Work

Metal-pad-roll instability theory for small-scale models of reduction cells

Year: 2026

Type: article

Abstract: We present a theoretical model for the metal-pad-roll instability in laboratory-scale experimental models of reduction cells consisting of two stably stratified liquid layers subjected to a vertical electric current and magnetic field. In contrast to most previous studies, we do not rely on the shallow-water approximation and can account for viscous and capillary effects that are prevalent in small-scale experiments. In small cells, dissipation effects are largely attributable to laminar viscous damping, which we calculate analytically using a perturbative formulation of the Stokes boundary layers forming at all container walls and on both sides of the liquid interface. The derived damping rates, which are also useful for modeling liquid-liquid sloshing in rectangular containers, are validated against direct numerical simulations conducted with the coupled level set and volume-of-fluid solver ARCHER. On this basis, we derive analytical solutions for the growth rates and instability onsets of the metal-pad-roll instability, which we compare with different theoretical descriptions and existing experiments. The presented solutions are intended to serve as a foundation for future benchmarking of multiphase solvers.

Source: Physical Review Fluids

DOI: 10.1103/5ynm-wdlr

Authors: Pranav Hegde, Wietze Herreman, Jorge César Brändle de Motta, Romain Canu, Marie-Charlotte Renoult, Gerrit Maik Horstmann