D. Jakubczyk

Evaporation of freely suspended single droplets: experimental, theoretical and computational simulations

Evaporation is ubiquitous in nature. This process influences the climate, the formation of clouds, transpiration in plants, the survival of arctic organisms, the efficiency of car engines, the structure of dried materials and many other phenomena. Recent experiments discovered two novel mechanisms accompanying evaporation: temperature discontinuity at the liquid-vapour interface during evaporation and equilibration of pressures in the whole system during evaporation. None of these effects has been predicted previously by existing theories despite the fact that after 130 years of investigation the theory of evaporation was believed to be mature. These two effects call for reanalysis of existing experimental data and such is the goal of this review. In this article we analyse the experimental and the computational simulation data on the droplet evaporation of several different systems: water into its own vapour, water into the air, diethylene glycol into nitrogen and argon into its own vapour. We show that the temperature discontinuity at the liquid-vapour interface discovered by Fang and Ward (1999 Phys. Rev. E 59 417-28) is a rule rather than an exception. We show in computer simulations for a single-component system (argon) that this discontinuity is due to the constraint of momentum/pressure equilibrium during evaporation. For high vapour pressure the temperature is continuous across the liquid-vapour interface, while for small vapour pressures the temperature is discontinuous. The temperature jump at the interface is inversely proportional to the vapour density close to the interface. We have also found that all analysed data are described by the following equation: da/dt = P(1)/(a + P(2)), where a is the radius of the evaporating droplet, t is time and P(1) and P(2) are two parameters. P(1) = -λΔT/(q(eff)ρ(L)), where λ is the thermal conductivity coefficient in the vapour at the interface, ΔT is the temperature difference between the liquid droplet and the vapour far from the interface, q(eff) is the enthalpy of evaporation per unit mass and ρ(L) is the liquid density. The P(2) parameter is the kinetic correction proportional to the evaporation coefficient. P(2) = 0 only in the absence of temperature discontinuity at the interface. We discuss various models and problems in the determination of the evaporation coefficient and discuss evaporation scenarios in the case of single- and multi-component systems.

Temperature dependence of the evaporation coefficient of water in air and nitrogen under atmospheric pressure: study in water droplets.

The evaporation coefficients of water in air and nitrogen were found as a function of temperature by studying the evaporation of a pure water droplet. The droplet was levitated in an electrodynamic trap placed in a climatic chamber maintaining atmospheric pressure. Droplet radius evolution and evaporation dynamics were studied with high precision by analyzing the angle-resolved light scattering Mie interference patterns. A model of quasi-stationary droplet evolution accounting for the kinetic effects near the droplet surface was applied. In particular, the effect of thermal effusion (a short-range analogue of thermal diffusion) was discussed and accounted for. The evaporation coefficient alpha in air and in nitrogen were found to be equal. The alpha was found to decrease from approximately 0.18 to approximately 0.13 for the temperature range from 273.1 to 293.1 K and follow the trend given by the Arrhenius formula. The agreement with condensation coefficient values obtained with an essentially different method by Li et al. [Li, Y.; Davidovits, P.; Shi, Q.; Jayne, J.; Kolb, C.; Worsnop, D. J. Phys. Chem. A. 2001, 105, 10627] was found to be excellent. The comparison of experimental conditions used in both methods revealed no dependence of the evaporation/condensation coefficient on the droplet charge nor the ambient gas pressure within the experimental parameters range. The average value of the thermal accommodation coefficient over the same temperature range was found to be 1 +/- 0.05.

Coefficients of Evaporation and Gas Phase Diffusion of Low-Volatility Organic Solvents in Nitrogen from Interferometric Study of Evaporating Droplets

Evaporation of motionless, levitating droplets of pure, low-volatility liquids was studied with interferometric methods. Experiments were conducted on charged droplets in the electrodynamic trap in nitrogen at atmospheric pressure at 298 K. Mono-, di-, tri-, and tetra(ethylene glycols) and 1,3-dimethyl-2-imidazolidinone were studied. The influence of minute impurities (<0.1%) upon the process of droplet evaporation was observed and discussed. The gas phase diffusion and evaporation coefficients were found from droplet radii evolution under the assumption of known vapor pressure. Diffusion coefficients were compared with independent measurements and calculations (in air). Good agreement was found for mono- and di(ethylene glycols), and for 1,3-dimethyl-2-imidazolidinone, which confirmed the used vapor pressure values. The value of equilibrium vapor pressure for tri(ethylene glycol) was proposed to be 0.044 +/- 0.008 Pa. The evaporation coefficient was found to increase from 0.035 to 0.16 versus the molecular mass of the compound.

Simultaneous determination of mass and thermal accommodation coefficients from temporal evolution of an evaporating water microdroplet

Scattering of coherent light by an evaporating droplet of pure water several micrometres in size was investigated. The droplet was levitated in an electrodynamic trap placed in a small climatic chamber. The evolution of the droplet radius and the evolution dynamics were investigated by means of analysing the scattering patterns with the aid of Mie theory. A numerical model of droplet evolution, incorporating the kinetic effects near the droplet surface, was constructed. Application of this model to the experimental data allowed us to determine the mass and thermal accommodation coefficients to be αC = 0.12 ± 0.02 and αT = 0.65 ± 0.09, respectively. This model enabled us to determine with high precision the temperature evolution of the droplet and the relative humidity in the droplet vicinity.

