Boundary-layer approach to the linear karren instability

• DOI: 10.1017/jfm.2023.932
• Publication Date: 2023-12-20T10:29:31Z
• Authors: Simeon Djambov; François Gallaire
• Keywords: Dispersion relation; Lubrication theory; Linear stability

The present paper concerns the linear fate of transverse perturbations in a gravity-driven, thin-film flow over soluble substrate. We propose reduced-order model, based on boundary-layer treatment solute transport and depth-integration Stokes equations, using two extended lubrication methodologies found literature. obtain closed-form dispersion relation, which we compare to previous, fully resolved analytical investigation (Bertagni Camporeale, J. Fluid Mech. , vol. 913, 2021, A34). results allow us distil essential physical mechanisms behind instability.