D Beysens

BROWNIAN MOTION IN STRONGLY FLUCTUATING LIQUID

In this paper is reported how the Brownian motion of colloids (beads) immersed in a liquid can be affected by the local properties of the fluid and how, in turn, it can alter them. Near-critical binary mixtures are known to exhibit important concentration fluctuations when nearing their liquid-liquid critical point (CP). Photon-beating spectroscopy measurements show that colloids immersed in such a critical mixture of isobutyric acid and water exhibit a slow-down of their Brownian motion due to the fluctuation-induced critical enhancement of viscosity. However, as the mixture temperature is brought close to the CP temperature, the fluctuations lifetime becomes large enough such that the fluctuations can be in turn strongly deformed by the shear flow around the colloids. Mean-field behavior, where the influence of fluctuations can be ignored, follows. Viscosity does not increase anymore and colloids motion ceases to slow down.

Introduction

Brownian motion of small particles (colloids) immersed in a liquid has been studied for more than a century since the works of Einstein and Perrin i, ii . Recently, the use of modern techniques (fast videos, optical tweezers) with high spatial and temporal resolution has given rise to the precise determination of instantaneous velocity iii-v . For the latter, the hydrodynamic coupling between the colloid and the fluid has been seen to dominate the dynamics of velocity fluctuations. In particular, the equipartition theorem is verified only if one considers the "added mass" of fluid accounting for the inertia of the displaced fluid in the colloid motion vi .

Local hydrodynamics around the colloids can thus affect their Brownian motion. Hydrodynamic coupling is enhanced when nearing a critical point where the local fluctuations of the order parameter (concentration fluctuations in a liquid mixture near its miscibility critical point) affect the fluid resistance to flow, resulting in viscosity enhancement vii . When a colloid is immersed in a binary liquid near its liquid-liquid critical point, its Brownian motion can therefore be seriously affected by the fluctuation-induced enhancement of viscosity. However, the shear flow around the colloid can in turn reduce the local concentration fluctuations, resulting in saturation of the friction (see below section 2.2). This complex hydrodynamic process disturbs the Brownian motion of colloids as shown by the result of photon beating light scattering experiments performed in the mixture of isobutyric acid and water above its critical point -where it is homogeneous. This paper is organized as follows. Firstly, the bases of critical point phenomena, shear flow effects and photon beating technique are exposed. Secondly the experimental methods are described and then the results are exposed and discussed.

Theoretical background

Miscibility critical point in binary mixtures

The vicinity of second-order phase transition (critical point) exhibit a number of universal, scaled behavior viii, ix . Fluids near their liquid-vapor critical point and partially miscible binary mixtures near their liquid-liquid critical point (the upper point in the temperature-density or concentration phase diagram) exhibit the same features as they belong to the same universality class. The class representative is the magnetic Ising model with magnetization M as the order parameter. In binary fluids, M is the concentration difference c-c c , with c the concentration of one of the components and c c the critical concentration. This class is characterized by the dimensionalities of space D=3 and dimensionality of order parameter, d=1. An important aspect of the critical region is that most of the anomalies of the thermodynamic and transport properties can be set in the form of scaled, universal power laws with respect to the critical point coordinates. For instance, the correlation length of concentration fluctuations, , asymptotically diverges with the reduced temperature (here T is absolute temperature and T c the critical temperature) along the c=c c thermodynamic path, as [1] Here is a universal exponent and is a system-dependent critical amplitude. The value of critical exponents depends on D. Above an upper space critical dimensionality D c =4, the effect of fluctuations on divergence can be neglected, mean field approach is relevant and =0.5. For the class of fluids where the space dimensionality D=3<D c , fluctuations have to be accounted for, which renormalizes the exponent value to =0.630 viii,ix .

The lifetime of concentration fluctuation corresponds to the diffusion of a component on lengthscale . The fluctuation indeed vanishes by a diffusion process, with a diffusion coefficient D  which can be related to the Brownian diffusion of a cluster of size ξ vii . With k B the Boltzmann constant and  the liquid mixture shear viscosity, the diffusion constant then reads as [2] Diffusion on length occurs on time such as [3] Shear viscosity, defined as the ratio of the shear stress to an infinitesimally small velocity gradient or shear flow S, the so-called Newton's law for fluids, is also affected by the coupling with critical fluctuation vii . Viscosity exhibits a (weak) divergence such as [4] Here the critical exponent is Y=0.04 and is a thermally activated regular (background) contribution of Arrhenius form. With E the activation energy and the amplitude: It means that the fluctuation lifetime is large enough to "feel" the shear. The above condition Eq. 6, when considering the fluctuation lifetime expression Eq. 3, corresponds to having a cross-over correlation length, , above which fluctuations become strongly deformed by shear:

[7]

When nearing a critical point on the thermodynamic path c=c c by changing temperature, the well-known "critical slowing down" where increases, ensures that the condition Eq. 6 will be eventually fulfilled. From Eq. 3 derives a condition on temperature, separating two regions of low and strong shear on both sides of where

[8]

The reduction of fluctuations in the strong shear region is such that mean-field behavior, where fluctuations can be ignored, becomes relevant very near the CP vii,x . In other words, the upper critical dimensionality is lowered (to D c = 2.4 vii ), below the space dimensionality D=3. As a matter of fact, viscosity in the mean-field approximation does not show any more a divergence and levels off vii,xi .

Colloid Brownian motion and shear flow

The mean value of the colloid velocity can be inferred from the equipartion theorem to be, for each Cartesian component of velocity:

[9]

In a liquid, the inertial mass of an object has to be modified by the inertia of the displaced fluid vi , (the so-called added mass m a ) which is half of the mass of the displaced fluid vi . For a sphere of radius a immersed in a fluid with density  f , ,

. The sphere mass being , with sphere density  s , the effective mass m * reads as

[10]

When dealing with spherical colloids in Brownian motion, the Reynolds number is generally very low (see below Eq. 18 and its evaluation), indicating that the flow is dominated by viscous effects around the sphere. Stokes damping can thus be successfully assumed.

Hydrodynamics can be considered as stationary as it corresponds to a diffusive behavior over times longer than the viscous time 2.6 ns for the colloids used here (see Table 1 for the numerical values). This time is much shorter than the binary liquid fluctuation time >50 ns (values from Table 1) in the studied temperature range.

The stationary velocity field around a sphere with velocity V at small Reynolds number is axisymmetric and is well-known xii . In polar coordinates (r, ), the components of fluid velocity, along r, and , perpendicular to r, are [11] and [12] The shear rate along r can be deduced by derivating Eq. 11 with respect to r for r/a>1. The maximum shear flows S corresponds to at =at , . The macimum shear rate perpendicular to r correponds to at = and , . One will thus consider in the following the mean value .

[13]

With the numerical values of Table 1, one finds V=<V>=3.510 -2 ms -1 , giving S=4.410 5 s -1 .

Light scattering (photon beating spectroscopy)

Colloids immersed in a liquid lead to concentration fluctuations and thus to refractive index fluctuations, which scatter light. The dynamics of these fluctuations is driven by the diffusion of colloids and can be analyzed by recording the frequency spectrum of the scattered light (Figure 1) or equivalently its autocorrelation function. In the photon beating homodyne arrangement used here the scattered light interferes with itself and the autocorrelation function is a decaying exponential function with typical time  0 such as xiii [14] Here D is the colloid diffusion coefficient

[15] and [16] is the transfer wavevector corresponding to the scattering angle (see Figure 1). The incident light wavevector K 0 reads, with n the liquid refractive index and  0 the wavelength of incident light:

[17]

Experiments and methods

The colloids considered here are latex beads from Dow Chemicals whose characteristics are listed in Table 1. The latex bead suspensions are composed mainly of polymer particles and water, with small amounts of surfactant, sodium bicarbonate and potassium sulfate. A typical suspension contains the following: water >69.0%, polymer 30.0%, surfactant 0.1-0.5%, inorganic salts 0.2%. A very dilute solution with water was added to the mixture of isobutyric acid and water. Photon beating spectroscopy of beads far from T c gives a = 8.010 -8 m from Eqs. 14, 15. It is implicitly assumed that the flow is dominated by viscosity around the colloids, as assessed by the Reynolds number <<1, see Eq.18. With a mean temperature dependence (dn/dT)  -2.510 -4 K -1 and a studied temperature range T-T c 20K, the refractive index thermal variation n < 510 -3 and can be neglected. In the following the value n=1.361 will be used (Table 1). Concerning density, its temperature variation will be also neglected and the value at T c , =0.99 xiv,xv is reported in Table 1. Isobutyric acid of quality better than 99.99 mol% was used without further purification. Ultrapure water from Millipore purification treatment device was used. The experimental isobutyric acid mass fraction used was 0.3887  0.0002, close enough to c c .

The mixture with colloids is set in a sealed glass sample, itself put in a thermostat with temperature regulation to within  10 -3 K. The beam of a 10 mW He-Ne polarized laser is slightly focused in the sample. Collimated light scattered at =90° is recorded by a photomultiplier, whose homodyne amplified signal is then analyzed by a correlator. The critical temperature is determined within  5mK by decreasing temperature step by step and looking at the phase separation process on a screen in front of the sample, perpendicular to the laser beam. The value T c = (301.130  0.005) K was found. Note that the signal due to light scattered by colloids is more important than the signal due to the mixture critical fluctuations, preventing from interfering in the analysis.

