Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries.

In this study the wetting behavior of converging-diverging and diverging-converging capillaries is investigated numerically using an in-house written, finite-element code. An interface tracking procedure based on the predicted change in the total liquid volume, to update the interface location, and Cox's formulation, to determine the dynamic contact angle and the interface shape, is proposed and used. Flow simulations revealed that both converging-diverging and diverging-converging capillaries exhibit significantly slower wetting behavior than straight capillaries and that any deviation in the capillary diameter necessarily tends to slow the overall wetting speed. This behavior was attributed to local regions of very low capillary pressure and high viscous retardation force when the capillary diameter at the interface was significantly larger than the capillary diameter over the upstream fluid. Though the local wetting velocities were different, when equivalent capillaries were compared it was found that both converging-diverging and diverging-converging capillaries had the same total fill time independent of the number of irregular regions, suggesting that the simple model is sufficient for predicting the overall effect. The influence of surface tension and contact angle on the total wetting time was found to be similar for both straight and irregularly shaped capillaries.