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The coexistence of film domains of different thickness in an evaporating film of a polar liquid on a solid substrate is studied using the multiscale expansion technique. The propagation speed of a straight-line front is computed both in the quasistationary approximation and in the comoving frame. The limit of long-scale zigzag instability is computed. The instability is observed during evaporation only and exists in a range of propagation velocities bounded both from below and from above; during condensation, the propagating front is always stable. Computations for a circular front yield a critical nucleation radius for a thin film and confirm the anomalous dependence of the evaporation rate on the droplet radius observed in recent experiments.
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L. M. Pismen (2004) studied this question.
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