Effective slip, plug formation and interface depinning in Bingham flow over superhydrophobic grooves

We examine the Poiseuille flow of viscoplastic fluids over superhydrophobic surfaces with transverse air-filled grooves, focusing on the deformation dynamics of the liquid–air interface and the resulting flow regimes. By combining a creeping-flow semianalytical model and finite Reynolds two-phase numerical simulations, we quantify how viscoplastic rheology, governed by the Bingham number ( upper B B B ), interacts with capillary and inertial forces, represented by the capillary number ( italic Ca Ca Ca ) and Reynolds number ( upper R R R ), as well as groove geometry characterized by the aspect ratio ( d d d ), to dictate meniscus behaviour. The analysis covers groove aspect ratios ranging from shallow ( d tilde upper O left parenthesis 10 Superscript negative 3 Baseline right parenthesis d ∼ O ( 10 − 3 ) d ~ O(10⁻³) ) to deep ( d tilde upper O left parenthesis 1 right parenthesis d ∼ O ( 1 ) d ~ O(1) ). The results reveal distinct interface morphologies, including flat (pinned at groove edges), deflected (pinned), depinned and collapsed states, depending on d d d , italic Ca Ca Ca