On Navier slip and Reynolds transpiration numbers

In this paper, based on the original argumentation of Reynolds and Maxwell, with consideration of previous experiences of the authors in the nano- and micro-flows area, a general form of boundary forces, that consist of contributions from the friction and the mobility components: f ∂V = f r + f m , has been extended to common effects of the bulk and surface motion. Hence, adopting Reynolds’ reasoning to a porous media as a whole, we reexamine the Poiseuille–Knudsen–Reynolds equation in terms of the sum of three contributions: the bulk pressure-driven flow, and two mobility surface forces, namely the Knudsen surface slip-driven flow and the Reynolds surface thermally-driven flow. The main motivation of our work is to find the dimensionless contribution of the Navier slip number and the Reynolds thermal transpiration number in materials with high volumetric surface density.