Lubricant viscosity effects on flow regimes of viscoplastic fluids over patterned surfaces

We study plane Poiseuille flow of a viscoplastic Bingham fluid over a lubricant-infused patterned wall using fully coupled two-phase numerical simulations, with viscoplasticity modeled via the Papanastasiou regularization. The effects of groove geometry (aspect ratio 𝑑 and periodicity ℓ ), flow parameters (Reynolds and Bingham numbers), and lubricant viscosity (viscosity ratio 𝜇 𝑟 ) are systematically examined. The morphology of the central unyielded plug depends strongly on 𝜇 𝑟 : low-viscosity lubricants promote penetration of wall-induced perturbations, leading to plug deformation and breakage, whereas high-viscosity lubricants suppress perturbation transmission and preserve an intact plug. The coupled influence of 𝜇 𝑟 and groove geometry also governs the formation of an unyielded region above the liquid/lubricant interface, yielding four distinct flow regimes distinguished by central plug breakage and interfacial yielding. Interface pinning and depinning are further controlled by groove geometry, flow inertia, and lubricant viscosity, with low-viscosity lubricants inducing earlier depinning and high-viscosity lubricants maintaining a pinned interface over a wider range of flow conditions.