Influence of Ribbon Structure Rough Wall on the Microscale Poiseuille Flow

The regular perturbation method is introduced to investigate the influence of two-dimensional roughness on laminar flow in microchannels between two parallel plates. By superimposing a series of harmonic functions with identical dimensional amplitude as well as the same fundamental wave number, the wall roughness functions are obtained and the relative roughness can be determined as the maximal value of the product between the normalized roughness functions and a small parameter. Through modifying the fundamental wave number, the dimensionless roughness spacing is changed. Under this roughness model, the equations with respect to the disturbance stream function are obtained and analyzed numerically. The numerical results show that flowing in microchannels are more complex than that in macrochannels; there exist apparent fluctuations with streamlines and clear vortex structures in microchannels; the flow resistances are about 5–80% higher than the theoretical value under different wall-roughness parameters. Furthermore, analysis shows that the effect of roughness on the flow pattern is distinct from that on the friction factor.