Three ways of getting contact lines to move without breaking the no-slip boundary condition

Tuesday, March 27, 2018 - 9:40am - 10:10am
Lind 305
Eugene Benilov (University of Limerick)
Recent comparisons of theoretical models of contact lines with experimental results (Podgorski et al. 2001, Winkels et al. 2011, Puthenveettil et al. 2013, Benilov & Benilov 2015) show that, in some cases, the most popular model – based on the Navier-slip condition and a prescribed contact angle – works only if the slip length is unreasonably small (subatomic). So far, the discrepancy has been observed for glycerine, glycerine/water mixture, ethylene glycol, and mercury, making one wonder whether the list of exceptions is long enough to cast a doubt on the actual rule.

In this talk, three different ways are outlined of reconciling moving contact lines with the no-slip boundary condition.

Firstly, it is shown that, if the contact angle is 180 degrees, the usual contact-line singularity does not arise in a free-boundary, no-slip Couette flow [as predicted by the local analysis of Benney & Timson (1980)]. Secondly, it is argued that a contact line can advance without slipping provided the liquid/gas interface is in a state of perpetual overturning (similar to a water wave running up a beach). Thirdly, a kinetic model is suggested, based on the so called Enskog–Vlasov equation describing contact lines on a molecular level – i.e., without imposing any macroscopic boundary conditions including the no-slip and Navier-slip ones.