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. Following Jacqmin (2000) the model is extended to include non-90 • contact angles. The diffuse-interface model applied 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. 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. The spreading of a liquid droplet on a solid surface under capillary action, referred to as spontaneous spreading, plays an important role in diverse technologies such as the application of paints, inkjet printing, adhesives and insecticides, migration of inks on paper, catalysis, oil recovery etc. The droplet spreads by displacing another immiscible fluid (ambient fluid) which usually is air but may also be a liquid. The spreading may be characterised, depending on whether the equilibrium contact angle is zero or finite, as being complete or partial wetting. The spreading kinetics in the complete wetting regime has been extensively studied and covered in several reviews and references therein, see (1993). In this case, it has been shown that at large times the radius of the contact area of the droplet with a solid surface follows r ∝ t 1/7 if the dissipation in the vicinity of the contact line dominates and r ∝ t 1/10 if the viscous loss inside the droplet dominates. On the contrary, only a few studies have explored the partially wetting regime insight although they use some simplifying assumptions with regard to flow (such as the lubrication approximation) and the shape of the droplet in order to yield an analytically tractable model. In general the assumptions made are only valid for very small equilibrium contact angles. So, when the equilibrium contact angle is large, e.g. θ ≈ 90 • , a detailed model with a possible numerical implementation may, in general, be required. The model applied should address the following issues: (i) tracking of the droplet-ambient fluid interface and accounting for the surface tension , Capillary …