The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion

Abstract

The motion of bubbles dispersed in a liquid when a small‐amplitude oscillatory motion is imposed on the mixture is examined in the limit of small frequency and viscosity. Under these conditions, for bubbles with a stress‐free surface, the motion can be described in terms of added mass and viscous force coefficients. For bubbles contaminated with surface‐active impurities, the introduction of a further coefficient to parametrize the Basset force is necessary. These coefficients are calculated numerically for random configurations of bubbles by solving the appropriate multibubble interaction problem exactly using a method of multipole expansion. Results obtained by averaging over several configurations are presented. Comparison of the results with those for periodic arrays of bubbles shows that these coefficients are, in general, relatively insensitive to the detailed spatial arrangement of the bubbles. On the basis of this observation, it is possible to estimate them via simple formulas derived analytically for dilute periodic arrays. The effect of surface tension and density of bubbles (or rigid particles in the case where the no‐slip boundary condition is applicable) is also examined and found to be rather small.