Contact angle ageing and anomalous capillary flow of a molten metal

Recent capillary flow experiments, conducted on a combined wetting/non-wetting assemble, consistently feature an anomalous flow over the non-wetting substrate: (i) apparent abrupt or gradual recession stages in the motion of the contact line, (ii) non-monotonic abrupt changes in the receding contact angle, and (iii) contact angle overshoot above the nominal equilibrium contact angle. We find that such behavior of a liquid metal alloy cannot be explained by the standard capillary flow models. However, a model that includes the ageing of the equilibrium contact angle predicts all the observed features qualitatively. We use the phase field formulation for capillary flows with a diffusive motion of the triple line to accommodate the novel diffusive boundary condition with the time-evolving quasi-equilibrium contact angle. We discover that the observed anomalies in capillary flow are qualitatively explained by two factors: (1) time evolution (ageing) of the quasi-equilibrium contact angle and (2) high viscosity of the partially molten braze. We also discover that for the given flow geometry, the transition from the initial to the final configuration may follow two distinct topological paths: one is characterized by a coalescence of liquid-solid contact domains, the other by a contact separation. The selection of the two paths in the configurational space is dependent on both contact ageing parameters and viscosity.