A flux-balanced diffuse-interface kinetic model for rarefied gas-solid boundaries with arbitrary absorption probability

Abstract

Rarefied gas--solid interactions determine mechanical loads, heat transfer, and material exchange in microscale devices and low-pressure processings. Modeling these interactions becomes challenging when gas non-equilibrium effect and complex moving boundaries must be resolved together. We develop a diffuse-interface kinetic model (DIKM) that describes rarefied gas transport and gas--solid interactions in one kinetic formulation on a single fixed Eulerian mesh. A smooth order parameter represents solid geometry, while a localized molecular flux operator incorporates boundary interactions directly into the kinetic equation by distinguishing incident and reflected distributions in the interface region and specifying their mass, momentum, and energy exchange, including prescribed surface absorption. Matched asymptotic analysis shows that the diffuse formulation recovers the corresponding partially absorbing diffuse-reflection boundary condition for smooth stationary or moving surfaces in the sharp-interface limit. Discretization uses Strang splitting, combining an order-parameter-weighted discrete unified gas kinetic scheme for the transport substep with a positivity-preserving update of the interfacial source. Benchmarks over planar and curved, stationary and moving boundaries reproduce rarefaction-dependent velocity slip and wall heat transfer, absorption-driven flow, and feedback between gas forces and solid translation and rotation. In final simulations, the order parameter evolves by a Cahn--Hilliard equation with degenerate mobility, and thin-film growth exhibits distinct surface profiles at different vapor incidence angles. By connecting implicit geometry to molecular surface exchange, DIKM provides a basis for coupling rarefied gas dynamics to solid motion and material evolution.