Computation of slip flow in microtubes with wall roughness

An analytical and numerical analysis of the flow field in axisymmetic microtubes and two-dimensional microchannels with wall roughness is conducted. Roughness geometry is modeled as a series of periodic triangular obstructions with relative roughness peaks ranging from 1% to 5% of the channel width or tube diameter. Two wall roughness shapes with randomly distributed triangular and rectangular peaks are also studied. An analytical solution is obtained following the work of Arkilic et al. [1] and Kunert and Harting [2], and numerical simulations are obtained using the Navier-Stokes CFD solver FLUENT. For the numerical simulations, a generalized Maxwell slip boundary condition for arbitrary rough boundaries is derived. Computations are performed for a range of channel/tube outlet Knudsen numbers ≤ 0.1. The solutions show that for a given inlet to outlet pressure ratio, an increase in roughness decreases the mass flow rate. The results also show that the "apparent slip" increases as the roughness increases. Additionally, an effective channel height between the roughness peaks and valleys is determined both analytically and numerically which is shown to change linearly with the average channel roughness.