Discussion notes: Thoughts on mesoscopic continuum models

Abstract

Questions and comments are provided for (1). I find Yulii Shikhmurzaev's opinion paper on the contact line problem interesting to read. It is helpful as it has allowed me to better identify the points where I disagree. First, he defines microscopic and macroscopic levels of continuum description (that may be applied to the contact line problem) as mutually exclusive. The definition is done in a way that excludes the mesoscopic models for the contact line problem used in the literature. Then he introduces his own model that in my view is also a mesoscale model. In contrast, I think that already his definition of levels of continuum description is not a good representation of reality, and I will below offer a slightly different one. If one accepts my classification, the widely employed mesoscale models become admitted again and Yulii Shikhmurzaev's model becomes one of them, and competes on a common ground. My first major concern is his classification of continuum descriptions. I do not un- derstand the way Yulii Shikhmurzaev draws the line between models in Continuum Mechanics and Statistical Physics. If statistical physics deals with "field variables describing statistical distributions of molecular properties" (1) then continuum me- chanics deals with field variables describing mean values of molecular properties (i.e., the lowest order moments of statistical distributions). Continuum mechanics is a part of statistical physics 1 . To obtain a valid description based on mean values (as in