on the dynamic contact angle in capillary flows

The displacement of the contact line (cl) between two arbitrary immiscible flowing fluids was modeled. the present model is valid for a wide range of viscosity ratios of the phases. the previously developed models reported in the literature were devoted to special cases, i.e., high viscosity fluid pushing the low viscosity fluid. the present model reveals a direct relationship among the dynamic contact angle, the dimensionless pressure difference in the channel/tube, the capillary numbers of both phases, and the characteristic length ratios of the channel/tube. the model was validated by agreeing with its predictions for the dynamic contact angle with the available data for a case of water-air flow inside a tube. then, it was applied to more general cases with different viscosity ratios. according to the results, by increasing the ratio of the advancing phase's viscosity to the receding phase's viscosity, the dynamic contact angle reaches more quickly to its final value. it was also seen that by increasing the ratio of the length to the diameter of the tube the evolution of the dynamic contact, angle becomes slower. the most interesting point is that a unique behavior is seen and a master curve is achieved if the time becomes dimensionless with a changing parameter (not a fixed parameter). this facilitates the way to predict and interpret the dynamic contact angle in the most general way.