Analytical solution for dynamic evaporation of liquid in isothermal condition

TL;DR

This paper presents an analytical solution for isothermal liquid evaporation using a diffuse interface model, offering new insights into the relationship between evaporation rate and viscosity, validated by numerical simulations.

Contribution

It introduces a novel analytical approach based on the free-energy method for modeling evaporation without relying on traditional jump conditions or kinetic theory.

Findings

Exact solution for inviscid case derived

Approximate solution considering viscosity proposed

Model validated with numerical simulations showing excellent agreement

Abstract

An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice Boltzmann literature, distinguishing our approach from conventional evaporation models that rely on jump conditions or pure kinetic theory. The interface behavior is fully described by differential equations, eliminating the need for assumptions such as local equilibrium at the interface. We derive an exact analytical solution for the inviscid case and propose an approximate solution when viscosity effects are considered. Our model unveils a novel relationship between evaporation rate and viscosity, providing new insights that have not been thoroughly explored in the literature. The analytical results are validated through numerical simulations using the open-source parallel library OpenLB, demonstrating excellent agreement in predicting the physical behavior of the evaporation phenomena within the framework of diffuse interface methods.