Temperature Dependence of Evaporation Coefficient for Water Measured in Droplets in Nitrogen under Atmospheric Pressure

Abstract The evaporation and the thermal accommodation coefficients for water in nitrogen were investigated by means of the analysis of evaporation of pure water droplet as a function of temperature. The droplet was levitated in an electrodynamic trap placed in a climatic chamber. The levitation time was in the range of seconds, which corresponds to the characteristic time scales of cloud droplet growth. Droplet radius evolution and evaporation dynamics were studied as a function of temperature, by analyzing the angle-resolved light scattering Mie interference patterns. A model of droplet evolution, accounting for the kinetic effects near the droplet surface, was applied. The evaporation coefficient for the temperature range from 273.6 to 298.3 K was found to be between 0.054 and 0.12 with a minimum of 0.036 ± 0.015 seemingly coinciding with water maximum density at 277.1 K. The average value of thermal accommodation coefficient over the temperature range from 277 to 289 K was found to be 0.7 ± 0.2.

Study of microscopic properties of water fullerene suspensions by means of resonant light scattering analysis

Scattering of coherent light by a droplet of water fullerene suspension was investigated. Two light wavelengths were used simultaneously. The evolution of the radius and refractive index of a droplet was examined. Resonant scattering was detected and analysed by means of a simple model and some conclusions were drawn on the microscopic properties of the suspension. The study was supplemented with atomic force microscopy measurements of samples obtained by drying the suspension.

Formation of Highly Ordered Spherical Aggregates from Drying Microdroplets of Colloidal Suspension

The formation of highly ordered spherical aggregates of silica nanoparticles by the evaporation of single droplets of an aqueous colloidal suspension levitated (confined) in the electrodynamic quadrupole trap is reported. The transient and final structures formed during droplet evaporation have been deposited on a silicon substrate and then studied with SEM. Various successive stages of the evaporation-driven aggregation of nanoparticles have been identified: formation of the surface layer of nanoparticles, formation of the highly ordered spherical structure, collapse of the spherical surface layer leading to the formation of densely packed spherical aggregates, and rearrangement of the aggregate into the final structure of a stable 3D quasi-crystal. The evaporation-driven aggregation of submicrometer particles in spherical symmetry leads to sizes and morphologies of the transient and final structures significantly different than in the case of aggregation on a substrate. The numerical model presented in the article allows us to predict and visualize the observed aggregation stages and their dynamics and the final aggregates observed with SEM.

Local-field resonance in light scattering by a single water droplet with spherical dielectric inclusions.

Light scattering by an evaporating water droplet several micrometers in size with spherical dielectric inclusions was investigated. The evolution of the droplet radius and the effective refractive index was determined. A deviation from predictions by standard effective-medium theories in the form of a resonance was encountered. Simple analysis of the phenomenon was conducted, and a qualitative explanation was proposed.

High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets.

Models describing evaporation or condensation of a droplet have existed for over a century, and the temporal evolutions of droplet radius and temperature could be predicted. However, the accuracy of results was questionable, since the models contain free parameters and the means of accurate calibration were not available. In previous work (Hołyst et al. Soft Matter 2013, 9, 7766), a model with an efficacious parametrization in terms of the mean free path was proposed and calibrated with molecular dynamics numerical experiment. It was shown that it is essentially possible to determine reliably the temperature of a steadily evaporating/condensing homogeneous droplet relative to ambient temperature when the evolution of the droplet radius is known. The accuracy of such measurement can reach fractions of mK. In the case of an evaporating droplet of pure liquid, the (droplet) temperature is constant during the stationary stage of evaporation. In this paper, we show that, in many cases, it is also possible to determine the temporal evolution of droplet temperature from the evolution of the droplet radius if the droplet (initial) composition is known. We found the droplet radius evolution with high accuracy and obtained the evolution of droplet temperature (and composition) for droplets of (i) a two-component mixture of pure liquids; (ii) solutions of solid in liquid, one that is non-surface-active and another that is; and (iii) suspensions of non-light-absorbing and light-absorbing particles.

Optical diagnostics of surfaces of single evaporating liquid microdroplet of solutions and suspensions

Experimental elastic-scattering characteristics of single evaporating liquid microdroplet of solution and suspension are reported. The microdroplets studied were composed of: (i) silica (SiO2) nanoparticles (225 nm radius) dispersed in diethylene glycol (DEG) liquid suspension (ii) DEG and Sodium dodecyl sulfate (SDS) solution, and (iii) SiO2 nanoparticles dispersed in DEG and SDS solution. We observed regular Mie type fringes from (i), (ii) and (iii) at the initial stages of the evaporation process followed by intensity fluctuations (speckles) for (i) and surface reflections (blinking of scattered light intensities) for (ii) during the inclusions surface layer formation. For (iii), Mie-type fringes, and a mixture of surface reflections (blinking of scattered light intensities) and intensity fluctuations (speckles) was observed. The changes in the intensities and polarization of the scattered light showed characteristic stages of evaporation driven processes occurring at the droplet surface. The observed phenomenon carry information about the inclusions’ mean distances, size, and stages of aggregation of SiO2 nanoparticles and crystallization of SDS nanocrystallites on the droplet surface. Additionally, we deposited samples of the final dried composite microobject on a silicon substrate and analyzed with SEM. The study provide different surface diagnostic methods of configuration changes in complex systems of nano-and microparticles evolving at the sub-wavelength scale and serves as an alternative method for studying stages of droplet with submicron inclusions evaporation processes.