Results and discussion

The procedure to collect data is to vary temperature in logarithmic steps of the difference T-T c in order to generate a uniform density of measurements when looking at the data in log-log scale. The correlation time data are reported in Supplementary Material. Log-log scale indeed evidences power laws (see Figure 2). 43 correlation times data have been obtained in the temperature range [0.019 -20.6] K. The use of Eq. 9 with laminar flow around the colloid and Stokes damping can be tested. Equation 9gives a velocity V=3.610 -2 m.s -1 , using the

Shear viscosity

Amplitude Activation energy

  (nm) n   (nm)  f (kg.m -3)  s (kg.m -3) a (nm)  0 (10 -6 Pa.s) E (10 -20 J)
IW liquid mixture 0.3625 (a) 1.361 (b) 632.8 990 (b) --1.4422 (b) 3.007 (b) Latex bead ----1053 (c) 80 (b) --data of Table 1. With liquid mixture viscosity  2.5×10 -3 Pa.s (Table 1), the associated Reynolds number is indeed very low:

 110 -3 [18]
From the correlation time an experimental diffusion constant can be obtained by using Eq. 14. The corresponding values are drawn in Figure 2. In the same Figure the data are compared with the calculated Brownian motion diffusion constant using viscosity data, Eq. 15. Viscosity is deduced from the capillary flow measurements of Ref. (xvi), whose mean shear rate as estimated in Ref. (xi) leads to ignore the data at T-T c < 310 -2 K as corresponding to the strong shear region (see above Section 2.2). A fit of the viscosity data is made to Eq. 4, which allows the background contribution to D to be evidenced (Eq. 5). One finds =(1.4220.25)10 -6 Pa.s and E=(3.0070.07)10 -20 J, with a linear correlation coefficient R=0.999 and =3.8910 -9 .

Two regions of high and low shear are clearly evidenced in Figure 2 depending on the value of with respect to 1, or equivalently T-T c with respect to 3.5 K (see Eq. 3 and numerical values in section 2.3, S=4.410 -5 s -1 ). The calculated D values using the background viscosity clearly do not fit the data . Using the total viscosity Eq. 4, in the low shear region (T-T c > 3.5 K), both diffusion constants take the same values accounting for the fluctuation-induced enhancement of viscosity with respect to temperature. It means that the Brownian motion of the colloids follows the viscosity enhancement, corresponding to an augmentation of the friction forces. The contribution of fluctuations is made apparent in this low shear region when one compares the values of the experimental diffusion coefficient with the value inferred from the background viscosity. In the high shear region (T-T c < 3.5 K), the experimental diffusion constant saturates, in relation with the fluctuations deformation leading to a saturation of the viscosity enhancement. In other words, mean-field where the influence of fluctuations is disregarded becomes relevant, as noted in Section 2.2.

It is interesting to compare those data with other data obtained with PTFE (Teflon) microspheres of 1.15 µm radius immersed in the same isobutyric critical mixture at critical concentration xvii . The data have been analyzed to determine viscosity assuming Eqs. 14, 15. Eight data have been obtained in the range T-T c = [0.6 -6.8] K. The transition high-low shear is expected to occur at T-T c =0.06 K, well below the investigated temperature range.

It is worthy to note that, in contrast to other colloids immersed in different liquid mixtures (e.g. silica beads in lutidine-water mixtures xviii, xix ), no colloid aggregation phenomena nor preferential component adsorption were observed onto the colloids. The latter would have increase a, that is, decrease D, an effect in opposition to the saturation effect observed in Figure 2.

Concluding remarks

Photon beating light scattering experiments as described in this paper show that the Brownian motion of colloids (beads) immersed in a liquid is closely related to the hydrodynamics around the colloids. This behavior is highlighted in a near-critical liquid mixture which undergoes large concentration fluctuations. In such a liquid, diffusion of immersed colloids is indeed seen to be sensitive to the augmentation of viscosity related to the critical enhancement of concentration fluctuations. However, as the liquid mixture is brought close enough to the critical point where fluctuations increase, it turns out that the concentration fluctuations are altered by the shear flow around the colloids. It follows a deformation of fluctuations and a saturation of the viscosity enhancement, resulting in a mean-field behavior which ignores the effect of fluctuations. Such results show that the Brownian motion of particles in a dense fluid can either reflect the fluid properties or modify them or both.

  Effect of shear flowSpatial fluctuations near the critical point can be strongly deformed by external influences like hydrodynamics. Shear flow alters the spatial fluctuations vii,x when the shear-induced fluctuation deformation, l, during the fluctuation lifetime , becomes larger than the fluctuation correlation length , that is > , or[6]

Figure 1 :

 1 Figure 1: Light scattering arrangement. : Incident light wavevector; : Scattered light wavevector;

  The binary mixture of isobutyric acid and water exhibits an upper critical point with a critical mass fraction of isobutyric acid c c =0.3889 and temperature T c = 301 K[14]. A precise value is not necessary, as minutes quantities of impurities can shift T c . What really matters is the temperature difference T-T c , with T c experimentally determined for each sample. The refractive index at the critical point is n c = 1.36105 for the laser wavelength  0 =632.8 nm.

Table 1 .

 1 Useful data. (a) Ref. (xx). (b) See text. (c) Ref. (xxi).

Figure 2 :

 2 Figure 2: Temperature dependence of the diffusion constant D (log-log plot) as obtained from the experimental correlation times (open circles, exp.), Brownian motion diffusion constant using full viscosity (Eq. 4) from Ref. (xvi) (interrupted line, calc.) or using only background viscosity from a fit to Eq. 5 (see text; dotted line, back.). The full line is a smoothing function of the data.

  xviii Beysens D., Esteve D., Adsorption Phenomena at the Surface of Silica Spheres in a Binary Liquid Mixture, Phys. Rev. Lett. 54, 2123-2126 (1985). xix Yabunaka S., Onuki A.: Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory, Physical Review E 96, 032127 (2017) and refs. therein. xx Beysens D., Bourgou A., Calmettes P.: Experimental determinations of universal amplitude combinations for binary fluids. I. Statics, Phys. Rev. A 26, 3589-3609 (1982). xxi Giddings J. C., Ho J.: Accurate Measurement of Density of Colloidal Latex Particles by Sedimentation Field-Flow Fractionation, Langmuir 11, 2399-2404 (1995).

	Calc.	high shear	low shear
	Exp. Back.	S>1	S<1
	0.04

Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI, PSL Research University, Sorbonne Université, Sorbonne Paris Cité, Paris, Francee-mail: daniel.beysens@espci.fr

Acnowledgments

I gratefully thank S. Perleaux for help in the measurements and A. Mongruel for a critical reading of the manuscript.


domain: phys sde

text:
Rukmava Chatterjee

Daniel Beysens

Sushant Anand
email: sushant@uic.edu

Delaying surface icing using thermo-responsive liquids

Preventing water droplets from transitioning to ice is highly advantageous for numerous applications. Herein, we demonstrate that droplets condensing on certain highly supercooled phase change materials, referred to as thermo-responsive liquids (TRL) can exhibit freezing delay lasting up to 10-300 orders of magnitude longer than superhydrophobic surfaces under identical environmental conditions. The delayed freezing of droplets is primarily a consequence of the trapped heat release in their vicinity due to condensation, but is also affected by the morphology of solidified TRL surface and its miscibility in water. Regardless of the surface chemistry, TRL infused textured surfaces can show very low droplet adhesion when operated at temperatures below the corresponding melting point of the TRLs, thus engendering icephobicity even on hydrophilic surfaces. Beyond anti-icing, such materials can potentially be used in diverse industrial applications such as drag-reduction and condensation enhancement.

Ice formation on surfaces afflicts various energy and transportation industries worldwide, causing extensive economic losses each year. For instance, the freezing upon impact of cloudborne supercooled water droplets 1 leads to ice accretion that alters in-flight aerodynamics and causes failure of critical aircraft instruments; jeopardizing their performance [START_REF] Lynch | Effects of ice accretions on aircraft aerodynamics[END_REF] . Surface icing also causes expensive power outages [START_REF] Farzaneh | Atmospheric Icing of Power Networks[END_REF] and compromises the operational safety of marine vessels [START_REF] Dehghani-Sanij | Sea spray icing phenomena on marine vessels and offshore structures: Review and formulation[END_REF] , off-shore oil rigs [START_REF] Ryerson | Ice protection of offshore platforms[END_REF] and wind turbines [START_REF] Lamraoui | Atmospheric icing impact on wind turbine production[END_REF] . Strategies to mitigate such deleterious effects of icing seek to either facilitate ice removal or delay icing on surfaces. Current industrial solutions based on either of these strategies rely on active mechanical [START_REF] Laforte | State-of-the-art on power line de-icing[END_REF] , chemical [START_REF] Ramakrishna | Environmental impact of chemical deicers -A review[END_REF] and electrothermal de-icing techniques [START_REF] Elsharkawy | Combating Frosting with Joule-Heated Liquid-Infused Superhydrophobic Coatings[END_REF] which are both energy and cost intensive. Hence, considerable efforts have been directed into developing passive techniques to design "icephobic" surfaces that impede ice formation via decreased ice adhesion onto the surface by tuning water-surface interactions [START_REF] Attinger | Surface engineering for phase change heat transfer: A review[END_REF][START_REF] Kreder | Design of anti-icing surfaces: Smooth, textured or slippery?[END_REF] . The pursuit of this goal has led to the development of engineered surfaces that show extreme water repellency, such as superhydrophobic surfaces [START_REF] Cao | Anti-Icing superhydrophobic coatings[END_REF][START_REF] Tourkine | Delayed freezing on water repellent materials[END_REF][START_REF] Meuler | Exploiting topographical texture to impart icephobicity[END_REF][START_REF] Mishchenko | Design of ice-free nanostructured surfaces based on repulsion of impacting water droplets[END_REF][START_REF] Farhadi | Anti-icing performance of superhydrophobic surfaces[END_REF][START_REF] Jung | Are superhydrophobic surfaces best for icephobicity?[END_REF][START_REF] Guo | Icephobic/anti-icing properties of micro/nanostructured surfaces[END_REF][START_REF] Boreyko | Delayed frost growth on jumping-drop superhydrophobic surfaces[END_REF][START_REF] Schutzius | Spontaneous droplet trampolining on rigid superhydrophobic surfaces[END_REF] . However, superhydrophobic surfaces (SHS) are intolerant of high humidity [START_REF] Kulinich | Superhydrophobic surfaces: Are they really ice-repellent?[END_REF] and occurrence of ice/frost nucleation, randomly within their surface texture causes loss of superhydrophobicity [START_REF] Varanasi | Frost formation and ice adhesion on superhydrophobic surfaces[END_REF] . Superhydrophobicity also warrants special consideration of surface chemistry and topology; loss of which exacerbates the icing problem [START_REF] Kreder | Design of anti-icing surfaces: Smooth, textured or slippery?[END_REF][START_REF] Lv | Bio-inspired strategies for anti-icing[END_REF] . Although some of these difficulties can be overcome by using lubricant infused surfaces (LIS) [START_REF] Kreder | Design of anti-icing surfaces: Smooth, textured or slippery?[END_REF][START_REF] Lv | Bio-inspired strategies for anti-icing[END_REF][START_REF] Lafuma | Slippery pre-suffused surfaces[END_REF][START_REF] Wong | Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity[END_REF][START_REF] Kim | Liquid-infused nanostructured surfaces with extreme anti-ice and anti-frost performance[END_REF][START_REF] Smith | Droplet mobility on lubricant-impregnated surfaces[END_REF][START_REF] Yao | Adaptive fluid-infused porous films with tunable transparency and wettability[END_REF][START_REF] Golovin | Designing durable icephobic surfaces[END_REF][START_REF] Park | Condensation on slippery asymmetric bumps[END_REF][START_REF] Sun | Suppression of Frost Nucleation Achieved Using the Nanoengineered Integral Humidity Sink Effect[END_REF] , the lubricant itself is prone to depletion due to wicking into the frost [START_REF] Rykaczewski | Mechanism of frost formation on lubricant-impregnated surfaces[END_REF] , thereby necessitating periodic lubricant replenishment for restoring "slipperiness".

