Scattering kernel and kinetic boundary condition with adsorption layers

Due to Van der Waals forces, gas molecules form an adsorption layer on solid walls. Understanding the influence of this adsorption layer on scattering and flow behavior holds both scientific and engineering significance. While the Cercignani-Lampis-Lord (CLL) scattering kernel effectively models rarefied gas interactions with clean surfaces, it fails to accurately describe scattering dynamics when gas-gas interactions arising from adsorption layers become significant. To address this limitation, the influence of adsorbed molecules is incorporated through an effective near-wall potential, and the fraction of gas molecules governed by the CLL kernel is assumed to decay exponentially with increasing surface coverage. This hypothesis leads to a new scattering kernel that linearly blends the CLL model with the fully diffuse Maxwell model via a surface-coverage-dependent weighting factor. Under low-pressure or high-temperature conditions, the adsorption layer is sparse, and the model naturally recovers the classical CLL kernel. In contrast, under high-pressure or low-temperature conditions, where a dense adsorption layer forms, the scattering behavior approaches fully diffuse reflection. Using the half-flux method, the modified velocity slip and temperature jump boundary conditions are derived, establishing a kinetic theory framework that explicitly includes adsorption layer contributions. Our results show that the presence of adsorbed molecules reduces velocity slip and strongly influences temperature jump behavior. The proposed models, validated through comparisons with molecular dynamics simulations and existing models, are applicable to gas flows over smooth surfaces covered with adsorption layers. They are expected to yield more accurate predictions of velocity and temperature distributions near solid boundaries under conditions where adsorption effects are non-negligible.