Hydrodynamics of Moving Contact Lines: Macroscopic versus Microscopic

The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nanodroplets be described by the same macroscopic equations as are used for macrodroplets? To the greatest degree, this question should be addressed to the moving-contact-line problem. The problem is naturally multiscale, where even using slip boundary conditions results in spurious numerical solutions and transcendental stagnation regions in modeling in the vicinity of the contact line. In this article, it is demonstrated through mutual comparisons between macroscopic modeling and molecular dynamics simulations that a small, albeit natural, change in the boundary conditions is all that is necessary to completely regularize the problem and eliminate these nonphysical effects. The limits of the macroscopic approach applied to the moving-contact-line problem have been tested and validated on the basis of microscopic first-principles molecular dynamics simulations.