Understanding and controlling stirring in micro-systems is necessary for the design of efficient passive micro-mixer. In this study, we focus on the dispersion of passive tracers injected in flows in between two rough surfaces under weak inertia influence (small but non-zero Reynolds number). The flow is induced by a constant applied pressure gradient between two cross-sections of the channel and the velocity field is calculated thanks to an extension of the lubrication approximation taking into account the first order inertial corrections. Tracers trajectories are obtained by integrating numerically the quasi-analytic velocity field. Our purpose is to examine the flow structure for various surface patterns and various Reynolds number. We focus on a simplified aperture field which is a smooth periodic function. This study puts forward interesting behavior of streamlines and show the dispersion of passive tracers in various geometries.

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