In this study, we introduce a new paradigm to delay ice formation on surfaces. We use materials that can trap the latent heat released during condensation to exist in a liquid state in the immediate vicinity of condensing water droplets, while still remaining in a solid state away from the droplets -even at large surface supercooling (ΔTs =Tsur-Tdp << 0°C, where Tsur is the surface temperature and Tdp is the dew point temperature). These materials, termed herein as thermo-responsive liquids (TRL), are organic phase change materials (PCMs) with melting points (Tmp) higher than the freezing point of water (Tfp). Typically, PCMs have been used in applications such as thermoregulation, thermal management/storage, data storage and drug delivery [START_REF] Zalba | Review on thermal energy storage with phase change: Materials, heat transfer analysis and applications[END_REF][START_REF] Sharma | Review on thermal energy storage with phase change materials and applications[END_REF] . Herein, we propose that their heat-trapping abilities can also be advantageously exploited to delay freezing of condensing droplets. The delayed freezing of droplets is a consequence of heat release due to condensation, but also depends upon the morphology of solidified TRL (henceforth referred as S-TRL) surface and its miscibility in water. Finally, micro-textured surfaces infused with TRLs operated below their respective Tmp resist TRL displacement out of the texture by water, thus engendering icephobicity even on hydrophilic surfaces.

Latent heat trapping in TRLs during vapour condensation

To establish TRLs' ability to trap the latent heat released during condensation, we selected cyclohexane as a test TRL and performed experiments by rapidly cooling 8 ml of the liquid to few degrees below its Tmp (6.52°C) in controlled environmental conditions (relative humidity, RH: 80%; air temperature, Tair: 25°C; Methods section) forming a 3.3 mm thick solidified film. As droplets condensed on solid cyclohexane (SCh), a myriad of unique droplet behaviours were observed continuing for a long duration. Firstly, the droplets (even smaller than the capillary length) showed very high mobility, gliding along the surface in a series of 'stick/slip' events. Secondly, as the droplets constantly moved along the SCh surface, they left distinct perimeter footprints at their previous locations (Fig. 1a and Supplementary Movie S01). Finally, it was observed that sometimes an intervening barrier film between the droplets delayed their coalescence (Fig. 1b). These observations are characteristic evidence of liquid cyclohexane in the vicinity of the droplets [START_REF] Steyer | Spontaneous jumps of a droplet[END_REF][START_REF] Narhe | Inverted leidenfrost-like effect during condensation[END_REF] . The competition between latent heat release and heat removal at the opposite faces of the SCh film leads to aperiodic solid-liquid-solid phase transitions of SCh beneath/around the droplets -engendering stochastic interfacial temperature gradient along the droplet contact line and their unique 'stick/slip' motion [START_REF] Narhe | Inverted leidenfrost-like effect during condensation[END_REF] . The droplet imprints and the barrier film between two coalescing droplets are remnants of the cyclohexane 'wettingridge' formed around the droplets because of interfacial interactions between water droplets and liquid cyclohexane [START_REF] Narhe | Inverted leidenfrost-like effect during condensation[END_REF] . The release of latent heat during condensation uniformly below a droplet, growing by vapour diffusion leads to a temperature increase at the substrate-drop interface given by where k, ρw, Lw, αs, and κs are the droplet growth constant, liquid water density, latent heat of condensation of water, thermal diffusivity and thermal conductivity of the substrate material respectively. For high thermal conductivity materials like Silicon, this temperature increase is negligible (~0.03°C), but for a low thermal conductivity material like SCh, the temperature increase can be significant (~3°C). Incorporating the heat transfer from the local environment, the total temperature increase at the SCh-air interface can be ~5°C -sufficient to cause localized SCh melting as observed in Fig. 1a-b (Supplementary Note 1).

Above arguments imply that the surface melting should be absent on highly supercooled SCh. However, the droplet 'stick/slip' motion, their footprints and the intervening barrier oil film were observed even when SCh was subjected to Peltier temperature (Tpel) of -15°C (Fig. 1c-d). Furthermore, such behaviour was also observed on solid cyclooctane (SCt) -a TRL with Tmp (~14°C) higher than that of cyclohexane (Fig. 1e-f) subjected to identical conditions. Additionally, water droplets remained in liquid state without undergoing freezing for an extended duration (>2 hours) on both SCh and SCt. Since Tfp remains unchanged on SCh/SCt because of their mutual immiscibility (Supplementary Note 2), these observations suggest that condensation heat release provided sufficient energy to cause local temperature increase greater than 10°Cand 20°C for the cases of SCh and SCt respectively. Although such temperature jumps can arise during condensation on aerosol nanoparticles [START_REF] Hinds | Aerosol technology: properties, behavior, and measurement of airborne particles[END_REF] , our experiments indicate that significant temperature jumps can also occur on subcooled TRL surfaces. These observations ΔT s ≈ kρ w L w πα s κ s can potentially be explained if we consider that the condensation mass transfer occurs primarily along the contact line of water droplets (Fig. 1g) wherein heat-transfer dominates [START_REF] Steyer | Growth of droplets on a substrate by diffusion and coalescence[END_REF][START_REF] Xu | Multiscale Dynamic Growth and Energy Transport of Droplets during Condensation[END_REF] -a phenomenon that may play a decisive role especially on low thermal conductivity materials [START_REF] Beysens | The formation of dew[END_REF] . Large temperature jumps, sufficient to locally melt solidified TRLs can potentially occur near the droplet contact line, provided that the length-scale (δ) of such heat transfer dominated region is <1 µm -a challenging task to measure and beyond the scope of the present work.

The non-uniform heat-flux distribution around droplets can have many consequences. For example, it could lead to uneven melting of S-TRL and convective flow within the condensing droplets and melt TRL film (Fig. 1g). The latter could also be subjected to the Laplace pressure at the water-TRL interface -similar to the case of vapour outflow in Leidenfrost droplets [START_REF] Biance | Leidenfrost drops[END_REF] . Consequently, the water droplets could be in partial or complete contact with TRL film of nonuniform thickness at any given instant that could then delay droplet freezing via two possible mechanisms. Firstly, the contact of water droplets with the insulating TRL film at a temperature higher than Tfp could make it thermodynamically unfavourable for icing to occur. Secondly, the relative smoothness of a liquid film beneath the droplets may increase the energy barrier for icing nucleation by eliminating the surface roughness ensued freezing of droplets. To elucidate the importance of surface melting in delaying freezing of droplets, we studied droplet freezing dynamics on supercooled SCh under conditions wherein its melting could be suppressed. A cold water droplet was deposited on SCh surface subjected to Tpel = -15°C in a very low humidity environment (4% RH) thereby precluding any condensation. It was found that the droplet froze within ~5 minutes of deposition (Fig. 1h-1i and Supplementary Movie S02), reconfirming that the condensation heat release plays a pivotal role in delaying freezing of condensing droplets on SCh.

Freezing delay potential of TRL

To put the freezing delay potential of S-TRL into perspective, we compared its anti-icing performance with superhydrophobic and Polytetrafluoroethylene (PTFE) surfaces under identical conditions (Tair: 25°C, RH: 80%). A nano-textured Silicon substrate (5.5 cm diameter) silanized with octadecyltrichlorosilane, exhibiting an average water contact angle (WCA) of 147° (Fig. 2a), was used as a representative example of superhydrophobic surface. The substrate was placed in a copper container and subsequently cooled to Tpel = -15°C. Because of large subcooling, high nucleation rate of droplets was observable on the surface accompanied by out-of-plane 'jumping-droplet' behaviour [START_REF] Boreyko | Self-propelled dropwise condensate on superhydrophobic surfaces[END_REF] . However, within 18±6 minutes an invading inter-droplet freezing wave engulfed the entire surface in a spate of freezing events (Fig. 2b). Next, we tested whether a hydrophobic surface with higher thermal resistance could perform better. A flat PTFE sample (5.5 cm diameter, 3.3 mm thick, WCA ~108°) was similarly subjected to Tpel = -15°C (Fig. 2c). Although thermal conductivity of PTFE (0.25 W/m/K) is significantly lower than that of Silicon (142.2 W/m/K), even droplets condensing on PTFE froze within 22±1 minute (Fig. 2d). Finally, we performed condensation-icing experiments under identical experimental conditions on SCh having thickness same as PTFE (3.3 mm). Upon freezing, SCh appeared to have a smooth surface. This was subsequently confirmed by imaging the SCh surface (Fig. 2e) in a Scanning Electron Microscope (SEM) using a replica moulding technique (Methods section) performed separately. As discussed earlier, droplets condensing on hydrophobic SCh surface (WCA ~104 o ) showed distinct behaviours compared to superhydrophobic or PTFE surfaces. Condensed droplets on SCh remained mostly unfrozen for as long as 229±25 minutes (Fig. 2f and Supplementary Movie S03). They froze eventually, primarily due to the gradual sublimation of cyclohexane itself which was further exacerbated by the inevitable "edge-effect" ensued freezing wave front propagation. Although SCh thermal conductivity is nearly the same as PTFE, yet the stark differences in the droplet motion and icing delay potential of SCh further illustrates that the latent heat trapping and surface melting is distinctive to SCh.

