Slip transition in dynamic wetting for a generalized Navier boundary condition

Computer fluid dynamics simulations of dynamic wetting are often performed using a slip model on the substrate. In previous studies, the generalized Navier boundary condition (GNBC) has shown promising results and could help clear the gap between molecular and continuum scales, but lacks quantitative comparisons to experiments. We seek to investigate the dependence between the contact-line velocity and the slip length in a GNBC, by confronting numerical simulations to experimental data.

The physical properties of a molten polymer (polyethylene glycol) were assessed thoroughly. Its dynamic contact angle on a cellulosic substrate was measured carefully using the Wilhelmy method. The experiment was reproduced in a finite elements model using a GNBC. It was repeated for capillary numbers between 10^-6 and 10^-1, and slip lengths ranging from 1 μm to 1 mm.

A realistic value of the slip length was selected by matching the dynamic contact angles issued from numerical simulations and their experimental counterparts. The slip length behavior as a function of contact line velocity displayed a clear transition. The model also reproduced a dynamic wetting transition between frictional and viscous dissipations, which seems to be linked to an increasing difference between microscopic and macroscopic contact angles.