From the nano- to the macroscale - Bridging scales for the moving contact line problem

Abstract eng:
The moving contact line problem is one of the remaining unsolved fundamental problems in fluid mechanics. At the heart of the problem is its multiscale nature: a nanoscale region close to the solid boundary where the continuum assumption breaks down, must be bridged with a macroscopic region where the usual laws of hydrodynamics apply. At the macroscale, we review our recent effort to show that direct matching between the inner (nanoscale) region and the outer (macroscale) region is possible through an overlap domain, thus simplifying the analysis presented to date in the literature. Our analysis is also in agreement with results from diffuse interface approaches. At the nanoscale, the density profile at the contact line region is obtained using classical density-functional theory. This is used in combination with extended Navier-Stokes equations to compute advancing and receding contact lines. Our results are compared with predictions from molecular kinetic theory.

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