Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Plane Poiseuille flow of a Bingham fluid in channel armed with superhydrophobic (SH) lower wall is analysed via semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents groovy structure air trapped inside its cavities. Therefore, the adjacent to undergoes stick–slip conditions. model developed based on introducing infinitesimal wall-induced perturbations into motion equations, followed Fourier series expansions, and solving resulting equations as boundary value problem. Navier slip law accounts for at liquid/air interface (assuming Cassie state). presented analysis fairly comprehensive, covering creeping inertial regimes thick channels (via DNS solutions). main dimensionless numbers are Reynolds ( $Re$ ), $Bi$ ) $b$ numbers, well groove periodicity length $\ell$ area fraction $\varphi$ ). By increasing , perturbation velocity fields grow. As increases, become asymmetric. For certain parameters, an unyielded plug zone may appear interface, while formation accelerated effects. results classify flows predicting onset wall.