Marcin Zientara

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.

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.

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.

Light scattering by microdroplets of water and water suspensions

We investigated elastic light scattering on isolated evaporating droplets of radius between 1 and 20 tim. The droplets were either pure water or a water based suspension they carried electric charge and were contained in an electrodynamic trap. The evolution of the trapped droplet was investigated by means of scatterometry. A numerical model of such evolution incorporating the kinetic effects near the droplet surface was constructed. For water droplets with spherical inclusions the radius as well as effective refractive index was determined. An essential deviation in the form of a resonance from predictions by standard effective medium theories was encountered. Simple analysis of the phenomenon was conducted and a qualitative explanation is proposed. Similar analysis was applied to fullerene water suspension droplets in order to investigate the real part of refraction index.

Determination of mass and thermal accommodation coefficients from evolution of evaporating water droplet

Evaporation of a droplet of pure water several micrometers in size was investigated. The droplet was levitated in an electrodynamic trap placed in a small climatic chamber. The evolution of the droplet and the evolution dynamics was studied by analyzing the coherent light scattering patterns with the aid of Mie theory. A numerical model of droplet evolution incorporating the kinetic effects near the droplet surface was constructed. By applying this model to the experimental data the mass and thermal accommodation coefficients were determined to be αC=0.12±0.02 and αT= 0.65±0.09. This model enabled to find the droplet temperature evolution and the relative humidity in the droplet vicinity with high precision as well.

Investigation of the evolution of charged water droplets in the electrodynamic trap

Water droplets of radius between 1 and 20 μm carrying electric charge were individually contained in an electrodynamic trap. The trap was kept in a small climatic chamber, which enabled imitating the temperature and humidity conditions of the lower troposphere. the sign of the charge of the droplet could also be controlled. for the humidity close to saturation, droplet injected into the trap was evaporating for a few seconds and could either undergo a Coulomb explosion and escape from the trap or stabilize at the size of a few μm. In such case the final droplet readius depended on the value of the droplet charge and of the humidity. The evolution of a trapped droplet was investigated by means of scatterometry. A numerical model of such evolution, incorporation the kinetc effects near the droplet surface was constructed. By fitting this model to the experimental data the evaporation coefficient was found to be 0.14±0.04 in average. Possibly a depend-ence of this coefficient upon the value of the droplet charge was found. An explanation of such dependence is suggested. The significant influence of the drople charge upon the evolution of small water droplets seems important for the detailed microphysical description of clouds.