Patterning flows using grooved surfaces

Through a simple analytical description we quantify how pressure-driven flows over grooved surfaces develop transverse components, which, for shallow grooves, can be modeled with simple anisotropic effective boundary conditions. Helical recirculation results in channels or capillaries with grooved walls. An experimental validation of our model is presented. Our analysis provides a workable guide for the design of 3D flows with simple patterns of grooved regions, e.g., to control the position of streams in the cross section of a channel or to promote mixing. Potential applications in microfluidics are outlined.