Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

Abstract

After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.