of a surface during condensation, with water droplets of high emissivity progressively covering the underlying surface.

Appendix A. Radiative heat flux

In order to validate the design of the radiative chamber, we have performed a modelling of thermal exchanges between the dew collector (2) and the rest of the chamber. The aim of the modelling is to calculate the incoming radiative heat flux on dew collector (2) and on sample holder heat flux density ϕ i i on surface i is calculated as

Finally, a system of N equations is obtained which is solved knowing the radiative properties and temperatures of each surface. Of particular interest are the following expressions for the incoming heat flux density on the different faces ( 5),( 7) and ( 11) of the sample holder :