Simulation of moving contact lines in two-phase polymeric fluids

We numerically study the influence of polymer additives on contact line dynamics using a sharp interface model. An additional term, which accounts for the polymer stress, is added to the two-phase Navier–Stokes equation. The polymer stress is modeled by the FENE-P model. The coupled dynamic equations are solved using the finite difference method. The interface is tracked using marker particles, and the interface conditions are imposed using the immersed boundary method. Simulations in a Couette geometry are carried out to study the effect of the polymer stress on the moving contact line. It is found that the large velocity gradient near the moving contact line results in large polymer stress, which retards the contact line motion. The polymer stress increases with the polymer viscosity but is insensitive to the change of the Weissenberg number. The strength of the polymer stress is also found to increase with the capillary number, especially when the capillary number is large. We also study the relation between the apparent contact angle and the capillary number. For Newtonian fluids, the relation fits well with Cox’s analytic result; however deviation occurs for polymeric fluids. The critical capillary number at which the transition to an unsteady state happens decreases as the polymer viscosity increases.