Capillary spreading of a droplet in the partially wetting regime using a diffuse-interface model

The spreading of a liquid droplet on a smooth solid surface in the partially wetting regime is studied using a diffuse-interface model based on the Cahn--Hilliard theory. The model is extended to include non-90$^{\circ}$ contact angles. The diffuse-interface model considers the ambient fluid displaced by the droplet while spreading as a liquid. The governing equations of the model for the axisymmetric case are solved numerically using a finite-spectral-element method. The viscosity of the ambient fluid is found to affect the time scale of spreading, but the general spreading behaviour remains unchanged. The wettability expressed in terms of the equilibrium contact angle is seen to influence the spreading kinetics from the early stages of spreading. The results show agreement with the experimental data reported in the literature.

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