From single bubble to global mixing: Added mass, drift, wake

Abstract

The goal was to present an approach where the micro-scale events related to single-particle motion directly translate onto higher levels and produce large-scale observable phenomena related to transport and mixing. Three multiphase hydrodynamic effects were considered, analysed and discussed: added mass, drift, wake. Although the results are of general validity, the spherical-cap shape (cap bubble) was used as the definite object for demonstration. It was shown how the unsteady inertial effect of added mass (coefficient C), irrelevant for mixing, is related to the steady kinematic concept of Darwin drift (coefficient D) that is directly associated with mixing. It was shown how the inviscid drift and the viscous wake operate and contribute to the resulting circulation and mixing. List of currently available formulas for C was completed, which are usable for estimation of D.