Icing delay on different solidified TRLs

To investigate whether surface melting and delayed freezing is observable on other TRLs with similar thermal properties, anhydrous TRLs were chosen; namely benzene (Tmp = 5.53°C), tetradecane (Tmp = 5.86°C), pentadecane (Tmp = 9.96°C), hexadecane (Tmp = 18.19°C) and dimethyl sulfoxide (DMSO, Tmp = 18.52°C) -a water miscible compound. Since surface structure can strongly influence nucleation behaviour, we first characterized the S-TRL surfaces by cooling them below their respective Tmp in a low humidity (15% RH) environment. Upon freezing, S-TRLs optically appeared (Fig 3a and Supplementary Movie S04) as transparent (e.g., SCh, SCt), semi-transparent (e.g., solid DMSO -referred henceforth as SD), or nearly opaque (e.g., solid hexadecane -referred henceforth as SH). Since the direct observation of solidified TRLs is not possible in SEM, we used the replica moulding technique (Methods section) to obtain the negative embossment of the corresponding surfaces on a photopolymer (Norland 80). The SEM of the hardened polymer revealed that TRLs had widely varying surface structure (Fig. 3b). SEM and optical images indicated that solidified tetradecane (ST), solidified pentadecane (SP) and SH have micro-structured surfaces (Supplementary Figures . S1-S3); in-line with previous observations that have shown that solidified n-alkanes have a macrocrystalline structure [START_REF] Maroncelli | Nonplanar Conformers and the Phase Behavior of Solid n-Alkanes[END_REF][START_REF] Craig | Investigation into the structures of some normal alkanes within the homologous series C13H28 to C60H122 using high-resolution synchrotron x-ray powder diffraction[END_REF] . On the other hand, cyclic alkanes (like SCh, SCt) and solid benzene (SB) have microcrystalline structure [START_REF] Obremski | Vibrational spectra of single crystals. polymorphic solids of cyclohexane[END_REF] and hence appear relatively smooth. Direct surface roughness measurements of S-TRLs were conducted next in a low humidity environment (5% RH) using a high magnification optical profilometer (Keyence 6000). It was found that ST has higher average roughness and Z-roughness (Supplementary Method 5.3) than SP and SH, while other S-TRLs have sub-microscopic roughness (Fig. 3d).

Following the characterization of S-TRL surface morphologies, we investigated condensation-icing dynamics on TRLs (8 ml) cooled down to Tpel = -15°C in a high humidity (80% RH) environment (Supplementary Movie S05). We evaluated the time when droplet freezing was first observed on S-TRL (referred as freezing initiation time) in the field of view and the total time it took for all the droplets on the entire surface to freeze (total freezing delay time). On SD, the combination of the condensation heat release and water miscibility causes continuous melting and mixing of the water-DMSO mixture, thereby preventing the freezing of the solution for >96 hours [START_REF] Havemeyer | Freezing point curve of dimethyl sulfoxide-water solutions[END_REF] . On SB the droplets showed the unique droplet 'stick/slip' motion similar to SCh/SCt. The microstructure morphology of ST, SH and SP surfaces occluded the visibility of condensed water droplets. We ascertained that while the 'stick/slip' motion of micro-droplets was still faintly visible on ST and SP, it did not appear at all on SH surface. Although ST and SCh have similar Tmp, droplets froze within 17±5 mins on ST and 57±3 mins on SH which showed no signs of surface melting. Putting the surface roughness measurements in the context of these results, it becomes perspicuous that higher the sample surface roughness, lower the droplet mobility and freezing delay (Fig. 3d) on it. The droplet size distribution on the surface just before freezing initiation revealed high droplet density with smaller inter-droplet distances on rougher surfaces (Supplementary Note 3). As a result, on ST, SP and SH surfaces, once nucleation initiates, the freezing front rapidly propagates over the entire surface, while on SCh, SCt and SB surfaces, it takes considerable time for it to spread resulting in isolated droplet freezing events.

Anti-icing potential of TRL infused textured surfaces

The discussion so far has been centred on the behavioural performance of TRLs in bulk. In the following part of the study, we investigate the dynamics of TRL infused micro/nano-textured surfaces. An oil film remains stably infused within a solid matrix in the presence of a water droplet provided the contact angle of the oil on the solid in the presence of water (θos(w)) is lower than the critical angle of impregnation (θc) i.e. when θos(w)<θc wherein θc=cos -1 [(1-ϕ)/(rϕ)], r is surface roughness and ϕ is the projected area of the surface occupied by the solid [START_REF] Smith | Droplet mobility on lubricant-impregnated surfaces[END_REF] . This condition can be achieved by attaching hydrophobic groups to a textured surface. [START_REF] Smith | Droplet mobility on lubricant-impregnated surfaces[END_REF] Thus when a water droplet interacts with a TRL (e.g. pentadecane) infused textured superhydrophobic surface fulfilling the above criterion, it shows very low adhesion and rolls down the composite surface regardless of the fact whether the sample is at room conditions (Fig. 4a, state I) of Tair = 23°C, RH = 24% or below the Tmp of TRL (Fig. 4a, state II) at Tpel = 2°C. On the other hand, when a water droplet under ambient conditions interacts with a textured surface that does not meet the aforementioned criterion (e.g. TRL infused hydrophilic surface), the droplet displaces the TRL out of the texture and gets strongly pinned on the surface (Fig. 4a, state III). However, this behaviour changes dramatically when the same TRL infused textured hydrophilic surface is operated below the Tmp of TRL (Tpel = 2°C). The freezing of TRL on and within the texture prevents its displacement out of the texture by water (Supplementary Movie S06). A droplet at room temperature has sufficient thermal energy to partially melt a fraction of TRL, resulting in in-situ formation of the lubricating liquid layer beneath such droplet -due to which the droplet glides on the surface (Fig. 4a, state IV).

Having shown that TRL infused hydrophilic surfaces can remain stable at subcooled temperature, we next sought to study their anti-icing potential (Supplementary Movie S07). For performance comparison, we conducted experiments on superhydrophilic surface (SPS), superhydrophobic surface (SHS) and LIS. For the bare SPS, SHS and LIS, a hierarchically structured Silicon substrate with 50 µm spacing was used (SEM image in Supplementary Figure S7a). The substrate was silanized using octadecyltrichlorosilane coating to prepare SHS and was subsequently infused with 10 cSt Silicone oil to prepare the LIS. TRL infused surfaces (TRL-IS) were prepared by lubricating a 10 µm spacing micro-structured (SEM image in Supplementary Figure S7b) hydrophilic surfaces with water miscible (DMSO and glycerol, Tmp =18.18°C) and water immiscible (cyclooctane) TRLs. These surfaces shall hereafter be referred to as SD-10, SG-10 and SCt-10 respectively. Condensation-icing experiments were performed by cooling the samples to -7°C and subjecting them to controlled environmental conditions (Tair = 25°C, RH = 60%). The tests showed that freezing of the entire surface occurred within 8 minutes for SPS, 30 mins on SHS and 17 mins for LIS (Fig. 4b). Analysis of the surface ice coverage revealed that the hydrophilic TRL-IS have orders of magnitude higher icing delay as compared to conventional surfaces (Fig. 4c and Supplementary Figure S9). The morphology and packing density of frost on different surfaces were conspicuous, varying between densely packed ice sheet on SPS to discreet parcels on LIS, edgy sheaf on SHS to a spongy packing on TRL-IS, owing primarily to their delayed frost growth and intermittent self-replenishment.

In addition to anti-icing, TRL-IS can also thwart the icing of impacting droplets. For example, in a frigid environment (Tair = -5°C, RH = 65%), droplets impacting on nano-textured SHS get pinned on the surface due to the loss of superhydrophobicity by frost formation (Fig. 4d) while the same droplets can glide effortlessly on TRL infused textured surfaces (Supplementary Movie S08). Finally, S-TRL surfaces also show self-healing properties during condensation. For example, a SCt surface subjected to critical mechanical damage eventually self-heals within 42 minutes of sustained condensation (Fig. 4e and Supplementary Movie S09).

Outlook

In conclusion, we have shown that TRLs can significantly delay condensation-icing when used either in bulk or infused into solid textures, imparting icephobicity even to hydrophilic surfaces. Concurrently, they also demonstrate other utilitarian features including optical transparency and in-situ self-healing upon getting critically damaged. Surface roughness effects can compromise the possible benefits of condensation induced surface melting on waterimmiscible TRLs. On the other hand, the synergistic effect of surface melting and freezing point depression can exhibit extraordinary freezing delays using water miscible TRLs. The intriguing phenomenon of condensation-icing delay on solidified TRLs provides a new construct about the nature of phase transitions on surfaces. While our study provides the first step in that direction, further studies are warranted to understand the extent of melting, the nanoscale temperature distribution within and around droplets. Although the TRLs studied in this work comprised mostly of alkanes, we envision that the vast library of TRLs available today including biodegradable vegetable-based TRLs could target a wide temperature range and consequently provide new opportunities to tune their performance for many industrial icing related problems.

Methods

Methods, including statements of data availability and any associated accession codes and references, are available in the online version of this paper.

Received: ((will be filled in by the editorial staff)) Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))

Methods

Liquids: All the chemicals used in this study were of analytical grade or higher, purchased from Sigma Aldrich and used without any further purification. Liquid properties are provided in Supplementary Table S1.

