We demonstrate using molecular dynamics simulations of the Lennard-Jones fluid that the evaporation process of nanodroplets at the nanoscale is limited by the heat transfer. The temperature is continuous at the liquid-vapor interface if the liquid/vapor density ratio is small (of the order of 10) and discontinuous otherwise. The temperature in the vapor has a scaling form T(r,t)=T[r/R(t)], where R(t) is the radius of an evaporating droplet at time t and r is the distance from its center. Mechanical equilibrium establishes very quickly, and the pressure difference obeys the Laplace law during evaporation.

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.

We performed molecular dynamics simulations of liquid film evaporation into vacuum for two cases: free evaporation without external supply of energy and evaporation at constant average liquid temperature. In both cases we found that the pressure inside a liquid film was constant, while temperature decreased and density increased as a function of distance from the middle of the film. The momentum flux in the vapor far from the liquid was equal to the liquid pressure in the evaporating film. Moreover the pseudopressure (stagnation pressure) was found to be constant in the evaporating vapor and equal to the liquid pressure. The momentum flux and its relation to the pressure determined the number of evaporating molecules per unit time and as a consequence the mass evaporation flux. We found a simple formula for the evaporation flux, which much better describes simulation results than the commonly used Hertz-Knudsen relation.

We use molecular dynamics (MD) simulations of a two-component Lennard-Jones (LJ) fluid to analyze the energy flux from an inert gas to the interface of an evaporating liquid droplet. Using this analysis we derive an analytical equation for the radius of the droplet, R(t), as a function of time, t. The formula is valid for evaporation of droplets of any material or size into the gas characterized by the mean free path, l, much larger than the molecular diameter, s. We find linear dependence R(t) $ t, for high l/R(t) ratios and standard law R 2 (t) $ t for small l/R(t) ratios. We apply equation for R(t) to experimental results of evaporation of water micro-droplets into air and glycerol, diethylene glycol and triethylene glycol microdroplets into the nitrogen gas evaporating in time from seconds to tens of minutes. The experimental results together with computer simulations span 12 orders of magnitude of evaporation times and more than 3 orders of magnitude of droplets' radii. In the experiments the evaporation rate is governed by a very small difference in temperatures (from one tenth of mK to a few K) between the gas far from the droplet and evaporating liquid. From MD simulations we also obtain suitable boundary conditions for the energy flux at the interface, used in irreversible thermodynamics, and the accommodation coefficients used in kinetic models of evaporation.