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A mathematical model of the evaporation of a thin sessile liquid droplet : comparison between experiment and theory

Dunn, G.J. and Wilson, S.K. and Duffy, B.R. and David, S. and Sefiane, K. (2008) A mathematical model of the evaporation of a thin sessile liquid droplet : comparison between experiment and theory. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 323 (1-3). pp. 50-55. ISSN 0927-7757

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Abstract

A mathematical model for the quasi-steady diffusion-limited evaporation of a thin axisymmetric sessile droplet of liquid with a pinned contact line is formulated and solved. The model generalises the theoretical model proposed by Deegan et al. [Contact line deposits in an evaporating drop, Phys. Rev. E, 62 (2000) 756-765] to include the effect of evaporative cooling on the saturation concentration of vapour at the free surface of the droplet, and the dependence of the coefficient of diffusion of vapour in the atmosphere on the atmospheric pressure. The predictions of the model are in good qualitative, and in some cases also quantitative, agreement with recent experimental results. In particular, they capture the experimentally observed dependence of the total evaporation rate on the thermal conductivities of the liquid and the substrate, and on the atmospheric pressure.