Flow in microchannels with rough walls: flow pattern and pressure drop

In this paper perturbation methods are introduced to study the laminar flow in microchannels between two parallel plates with rough wall surfaces. By a coordinate transformation, the physical domain of the microchannel is transformed into the computational one. The relative roughness as a small parameter presents the governing equations resulting from the coordinate transformation. The equations are linearized through applying the perturbation method, and the spectral collocation method is employed to solve the perturbation equations. Furthermore, the boundary perturbation method is used to analyze the spatially-averaged pressure drop of the microchannel. The numerical results show that flow in microchannels with rough surfaces is quite different from Poiseuille flow: there exist apparent fluctuations and periodic variations of vorticity along the flow direction in the flow field; flow is viscously dominant under the conditions of a low Reynolds number and the flow separations happen in the troughs of wavy walls at a high Reynolds number. The spatially-averaged pressure drop being subject to the invariable flow rate could be greater than, equal to or even less than the theoretical value, which is qualitatively consistent with the results of the microfluidic experiments.