Pattern formation in drying water films

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Abstract
A film of a volatile medium in contact with unsaturated vapor is bound to a plane substrate by both van der Waals and polar forces. We present a thermodynamic description of this system, including exchange of material between the fluid and the vapor under nonequilibrium conditions. For a range of values of the vapor pressure, a two-phase system develops, involving the coexistence of molecularly thin and macroscopically thick layers whose dynamics are controlled by the vapor pressure. The theory is used to explain the origin of experimentally observed spatial patterns in water films evaporating from clean mica substrates, where scale and other features are a function of the vapor pressure. An analogy is developed between the initial stages of the pattern formation and the diffusion-controlled solidification problem in two dimensions and typical features such as “doublons” or parity-broken dendrites are observed. At later stages in the pattern formation hydrodynamics becomes important.

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