  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.