Fabrication of micro-nano patterned surfaces: Silicon wafers were first cleaned by sonicating them sequentially in a bath of acetone, methanol, isopropyl alcohol and deionized water and later dried. To prepare the nanograss surface, black Silicon method was used wherein four-inch Silicon wafer (525 µm thick, p-type) was etched using Deep Reactive Ion Etching (DRIE) under the continuous flow of an etchant gas (SF6) and a passivation gas (O2). To obtain the micropost surfaces (10 µm post width, 10 µm pillar height, 10 µm edge-to-edge spacing), four-inch Silicon substrates were first patterned via standard photolithography using Heidelberg MLA 150 Direct Write Lithographer, followed by dry etching using a Bosch DRIE process. To obtain the hierarchically textured surfaces, the micropost surfaces (50 µm edge-toedge spacing) were further etched in a plasma of SF6 and O2 rendering nanograss texture on the top and in the spaces between the microposts. After fabrication, all the samples were examined under a FEI Quanta 650 FEG SEM. TYKMA Electrox Laser Marking System was used to laser cut the fabricated 4-inch sample into the desired size, as required for experimentation.

Preparation of impregnated samples:

The fabricated Silicon samples were first thoroughly cleansed by sonicating them in a bath of acetone, ethanol, isopropyl alcohol and deionized water. After drying the samples with nitrogen gas, they were plasma cleaned (Herrick Barrel Plasma Etcher) to remove any organic contaminants. TRL infused hydrophilic surfaces were prepared by initially spreading out excess TRL in order to completely cover the textured surfaces. Uniform impregnation of samples without any excess lubricant was achieved by next spinning the impregnated samples at 1500 rpm for one min using a spin coater (Laurell Technologies WS-650Mz-23NPPB) and subsequently mounting them vertically for 10 minutes to gravity-shed any excess lubricant. To prepare lubricant infused superhydrophobic surface, the plasma cleaned sample was silanized with octadecyltrichlorosilane (OTS) and then lubricant impregnated, following the same protocol as mentioned above.

Setup for performing condensation-icing experiments:

All the condensation-icing experiments were performed in a custom-built environmental chamber capable of controlling the ambient temperature and relative humidity of the enclosure while maintaining a contaminant-free, positive-pressure environment with negligible air convection effects (see also Supplementary Methods 5.1). The humidity of the environmental chamber was measured by the glovebox humidity sensor (measuring range: 0-100% RH, accuracy: ± 2% RH at 20°C). Additionally, the local humidity and temperature around the test samples were monitored using a Sensirion sensor (SHT71) throughout the experimental duration. A water-cooled thermoelectric cold plate (TECA LHP-800CP) capable of lowering the temperature from 20°C to -15°C within 5 minutes was used for all the condensation-icing experiments. The Peltier surface temperature was controlled using a PID temperature controller. Electrically insulated thermocouples (Type K, OMEGA) were bonded onto the Peltier surface to continuously record the Peltier surface temperature using a digital data acquisition system (OMEGA-DAQPRO-5300). For optical recording of the condensation-icing experiments, videos were shot from a top-down view using a Nikon D810 DSLR camera (1920×1080 resolution, 29.97 fps) fitted on a high zoom microscope (Carl Zeiss Axio Zoom V16 equipped with a Zeiss Plan Apo1.5x lens). The microscope uses a CL 9000 LED co-axial cold light source for illumination thereby eliminating the possibility of local heating of the test sample surface even while observing at very close working distances.

Protocol for performing condensation-icing experiments on bulk samples: Samples (bulk liquid TRL, structured Silicon surfaces, PTFE) were placed in a specially built annular copper container (inner diameter: 5.5cm, capacity of 10 ml) fitted with a matching PTFE ring (1 cm thick). The PTFE ring aided in suppressing the icing/frosting due to edge effects to some extent. The bottom of the copper chamber had a highly polished flat surface which ensured good thermal contact with the Peltier cooler surface. A rectangular PTFE block (1.5 cm thick) with an annular hole in the middle, to incorporate the copper chamber and covering the Peltier surface area was used to insulate the latter, thereby ensuring that the Peltier only cooled the copper chamber and its contents. For experiments corresponding to condensation-icing on bulk S-TRL surfaces (refer Fig. 1a-f, 2, 3d), a smooth bare Silicon wafer was placed on the base of the copper container for enhancing the experimental visualization. Before each experiment, the copper chamber, the PTFE ring and the Silicon wafers were thoroughly cleansed using acetone, ethanol, isopropanol, DI water and then finally dried using Praxair nitrogen gas (99% pure). For each of the aforementioned experiments, 8 ml of TRL (~3.3 mm thick layer of TRL on solidification) was filled into the container. After putting the test samples inside the glovebox, it was air-locked and experiments were conducted using the setup described earlier. Continuous video recordings were made for all the experiments and analysed later using ImageJ and MATHEMATICA software.

Protocol for performing condensation-icing experiments on functional surfaces: Antiicing potential of the bare/textured surfaces (with/without lubricants) was investigated in the glovebox under controlled environmental conditions. The test substrates (6.45 cm 2 each) were bonded with a highly thermally conductive double-sided tape onto a copper plate (6×6 cm 2 , 0.2 cm thick) that was bolted directly to the centre of the water-cooled Peltier surface to abate the "edge-effect" ensued ice formation to some extent. To negate the effect of spatial temperature variation across the Peltier surface and ensure experimental uniformity, the test samples were attached to the same central location for each of the trials. Once attached, the Peltier assembly was mounted vertically and experiments were performed inside the glovebox (see also Supplementary Methods 5.2).

Contact angle measurements:

WCAs of superhydrophobic and PTFE surfaces were measured using a video based optical contact angle measurement system by virtue of a SCA20 software on a goniometer (OCA 15Pro, Dataphysics GmbH, Germany) at ambient conditions (23°C, 20% RH). WCA measurement of the solidified TRL surface was carried out inside the glovebox, maintained at a very low humidity (4% RH) environment in order to prevent any condensation. The liquid TRL (8ml) was cooled below its corresponding Tmp using the TECA Peltier cooler. A deionized water droplet (~5 µL), at a temperature lower than the melting point of the TRL was gently deposited on the solidified TRL surface and imaged from the side using a PointGrey camera fitted with a InfiniProbe (TS-160 MACRO) lens and backlit by Nila Zaila light source. Subsequently, the images were analysed in ImageJ software to obtain the corresponding WCAs. All reported CAs are averages of five independent measurements on different locations of a single sample. The accuracy of the measured contact angle is ±1°.

Protocol to obtain the negative replica of solid TRL surfaces: Experiments were performed in the glovebox in a very low humidity (RH: 11%, Tair: 22°C, Tdp: -8°C) environment. A rectangular copper container (5×5×3 mm 3 ) was partially filled (80% of its volume) with TRL and cooled to -5°C using the Peltier. Once the TRL froze, cooled liquid photopolymer from Norland Optics (NOA-89 for ST, SP, SH; NBA-108 for SB, SCh, SCh, SD) was gently poured over the frozen TRL to fill up the remaining volume of the container. Prior deposition, the photopolymer was maintained at a temperature below the melting point of each TRL so as to prevent any TRL melting upon contact. The photopolymer spread completely on the surface of the frozen TRLs. Thereafter, the photopolymer was quickly polymerized using a UV lamp (exposure of 5-10 minutes). Post curing, the Peltier was set to the ambient temperature which caused the TRL to melt, but caused the cured polymer film to detach. The cured polymer film (having the negative embossments of the solid TRL surface) was carefully withdrawn and any excess oil on it was removed by placing it in a vacuum oven at 30°C. Thereafter, it was kept in an air-tight container and immediately taken for surface characterization by SEM.

Surface roughness measurements of solidified TRL surfaces: Surface roughness measurements were obtained by scanning the S-TRL surfaces (cooled down to 5°C) using an optical profilometer (Keyence VHX6000) placed inside the glovebox, which was maintained in a very low humidity (5% RH) environment (see also Supplementary Methods 5.3).

Droplet mobility on different surfaces:

A 10 µL cold droplet (at 0°C) was deposited on various test substrates using an insulated glass needle, fixed at a height of 0.5 cm above each test substrate. The experiments were carried out at an ambient temperature of 23°C and 24% RH. The test substrates were thermally bonded using a double-sided copper tape onto a Peltier stage (TE Technology CP-061) fixed at an angle of 45° (see also Supplementary Methods 5.4).

Ice-repellency experiments of TRL-IS in outdoor freezing environment:

The experiments demonstrating the ice-repellency of TRL-IS were performed outdoors in Chicago, Illinois on 14th March, 2017 when the ambient conditions were: Tair of -5°C (feels like temperature of -13°C), RH of 65% and light snow. A nanostructured superhydrophobic surface and a TRL (pentadecane) infused hierarchically textured (50 µm edge to edge spacing) superhydrophobic surface, each of 6.45 cm 2 size, were thermally bonded to an aluminium plate (2 mm thick) using a double-sided copper tape and initially held horizontally. After the surfaces had equilibrated with the outdoor ambient conditions, a dyed cold water droplet (~70 µL) was gently deposited on each of the test substrates successively (Supplementary Movie S08). On tilting the base plate gradually, it was observed that the water drop on the superhydrophobic surface remained strongly pinned, while the same was seen to glide off on TRL-IS (Supplementary Movie S08).

Self-healing test of TRLs: An aluminium plate (0.5 cm thick) with a rectangular cavity (3×2.4 cm 2 , 0.1cm deep) was filled with a TRL (cyclooctane) and bolted onto the Peltier surface. After cooling it to Tpel = 5°C, the setup was tilted at an angle of 90°. Mechanical damage was inflicted on the TRL surface in the form of a series of surface incisions (~400 µm wide, ~800 µm deep) using a sharp metal blade. Experiments were carried out under environmental conditions of 25°C, 80% RH. After 42 minutes, the surface was seen to self-heal with the disappearance of the incisions.

Data availability.

The data that support the findings of this study are available upon request from the corresponding author. The 'freezing initiation time' depicts the occurrence of first condensed droplet freezing event in the field of view, while the 'total freezing delay time' is representative of the time it took for all the condensed droplets on the S-TRL surface to freeze. The roughness characterization for each of the bare S-TRL surface was performed using an optical profilometer in a very low RH (5%) environment to prevent condensation. 'Average roughness' is the arithmetic mean of the absolute height shifts about the mean reference plane while 'Z-roughness' is indicative of the distance between the highest peak and lowest valley on the surface. The error bars (both left and right) denote standard deviations, obtained from experimental measurements on different TRLs repeated at least four times each. Analysis of S-TRL surface roughness (left) elucidated that smaller the S-TRL surface roughness, higher is the freezing delay.

