Stokes flow through a microchannel with periodical protuberances on the wall

In this study, we analyze the Stokes flow through a microchannel with semicircular periodic protuberances on the walls. The radius and period of semicircular protuberances and the stagger ratio of the staggered protuberance arrangement on both walls are arbitrary. Considering the periodicity and symmetry of the flow, the Fourier series expansion and least squared error method are applied. The stream function, pressure distribution in the flow region, and shear stress distribution on the semicircular protuberances are determined, and the results for some cases of arrangement of protuberances are presented in this paper. In particular, the average pressure gradient along the microchannel is calculated as a function of the size, period, and the stagger ratio of the protuberances on the walls. The results are compared with those obtained by lubrication analysis when the protuberances are close to the opposite protuberances or the opposite wall. As the limiting case of large periodicity, the induced pressure drops attributed to a single pair of semicircular protuberances on both walls and attributed to a single semicircular protuberance on a wall are also considered.