Efficient simulation of non-classical liquid-vapour phase-transition flows: a method of fundamental solutions

TL;DR

This paper introduces a novel fundamental solutions-based numerical method for simulating small-scale liquid-vapor phase transitions, incorporating extended continuum models to account for rarefaction effects at nanoscales.

Contribution

It develops a new fundamental solutions approach for the coupled constitutive relations model, enabling efficient 3D micro-flow simulations of phase change at small scales.

Findings

Accurately captures rarefaction effects in nanodroplet evaporation.

Provides a low-cost computational framework for 3D phase-change simulations.

Benchmarks against classical results demonstrate improved modeling accuracy.

Abstract

Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example). However, for phase transitions processes at small scales, such as the evaporation of nanodroplets, the assumption that the temperature is continuous across the liquid-vapour interface leads to significant inaccuracies (McGaughey & Ward 2002; Rana et al. 2019), as may the adoption of classical constitutive relations that lead to the Navier-Stokes-Fourier equations (NSF). In this article, to capture the notable effects of rarefaction at small scales, we adopt an extended continuum-based approach utilizing the coupled constitutive relations (CCR). In CCR theory, additional terms are invoked in the constitutive relations of NSF equations originating from the arguments of irreversible thermodynamics as well as consistent with kinetic theory of gases. The modelling approach allows us to derive new fundamental solutions for the linearised CCR model and to develop a numerical framework based upon the method of fundamental solutions (MFS) and enables threedimensional multiphase micro-flow simulations to be performed at remarkably low computational cost. The new framework is benchmarked against classical results and then explored as an efficient tool for solving three-dimensional phase-change events involving droplets.