zbMATH — the first resource for mathematics

Contact-line dynamics of a diffuse fluid interface. (English) Zbl 0984.76084
From the summary: An investigation is made into the moving contact line dynamics of a Cahn-Hilliard-van der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can evolve either through convection or through diffusion driven by chemical potential gradients. The purpose of this paper is to show how the CHW moving contact line compares to the classical sharp interface contact line. It therefore discusses the asymptotics of the CHW contact line velocity and chemical potential fields as the interface thickness \(\varepsilon\) and the mobility \(\kappa\) both go to zero. The CHW and classical velocity fields have the same outer behaviour but can have very different inner behaviours and physics. In the CHW model, wall-liquid bonds are broken by chemical potential gradients instead of by shear, and change of material at the wall is accomplished by diffusion rather than by convection. The result is, mathematically at least, that the CHW moving contact line can exist even with no-slip conditions for the velocity.

76R50 Diffusion
76D99 Incompressible viscous fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
Full Text: DOI