Control of viscoplastic fluid dynamics in superhydrophobic channels with asymmetric groove configurations

We study the plane Poiseuille flow of viscoplastic fluids in channels with asymmetric superhydrophobic (SH) walls featuring transverse groove configurations in the thin channel limit. We use OpenFOAM simulations and the Papanastasiou regularization method to approximate the Bingham model. Focusing on variations in the upper SH wall’s characteristics, we explore the effects of slip number ($b_2$), groove periodicity length (${\ell }_2$), slip area fraction (${\phi }_2$), and Bingham number ($B$) on flow dynamics, flow metrics and unyielded center plug morphology. We find that increasing $b_2$, ${\phi }_2$, and ${\ell }_2$ enhances slip velocity on the upper SH wall and reduces the normalized plug area ($A/A_0$) up to ${\phi }_2=0.5$, while higher $B$ amplifies flow asymmetry, shifting and breaking center plugs. By introducing the concept of slippery equivalent systems, we demonstrate that varying groove configurations can yield identical effective slip lengths (${\chi }_T$) with distinct plug morphologies, enabling precise control of viscoplastic fluid dynamics. We derive a simplified model to predict ${\chi }_T$ and $A/A_0$, identifying a critical threshold at $A/A_0\approx 0.68$ for regime transitions between unbroken (Regime I) and broken (Regime II) center plugs, leading to a six-dimensional manifold equation for classifying these regimes across parameter space.