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