Figure 1 |

 1 Figure 1 | Effects of latent heat trapping during condensation on TRL. a,c, e, Optical image of a condensed water droplet in an environment with relative humidity, RH = 80% on: (a) SCh surface subjected to Peltier temperature, Tpel = 2°C, (c) SCh surface subjected to Tpel = -15°C and (e) SCt surface subjected to Tpel = -15°C. Droplet positions at prior time instants are shown using overlapping circles. Droplet perimeter footprints (liquid tracks) are visible at each prior position. b,d,f, Optical image of two condensed water droplets in an environment with RH = 80% separated by: (b) the cyclohexane film at Tpel = 2°C, (d) cyclohexane film at Tpel = -15°C and (f) the cyclooctane film at Tpel = -15°C. g, Schematic elucidating the underlying mechanism of latent heat trapping in solidified TRLs during vapour condensation. h, Time-lapse images of a water droplet freezing on SCh surface under conditions of Tdp<Tfp. The cooled water droplet (~0.1 µl) was deposited on the SCh surface subjected to Tpel = -15°C in an environment where ambient temperature, Tair = 25°C and RH = 4%. i, Schematic illustrating the droplet freezing behaviour on solid TRL surface when the dew point temperature (Tdp) is far below the freezing point (Tfp). Scale bars, (a-f) 25 µm, (h) 500 µm.

Figure 2 |

 2 Figure 2 | Freezing delay potential of TRL compared to conventional anti-icing materials a,c,e, SEM images of (a) nano-textured superhydrophobic surface (SHS) with WCA of ~147 o , (c) Polytetrafluoroethylene (PTFE) surface with WCA of ~108 o and (e) S-TRL (SCh) surface with WCA of ~104 o . WCA of S-TRL surface was measured in a low humidity (RH = 4%) environment. b,d,f, Image sequence showing the droplet freezing behaviour on (b) SHS, (d) PTFE and (f) S-TRL (SCh) surfaces at different times as observed under the optical microscope. All surfaces were subjected to Tpel = -15°C under environmental conditions of Tair = 25°C, RH = 80%. Corresponding macroscopic images in the third row denote the bulk frozen sample at the end of each experiment. TRL was seen to outperform the conventional anti-icing materials by orders of magnitude. Scale bars, (a, c, e) 4 µm, (b, d, f) 100 µm.

Figure 3 |

 3 Figure 3 | Anti-icing potential of different TRLs. a, Optical transparency of aluminium surfaces coated with different TRLs (dimethyl sulfoxide, cyclohexane and hexadecane) subjected to Tpel = 4°C in an environment of Tair = 25°C, RH = 15%. b, SEM images (imaged at an angle of 45°) of photopolymer replica moulds delineating the surface morphologies of different TRLs (at Tpel = -5°C, Tair = 22°C, RH = 11%). Scale bars, 25 µm. c, Images showing the typical condensation behaviour on the corresponding solidified TRL surfaces (at Tpel = -15°C, Tair=25°C, RH=80%). Scale bars, 200 µm. SD appeared to have a condensed film on its surface. Condensing droplets on SCh surface manifested a distinctive 'stick/slip' motion while they were virtually immobile on SH surface. d, Surface roughness and condensation-icing dynamics of various S-TRLs cooled to Tpel= -15°C in a high humidity (80% RH) environment.The 'freezing initiation time' depicts the occurrence of first condensed droplet freezing event in the field of view, while the 'total freezing delay time' is representative of the time it took for all the condensed droplets on the S-TRL surface to freeze. The roughness characterization for each of the bare S-TRL surface was performed using an optical profilometer in a very low RH (5%) environment to prevent condensation. 'Average roughness' is the arithmetic mean of the absolute height shifts about the mean reference plane while 'Z-roughness' is indicative of the distance between the highest peak and lowest valley on the surface. The error bars (both left and right) denote standard deviations, obtained from experimental measurements on different TRLs repeated at least four times each. Analysis of S-TRL surface roughness (left) elucidated that smaller the S-TRL surface roughness, higher is the freezing delay.

Figure 4 |

 4 Figure 4 | Anti-icing potential of TRL infused textured surfaces. a, Regime map showing the mobility of a cooled (0°C) water droplet (10 µL) on TRL (pentadecane) infused textured superhydrophobic surface maintained above its Tmp (I), TRL infused textured superhydrophobic surface maintained below its Tmp (II) at Tpel = 2°C, TRL infused textured hydrophilic surface maintained above its Tmp (III) and TRL infused textured hydrophilic surface maintained below its Tmp (IV) at Tpel = 2°C. Experiments were carried out on samples (6.45 cm 2 in size) tilted at 45° in an environment of 23°C and 24% RH. b, Time-lapse images of condensation-icing experiments conducted at Tpel = -7°C in an environment of 60% RH on vertically mounted bare textured superhydrophilic surface (SPS), lubricant infused textured superhydrophobic surface (LIS) and TRL infused hydrophilic surface. Each substrate was 6.45 cm 2 in size. c, Plot showing the corresponding surface ice coverage evolution with time on different test substrates at -7°C and 60% RH. d, Ice-repellency of a TRL (pentadecane) infused textured superhydrophobic surface compared to a nano-textured superhydrophobic surface. A dyed cold water droplet (70 µL) slides on the TRL infused surface under the action of gravity while a similar droplet remains strongly pinned on a superhydrophobic surface. The experiments were performed outdoors in Chicago, Illinois on 14th March, 2017 when the ambient temperature and relative humidity were -5°C and 65% respectively. e, Time-lapse images exhibiting the potential of TRLs to self-heal from critical mechanical damage (~400 µm wide, ~800 µm deep) inflicted by a sharp metal blade. Experiments were carried out on SCt tilted at 90°, subjected to Tpel = 5°C and environmental RH = 80%.

Acknowledgements

The fabrication of Silicon surfaces was performed at Pritzker Nanofabrication Facility (University of Chicago). The SEM of the samples was obtained at the Electron Microscopy Service (Research Resources Centre, UIC). We thank Dr. Dong Jin Kang for obtaining the SEM of samples and Ms. Sameera Khan for providing us with etched Silicon samples. We thank Mr. Eric Schmidt and UIC machine shop for their valuable help in fabricating the experimental setup. We thank Mr. Mike Bailey from Keyence Corporation for assisting in obtaining the surface roughness of solidified TRLs. S.A. sincerely thanks Prof. Kripa Varanasi for the workspace where some preliminary experiments were conducted. S.A. thanks the financial support of Branco Weiss Fellowship, UIC College of Engineering and NSF (CBET-1644815).

Author Contributions

Additional Information

Supplementary information is available in the online version of the paper. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S. A. (sushant@uic.edu).

Competing Interests

The authors declare that they have no competing interests. S.A. is involved in commercialization efforts for the technology presented here through UIC Office of Technology Management.


Gabin Koto N'gobi

Basile Kounouhéwa

Clément Kouchadé

Romuald Anago

Daniel Beysens
email: daniel.beysens@espci.fr

Perception of Dew by Cereal Growers in Semi-Arid Climate (Guéné, North Benin)

Keywords: Dew, Survey, Cereal Growers, Semi-Arid Area, Guéné, Northern Benin 1

In the context of global warming, a study was performed of the sociological perception of dew as alternate source of water by cereal's growers in Guéné (semi-arid region, north Benin).

the most vulnerable to extreme climate variability [START_REF] Field | Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation[END_REF]. Population is indeed mostly rural with agriculture as the main source of income. This is especially true in the extreme northern part of Benin, where water is often scarce. In these regions, growers are said to produce several varieties of cereals every year (maize, sorghum and millet) thanks to a traditional knowledge in dew water management, even though the yields are low. Unfortunately, these traditional methods of agricultural and water management are often lacking of scientific knowledge and never cited.

Dew is an ubiquitous phenomenon in which water vapor condenses on various types of natural or artificial surfaces, such as grass, crops, roofs or vehicles. Dew occurs at night when humid air condenses on surfaces as its temperature falls below the dew point temperature of the surrounding atmosphere. Substrate cooling is ensured by the nocturnal radiative deficit with atmosphere. Low wind speed and clear skies are favorable to dew events. Dew formation has been the object of scientific researches over many years [START_REF] Beysens | Dew Water[END_REF]. There is abundant literature reporting that, even though dew amount is small, it can be beneficial to humans [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF]. Dew water can be used as fresh water and can give additional water to plants and desert animals, not only in arid and semi-arid areas, but also in humid regions where drought can suddenly occur for more than weeks or months during the rainy seasons. Dew, however, can cause plants diseases through stagnant dew water on their surfaces. Dew can indeed promote the development of pathogenic gems and increasing disease frequency in crops [START_REF] Fang | A review on eco-hydrological effects of condensation water[END_REF].

To our knowledge, no sociological studies have been conducted so far to explore the use of dew water in agriculture. It is thus worth looking more closely at these aspects of human adaptation as far as dew water is concerned. Extreme weather and climate events have major negative impacts on food security and economy income. These realities illustrate the need to understand the sociological knowledge of dew in relation with cereal growth in view of its possible utilization as alternate or adaptive technology for improving agriculture and mitigate climate extreme impacts. As a matter of fact, since the 1990's, experimental studies have been conducted on dew collection throughout Benin, using efficient conical dew condensers [START_REF] Awanou | Study of natural condensation of atmospheric humidity[END_REF][START_REF] Koto N'gobi | Faire de l'eau à partir de l'air[END_REF].

The following is thus concerned with the perception of dew by the grower's rural population through a statistical investigation at Guéné, a typical village in a semi-arid region of northern Benin. The objective of this study is to highlight the understanding of cereal's growers in Guéné concerning the significance of dew in their daily agricultural activities. In particular, correlation analyses are performed between (i) the responses and the respondent gender, (ii) the responses and the respondent ages and (iii) the responses and the type of sown cereals.

