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The fluid-mechanics community is currently divided in assessing theboundaries of applicability of the macroscopic approach to fluid mechanicalproblems. Can the dynamics of nano-droplets be described by the samemacroscopic equations as the ones used for macro-droplets? To the greatestdegree, this question should be addressed to the moving contact-line problem.The problem is naturally multiscale, where even using a slip boundary conditionresults in spurious numerical solutions and transcendental stagnation regionsin modelling in the vicinity of the contact line. In this publication, it hasbeen demonstrated via the mutual comparison between macroscopic modelling andmolecular dynamics simulations that a small, albeit natural, change in theboundary conditions is all that is necessary to completely regularize theproblem and eliminate these nonphysical effects. The limits of macroscopicapproach applied to the moving contact-line problem have been tested andvalidated from the first microscopic principles of molecular dynamicsimulations.

Hydrodynamics of moving contact lines: macroscopic versus microscopic