Nanoscale transport of energy and mass flux during evaporation of liquid droplets into inert gas: computer simulations and experiments

Abstract

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, λ, much larger than the molecular diameter, σ. We find linear dependence R(t) ∼ t, for high λ/R(t) ratios and standard law R²(t) ∼ t for small λ/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 micro-droplets 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.