MATERIALS AND METHODS

Site description

The survey was performed in the village of Guéné (∼1,560 km 2 ), located in West Africa in the northern part of Benin. Guéné is located within about 750 km from the economical capital city Cotonou, at 11˚20'-12˚ latitude north and 2˚5'-3˚05' longitude east (Fig. 1). The elevation is about 250 m a.s.l. Guéné is characterized by a north Sudanian climate with two different seasons per year [START_REF] Lélé | Variability of Intertropical Front (ITF) and rainfall over West African soudano-sahel[END_REF]. The rainy season period often lasts from May to September; it is followed by a long and dry season from October to April. Harmattan is a dry and dusty wind, which blows north-east, from the Sahara desert and frequently reaches Guéné between November and February [START_REF] Lélé | Variability of Intertropical Front (ITF) and rainfall over West African soudano-sahel[END_REF]. Guéné is at about 30 km from the south Niger River. The climate is semi-arid and the area's precipitations highly vary in both volume and spatial distribution from year to year. Alike certain western African countries, the Guéné area suffers from unpredictable extreme weather conditions, heavy floods and droughts. Mean annual rain amount and temperature are respectively ∼750 mm and ∼30.6°C. December is the coldest month (∼20.3°C) and April is the hottest month (∼42.1°C).

Data collection and analysis methods

Data are collected during an investigation carried out in Guéné from July 19, 2014 to July 26, 2014. For this investigation, 10 data collectors, natives of Guéné, assisted in filling out the questionnaires after talking with the respondents. The main reasons for using natives of Guéné are the following. (i) Facilitate the immersion of the investigators in the population, (ii) ensure confidence between the growers and the interviewers, a necessary condition to maintain credibility of their information and (iii) guarantee that the collectors will rapidly master the questionnaires thanks to their good education level.

The interview is based on "face-to-face" conversations, using the language chosen by the farmers (French or Dendi, a local language). The main indicators or information that the questionnaires aim to collect are organized in four main aspects. (1) Demographic information about the growers, particularly their name, gender, age, level of education, the type of cereals sown, their experience as producer of cereals, etc. Their ages were divided in three intervals: After the collection and quality-control, the respondent's data were transferred to a database in a saving system "Census and Survey Processing System (CSPro 5.0)". A double entry was done in order to correct the eventual data entry mistakes. Then the tabulations and the statistical analyses were performed simultaneously with SPSS for Windows (SPSS Inc., Chicago, Standard version 17.0) and STATA statistical software. Descriptive analysis in terms of frequency and percentage were performed on questionnaires data.

Samples presentation

The investigated sample is constituted of 100 representative producers of cereals in which 97 growers are mainly from Guéné and 3 other growers from neighboring villages. The sample counts 93 men and 7 women. Unfortunately, only 7 women had accepted to answer the questionnaires. The majority of the interviews were carried out in Dendi language (94%), since nearly 78% of the growers had a level of instruction that does not exceed the primary level. Table 1 presents the characteristics of the sample.

The mean age of the growers is ∼37 years, with an average of 20 years in agriculture practice. The mean surface allocated to cereals growth in the sample is 7.2 ha, with a minimum area of 1 ha and a maximum area of 60 ha. The sample represents well the diversity of main cereal tendencies in the region. Among the respondents, maize is cultivated by 99%, Sorghum by 76% and millet by 58%. Only 1% of the farmers produce "fonio", a regional cereal. All producers report that they cultivate the cereals in the rainy season. Only 9% of the growers produce cereals for sale, 24 % cultivate for subsistence while 64% of the farmers produce cereals for both trade and subsistence. The results are presented, analyzed and discussed in the sections below.

RESULTS

Results are analyzed regarding the following four main points: (i) knowledge of seasons, rain and wind; (ii) farmers experience of dew process in their environment, its utility and utilization; (iii) attitudes towards adoption of new technologies (dew harvesting) and (iv) analysis of answers in view of respondents' gender, ages and type of cereals they cultivate.

Farmers knowledge of seasons, rain and wind

Water is an important factor that determines the success of agriculture in general and cereals production in particular. In order to facilitate the dialogue, some of the questions were intentionally very basic.

It is obvious that most of the farmers master the rainy and dry seasons of the study area because they are native of the village and have lived there for long. However, different answers are obtained when it is asked «in which months does each of the seasons usually start or end? » The majority agrees that the rainy season usually begins in May (86%) and ends in October (74%). The dry seasons often starts in November (51%) and ends in April (62%).

To the question whether rain is often sufficient for cereals growth, farmers answer that rain is not always sufficient (73%). A majority of the growers (99%) declares that their cereals are often victim of rain shortages during the rainy season, which can last up to 23 days on average. In this case, to compensate for the lack of water, 44% declare that they rely on dew occurrence in their fields. Otherwise, for wind regimes, the growers believe that wind is more abundant in the morning (48%) and during night (46%).

Farmers have thus a good knowledge of their environment. What they know about dew is discussed below.

Dew: knowledge, utility and various utilizations

All the growers (100%) have their own idea of what dew is, because they observe it for a long time. They try accordingly to give a definition of dew. For instance, most of them think that «dew is water, or drops of rain fallen down from the sky and usually observed in the early morning on objects such as vegetables, canopy, plants leaves, shrubs, etc.». Interestingly, they also notice (81%) that dew is different from fog.

When one asks in which month dew is mostly observed, different responses are given.

According to 45% of the investigated people, dew is abundant during August, 83% declare that dew is most abundant in September and 66% declare that October is the month in which dew is the most abundant in Guéné. In addition, 80% of the growers declare that dew can be observed in the morning; in contrast 46% of them declare that dew is usually observed during the night. Growers also say that the substrates on which they often observe dew are: leaves of plants (100%), roofs of the houses (44%), soil (25%) and vehicles (19%). In addition, the growers highlight factors inhibiting dew formation. For example, they cite a hot soil temperature during night (44%), cloud cover (34%) and large wind speed (31%). They also indicate that dew formation can vary dependently from the season (42%).

From the survey, regarding the utility of dew for cereals growth, respondents' opinion is almost unanimous (99%) in saying that dew plays an important role for cereals growth. Some declarations were mentioned: «after dew events, cereals plants or vegetables that greatly need little water come back to life», «dew helps plants by wetting them, bringing them water through soil and humidity when rain is lacking or in period of long drought», «dew can help certain plants to grow, even when there is a lack of rain», «dew helps plants in difficult growing times», «it contributes to reinforce plant's roots», «dew permits several cereals' leaves to become green», «dew helps the survival and the growth of plants», «dew helps plants to finish their vegetative growth», etc.

Otherwise, when one asks the farmers in which phase dew is most useful, regarding the six main stages of cereals growth, 64% declare that dew is more useful for cereals during the maturation phase (called physiological maturity phase), 52% think that dew is more useful during the stage of flowering, 32% think that dew is more important in the raised up phase, 10% think that dew is most important for the germination phase. For 2% of the growers, dew is of benefit for cereals during the stages of harvest (tasseling) and the stage of senescence (1%).

In contrast to the positive perceived benefits of dew, some growers declare that dew could be harmful for cereals (17%). For example, some of them say that dew is especially harmful for the «abandoned harvests», «it is harmful for fruits especially when they fall down» and «dew can also contribute to turn black certain cereals seedlings, such as millet and sorghum». In addition, when one asks them about the particular stage of cereals growth in which dew could be harmful, the growers believe that dew is more harmful in the harvest stage (11% of the sample or 65% of those who declared that dew could be harmful to plants).

Finally, dew is thought to have also harmful effects on cereals in the stage of maturation (4%, or about 24% of those who declared that dew could be harmful to the growth of cereals).

Concerning dew utilization, 80% of the growers declare that they account for dew before and during the growth of their cereals. Close to 80% of the growers affirm that, in their own experience, dew has assisted their cereals growth. Most growers illustrate the role of dew by affirming that «dew helps cereals in the periods of drought or during rain shortage», «it brings humidity to the plants», «dew impact is especially great after the last weeding toward the end of the rainy season», «dew improves cereals good maturation», «it comes in support to the cereals, two or three days after a rainy day», «dew contributes to the growth of cereals as sorghum, millet, maize in period of rainy break».

When one asks them what source of water they substitute for rain when lacking or not sufficient, 56% of growers declare to use water from wells for irrigation, 44% declare to count on dew. They gather wild grasses around cereals plants, dew condensed from the leaves into the gathered grasses and reach the roots of the plants. They also think that plants absorb dew from atmosphere directly.

Attitudes towards adoption of new technology for dew water

A number of questions were asked to the growers in view of the promotion of a new technology that could help to collect and store dew water for utilization in agriculture. It was asked «whether they think possible to collect dew water?», «would they agree to adopt a technology that would permit them to collect dew water and in what conditions could they use dew water?». Only 15% of the respondents believe that it is possible to collect dew water using materials. They proposed many ways to collect it. Among the possibilities of dew harvesting, they answered that «bowls» or «calabashes» can be deposited for recovering dew at night or early morning. They also mentioned «enter in the moistened shrubs and let their cloths absorb dew that may be squeezed from cloths», «utilize cloths to collect dew from roofs or plant's leaves». Moreover, 87% say that they can adopt new technology that could help them to collect dew, at least if it is feasible and unexpansive. However, they remain doubtful regarding the efficiency of any method for collecting a sufficient amount of dew.

Analysis of responses regarding ages, gender and the kind of cultivated cereals

Table 2 presents the results of the survey taking into account the way that farmers respond in the three different groups of ages (G1, G2 and G3) and the gender (male or female). Several points are concerned from the table. Maize is the cereal most sown regardless the group of ages (100% G1, 98% G2 and 99% G3) and the gender (98% male, 100% female) of the respondents. However, regarding the sufficiency of rain to cereals growth, 75.3% and 42.9% of males and females, respectively, agree, no matter what age they are (80.5% G1, 63.7% G and 71.4% G3), that rain is insufficient. So 98.9% and 100% respectively of males and females, regardless the ages (100%, 98%, 100%) are aware of rain interruptions during the rainy seasons. Furthermore, in order to compensate the lack of water during those rain interruptions, most of the elders (71.4% G3,) believe that dew is mostly used by cereals to mitigate water scarcity. However, 71.4 % of females of the same group of age have opposite opinion.

