Boundary vorticity dynamics of two-phase viscous flow

Abstract

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.