The transport of viscoplastic fluids through channels with grooved superhydrophobic (SH) walls, using a comprehensive modeling approach and numerical simulations, has been investigated. The goal is to understand the interactions between the viscoplastic fluid and the superhydrophobic surface and identify factors that influence the flow behaviour. It is assumed that the grooves trap air pockets on the SH surface, keeping the liquid/air interface flat and pinned at the groove edges, resulting in a slip-stick condition. The analysis is comprehensive, covering both creeping and inertial regimes in thick and thin channel limits. In particular, six parameters, including the Reynolds number (R), Bingham number (B), slip number (b), groove periodicity length (), slip area fraction (), and groove orientation angle (), are considered. Subsequently, the effects of these parameters are analyzed on the flow variables of interest, such as the perturbation field, velocity field, strain-rate magnitude, unyielded plug zones, effective slip length, friction factor, flow asymmetry, mixing, and regime classifications. In thick channels ( << 1) with transverse grooves ( =90), increasing B and b leads to growing the perturbation and slip velocity fields, which become asymmetric by increasing R. Under certain flow conditions, the center plug breaks or an unyielded plug zone can form on the SH wall liquid/air interface, allowing us to classify the flow regimes. In thin channels ( >> 1), increasing either b or  causes the the unyielded center plug to deform and eventually break, except for flows with longitudinal grooves ( =0). For the oblique grooves (0 <  < 90), a secondary flow appears, triggering flow mixing. Finally, the linear stability analysis of the homogeneous slip condition ( = 1) reveals stabilizing/destabilizing effects of the streamwise/spanwise slip conditions.

Refreshments will be served preceding the talk, beginning at 2:45.