Fingering instability of thin evaporating liquid films

Abstract

The fingering instability of growing dry patches in an evaporating film of a polar liquid placed on a solid substrate is investigated. The instability manifests itself as fingering of mobile fronts between growing "dry" (thin) and shrinking "wet" (thick) regions of the film corresponding to two stable states of the evaporating film in contact with its vapor. The boundaries of the fingering instability are found through linear stability analysis of numerical solutions of the nonlinear evolution equation defining the film profile, and the influence of the evaporation rate, polar intermolecular forces, and chemical heterogeneity of the substrate is investigated.