Diffusion-Slip Boundary Conditions for Isothermal Flows in Micro- and Nano-Channels

Abstract

Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects such as slip at walls, surface diffusion, Knudsen diffusion and others. While all these effects are derived from various phenomenological formulations, a sound theoretical ground unifying these effects and observations is still lacking. In this paper, adopting the definition and existence of various type of flow velocities beyond that of the standard mass velocity, we suggest derivation of model boundary conditions that may systematically justify various diffusion process occurring in micro- and nano-flows where the classical continuum model breaks down. Using these boundary conditions in conjunction with the classical continuum flow equations we present a unified derivation of various expressions of mass flow rates and flow profiles in micro- and nano-channels that fit experimental data and provide new insights into these flow profiles. The methodology is consistent with recasting the Navier–Stokes equations and appears justified for both gas and liquid flows. We conclude that these diffusion type of boundary conditions may be more appropriate to use in simulating flows in micro- and nano-systems and may also be adapted as boundary condition models in other interfacial flow modelling.