Computation of slip flow in microchannels with wall roughness

An analytical and numerical analysis of the flow field in 2D microchannels with wall roughness is conducted. Roughness geometry is modeled as a series of triangular obstructions. Relative roughness from 0% to 5% is considered. An analytical solution is obtained following the work of Arkilic et al. [1] and Kunert and Harting [2]. The solution shows that for a given inlet to outlet pressure ratio, increase in roughness decreases the mass flow in the channel. The results also show that the "apparent slip" increases as the roughness increases. Analytical solution assumes that there is no flow separation due to triangular obstructions. In order to analyze the details of the flow field near the rough wall, numerical simulations are performed by employing the well known CFD software FLUENT. A generalized Maxwell slip boundary condition for arbitrary rough boundaries is derived. The computations are performed on an unstructured grid for outlet Knudsen numbers < 0.1. The flow is assumed to be nearly incompressible (M < 0.2). A uniform free-stream condition is employed at a distance of four channel heights upstream of the inlet. Computations show that the roughness decreases the reduction in pressure loss due to rarefaction. Thus, the roughness effects become stronger at higher Knudsen numbers.