Even if a significant proportion of females (100%) and males (79.6%) think that dew is different from fog, female (42.9%) think that dew is not abundant in early mornings against males (82.8%) regardless their ages, respectively 80.5% in G1, 83.7% in G2 and 71.4% in G3.

However, females (100%) believe that dew is abundant at night time.

All the respondents (100%) believe that dew can form on grasses. Coming to the identification of the main factors affecting dew occurrence: wind, cloud cover, soil temperature and seasons, respectively, 33.3%, 34.3%, 46.2% and 38.7, answer that these factors affect dew formation. Both females (100%) and males (78.5%), respectively, estimates that dew occurrence is one of the main source of water during the seeding seasons for cereals, no matter in which group of age they are (82.9% G1, 75.5% G2 and 85.7 G3). 79.6% of male and 85.7 of female agree that dew helps cereal's growth.

Concerning the responds regarding the type of cereal the farmers grow, one can find that farmers in Guéné do not sow other cereals out of sorghum, millet, maize or fonio. The statistics show that the majority of the farmers sow maize (99%) and sorghum (58%), indicating that there is less influence of the farmers who sow millet (58%) and fonio (1%) in the responses. The respondents (80%) who cultivate maize plan a probable contribution of dew before they sow their cereals and those (87%) who sow sorghum agree to adopt any technology of dew collection in their farm. But 49% of maize and sorghum sowers require an efficient technology. 99% of the two cereal sowers claim that dew contribution is spontaneous in plant growth especially at the ripening (64%) and flowering (52%) stages of growth.

However 69% think that dew can be harmful. The answers from this category of investigation indicate that 100% of the farmers sowing both maize and sorghum know dew and fog and 76% of them indicate that the two phenomena are different. On the other hand, 66% think that dew can be used for irrigation.

Even if the percentage can somewhat vary from a group of age or the gender to another, all the answers to the main questions concord when the analyses are performed taking into account the ages and the gender of the respondents. However, the correlation of the responses from the farmers who sow sorghum and millet indicate that the answers depend on these sowers.

CONCLUDING REMARKS

The recognition of rain shortage constitutes a core knowledge that makes growers sow their cereals at the best moment of the rainy season to prevent unpredictable rain shortages (99% of the respondents are victim of rain shortage). For that purpose, they rely on dew as an alternate source of water for their cereals, suggesting that dew directly influences water management for cereals growth: 99% of the respondents agree that dew water is beneficial to cereals growth. These responses suppose that the majority of farmers, in their experience for agriculture, notice the diminution of water resources and also relate meteorological parameters (wind, rain, temperature) to dew formation. The high percentage regarding the questions related to the seasons is in agreement with scientific literature data [START_REF] Lélé | Variability of Intertropical Front (ITF) and rainfall over West African soudano-sahel[END_REF] concerning the region.

The definitions and justifications that growers give to illustrate how they understand the dew process contain the main scientific terms to build a real definition of what is dew.

They mention words like "high air humidity", "night time", "and early morning", "clear sky, leaves"," plants "," dew substrates and air temperature". Even if they do not mention the dew point temperature (the temperature at which water vapor reaches 100% relative humidity and can condense into liquid), the terms that they use, in trying to give dew definition, are mainly used to build an exact scientific definition of dew. Growers also differentiate dew from fog, using the same wording as in literature [START_REF] Shemenauer | Fog collection's role in water planning for developing countries[END_REF]. But they mistake dewfall as rain droplets falling from the sky. This is presumably because they usually observe abundant dew in September (83%), a transition month between the end of rainy season and the beginning of dry season.

Confusion could be made between rain droplets and dew drops condensed on plant's leaves, on which 100% declare to often observe dew. Also the confusion could be explained by their low academic instruction level, which may make them misunderstand the questions to indicate exactly the difference between rain and dew. Nevertheless, respondents affirm that dew is not fog, as declared by 81% of them regardless of their gender or ages (Table 3). But when one considers the responses they give in view of the sown cereals, the growers responses depend mainly on maize (99%) and sorghum (58%) sowers. The answers indicate that 100% of the farmers sowing both maize and sorghum know dew and fog, which are two different phenomena. On the other hand, they think that dew can be used for irrigation. In addition, farmers indicate that cloud cover and high wind speed inhibit dew formation, as noted in literature [START_REF] Field | Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation[END_REF][START_REF] Ben-Asher | Dew is a major factor affecting vegetation water use efficiency rather than a source of water in the eastern Mediterranean area[END_REF]. They also report that the period from August to October is beneficial to dew formation. Meteorological observations in Guéné [START_REF] Lélé | Variability of Intertropical Front (ITF) and rainfall over West African soudano-sahel[END_REF] show that this period coincides with the transition period from rainy to dry season. Hence, the crops that are delayed because of lack of rain can benefit from dew season to finish their growth cycle and ripen.

Based on their experience, most of the growers thus confirm that dew contributes in cereal growth, particularly in flowering and maturation stage (52% and 64%, respectively), where a lack of water is critical for fruit formation. While they do not precisely know the process by which dew forms from humid air and is utilized by plants, farmers utilize dew for cereals by enhancing it accumulation around plant's roots. The majority of farmers declare to forecast (80%) and integrate dew periods in their annual agricultural activities. Growers think that dew and humidity around cereals allow their leaves to be green thanks to the contribution of dew to plant photosynthetic activities. Dew is said to be a major factor affecting water use efficiency in the water-stressed regime, in agreement with literature [START_REF] Ben-Asher | Dew is a major factor affecting vegetation water use efficiency rather than a source of water in the eastern Mediterranean area[END_REF]. Growers also claim that dew is an important source of moisture in the air in semi-arid areas (like Guéné) and creates the best conditions for plants growth on early morning for two to three hours after sunrise. It is why 80% experienced farmers take account of dew before and during cereals growth. This practical knowledge of dew formation and dew effects on plants is important for agriculture in general and for cereals in particular at Guéné. On the other hand, some growers also indicate that dew can be harmful for plants and cereals seedling, in accordance with literature [START_REF] Tomaszkiewicz | Dew as a sustainable non-conventional water resource: a critical review[END_REF]. Growers highlight the interest of having a technology for dew collection but are uncertain about the water amount that could be collected.

Eventually, the study concludes that farmers' perceptions of dew mirror the scientific literature, though their perceptions are based on practical experience. The grower's opinion indeed reflects their life and agricultural work conditions, characterized by a keen knowledge of meteorological environment and poverty of means and life conditions. One notes that the responses to the main questions are not related to gender and ages as shown in Table 3. All the farmers respond to the different questions in the same way, however the responds vary dependently from the sown cereals.

ACKNOWLEDGMENT

Figure and Table Legends

[

  19 -35[ years (G1), [35 -55[ years (G2) and [55 -70] years (G3), as frequently appeared in the sample. (2) Specific information from the respondents regarding climatic parameters that often influence the production yield. (3) Information concerning dew knowledge (regarding the utility of dew and their experience of dew water contribution in agriculture). (4) Information on grower attitudes concerning the adoption of new technologies for dew harvesting.

Fig. 1 .

 1 Fig. 1. (a) Location of Benin in West Africa, (b) Location of Malanville region in Northern Benin, (c) Location of Guéné area in Malanville region.

Figures

  Figures

Fig. 1

 1 Fig. 1. (a) Location of Benin in West Africa, (b) Location of the Malanville region in Northern

  Fig. 1. (a) Location of Benin in West Africa, (b) Location of the Malanville region in Northern Benin, (c) Location of the Guéné area in the Malanville region

Table 1 .

 1 Summary of demographic and farming characteristics.

Table 2 .

 2 Results of the survey taking into account the knowledge of seasons, the role of dew in cereals growth, the factors affecting dew amounts and the farmers attitude in adapting anydew harvesting technology.

Table 3 .

 3 Results of the survey taking into account the gender and the ages of the respondents.

Table 2 .

 2 Results of the survey taking into account farmers knowledge of: seasons, dew role in cereals growth, factors affecting dew amounts and farmers attitude of adapting any dew harvesting technology

	Rain season start month	Number	Percentage	Valid Percentage
	Avril	1	1	1.0
	Mai	86	86	86.0
	June	12	12	12.0
	Rain season end month	Number	Percentage	Valid Percentage
	June	1	1	1.0
	September	20	20	20.0
	October	74	74	74.0
	November	4	4	4.0
	Dry season start month	Number	Percentage	Valid Percentage
	September	6	6	6.0
	October	34	34	34.0
	November	51	51	51.0
	December	7	7	7.0
	Dry season end month	Number	Percentage	Valid Percentage
	February	1	1	1.0
	March	12	12	12.0
	April	62	62	62.0
	May	20	20	20.0
	June	3	3	3.0
	Rain sufficiency during rainy seasons
		Number	Percentage	Valid Percentage
	Yes	27	27	27.0
	No	73	73	73.0
	Cereals are victims of shortage during rain season
		Number	Percentage	Valid Percentage
	Yes	99	99	99.0
	No	1	10	1.0
	Source of water during shortage in rainy season
		Number	Percentage	Valid Percentage
	Backwater No	100	100	100.0
	Yes	0	0	0.0
	Well Yes	2	2	2.0
	No	98	98	98
	Dew Yes		44	44.0
	No		56	56.0
		Wind occurrence period
	None period Yes	2	2	2.0
	No	98	98	98.0

Table 2 .

 2 Results of the survey taking into account the gender and the ages of the respondents

		Gender (%)				Ages (%)
		Male		Female		19-35 Years	35-55 Years	55-70 Years
	Parameters	Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
	Cultivated Cereals
	Sorghum	75.3 24.7	85.7 14.3	75.6	24.4 71.4	28.6	100.0	0.0
	Millet	59.1 40.9	42.9 57.1	41.5	58.5 65.3	34.7	85.7	14.3
	Maize	98.

We thank the International Foundation for Science (IFS) and the International Development Research Center (IDRC) and Stockholm Environment Institute (SEI) for their research grant support.