A Procedure for Calculating Wall Distance in Arbitrary Microchannel Geometries

This paper describes a continuum-based CFD solution for flow in a microchannel using near-wall scaling and first-order slip conditions. This near-wall scaling approach is used in an attempt to capture the Knudsen layer effects. The near-wall scaling itself requires the distance to the nearest wall as an input parameter and this distance is calculated using a simple technique which involves the solution of a diffusion equation for a scalar value φ of the form div(gradφ) = −1. The wall distance is then deduced for this scalar field and implemented in the near-wall scaling function. In order to demonstrate the efficacy of the wall distance/near-wall scaling technique the methodology is applied to two practical cases. The first case describes Poiseuille flow in a microchannel (for which analytical solutions exist) and the second considers flow in a microchannel with two 90° bends. The results show that the implementation of the wall distance procedure is relatively straightforward and that the use of the near-wall scaling increases the mass flow rates in both of the cases considered.