The Flow of a Viscous Fluid through a Porous Wall into a Narrow Gap : A Consideration of the Slip of Fluid on a Porous Wall Surface

Abstract

An exact theoretical analysis is presented for the axi-symmetric flow of a viscous fluid through a porous wall into a narrow, uniform gap. In this analysis, the two equations of motion, one for the flow in the gap and the other in the porous medium, are solved under the generalized condition that the fluid may flow radially in the porous medium and as the result may slip on the porous wall surface. The important conclusions confirmed through this research are as follows. The flow characteristics are governed by the two non-dimensional parameters, [numerical formula] and [numerical formula] (k : permeability of the porous medium, h : gap width, ν₀ : constant normal velocity component at the porous wall surface). Except the limiting case λ→0, the flow generally has a tangential velocity component at the porous wall surface, and especially for the flow with large values of R, the no-slip assumption which has been made customarily to date, becomes invalid even when λ is very small. For the flow of boundary-layer type the slip of fluid may usually be ignored, but for the flow through a porous wall into a narrow gap, such as in the porous gas bearing, it is necessary to take account of the new phenomena found by the present research.