First Order Approximation to the Average Velocity of Rise of Bubbles in Fluid NotIncluding Inertial Forces

摘要

Considered is a homogeneous swarm of massless bubbles rising under gravity andfilling an infinitely large container. The paper is concerned with the prediction of the ensemble averaged steady velocity of rise. The prediction requires an analysis of the hydrodynamic interaction between the bubbles in the swarm. Typically, the authors consider bubbles of about 1 mm diameter. Bubbles of this size are still spherical while the Reynolds number based on the diameter and on the velocity of rise is of the order of one hundred. This is sufficiently large to guarantee that boundary layer and wake are very thin and that the actual fluid motion around the bubble may be replaced by a potential one. The bubbles in the swarm are assumed to be distributed in a statistically homogeneous way. In the thermodynamic limit, in which the container becomes infinitely large, all macroscopic variables are necessarily spatially uniform and stationary once the system has reached equilibrium. The macroscopic variables involved are the volume concentration of the bubbles, the average fluid velocity, and the average velocity of rise.