Modelling viscoplastic interfacial flows inclusive of curvature effects

Abstract

This study presents a theoretical and numerical investigation of interfacial flows of oxidised liquid metals in a shallow annular channel in the absence of inertial effects. For the first time, viscoplastic surface behaviour induced by oxidation is modelled using a bi-viscosity law within a framework that also accounts for interfacial curvature governed by the Young–Laplace equation. By solving a coupled bulk-surface flow system, the effects of surface rheology, contact angle, and dimensionless capillary length on surface velocity and surface shear rate profiles are quantified. Results highlight the competing influences of hydrophobicity and viscoplasticity on surface and bulk flow characteristics and demonstrate that accurate modelling of such systems necessitates inclusion of both curvature and non-Newtonian surface effects. In appropriate limits, our numerical results are validated against semi-analytical solutions. Our findings offer insights relevant to metal casting applications.