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.
Highlights
The European Physical Journal Special Topics backgrounds many of whom come up with what they regard as ‘mathematical models’. These models eagerly embrace the accepted views as something ‘we know’ and add refreshing new elements. They hybridize concepts taken from different modelling frameworks, use molecular scales in continuum models, add intermolecular forces on top of the continuum description, associate slip featuring in continuum models with molecular slip reported in molecular dynamics simulations, to mention but a few creative innovations
– Can we suggest a class of flows which would settle the above question regardless of such issues as the accuracy of measurements and/or physical factors additional to dynamic wetting?
‘Litmus test’: if a mathematical model of dynamic wetting has the velocity-dependence of the dynamic contact angle, actual or apparent, as an input, presuming the same curve in the angle-versus-speed plane irrespective of the flow, this model will fail to describe, even on a qualitative level, a multitude of capillary flows and, as a contribution to theoretical fluid mechanics, does not deserve further attention
Summary
The European Physical Journal Special Topics backgrounds many of whom come up with what they regard as ‘mathematical models’ These models eagerly embrace the accepted views as something ‘we know’ and add refreshing new elements. The test focusses on the key element of every theory formulated in the framework of continuum mechanics, namely the behaviour of the dynamic contact angle, and points out a class of capillary flows to be looked at. These flows show on a qualitative level whether or not this key element is correct in principle, on the level of the model’s mathematical structure. It is argued that it is this duality of modern continuum mechanics not reflected in how this subject is being taught that is largely behind the misdirection of research effort in the area of dynamic wetting which this paper describes
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