Bubbles rising in line in polluted liquid
by
J. F. Harper
Victoria University of Wellington

To observe bubbles rising in a vertical line one need only pour out a glass of lemonade, lager or champagne, but to explain fully what physical and chemical mechanisms determine the course of events, and how, is so difficult that many fundamental questions remain.

The wake beneath a bubble contains rising liquid (fastest at the centre-line, gradually decreasing away from it), with an impurity concentration highest at the centre-line, decreasing with distance to a minimum value and then gradually increasing again to its value at a large distance. A second bubble rising underneath the first is affected by these variations in both velocity and concentration. Theory (given first by me in 1970 with subsequent improvements by Yuan and Prosperetti of Johns Hopkins University in 1994 and by myself in 1997) suggests that the second bubble should be stable to sideways displacements if impurities are present, and that it should reach a stable separation vertically if the liquid is pure.

Experiments (also from the Johns Hopkins group) suggest that the first conclusion may be right but the second is wrong, and that the first and second bubbles in a line move closer until they coalesce, and so do the third and fourth, fifth and sixth, and so on.

However, the theoretical work has not hitherto addressed the effect of impurities on the vertical distance between bubbles. Because the first bubble ``pulls in'' surface contamination towards the centre-line of its wake, the second bubble's top stagnation point should have a surface tension lower than the first bubble's. This would reduce the drag on the second bubble, by an amount which is now calculated for the first time, in the special case of very nearly pure liquids, where Green's functions simplify the calculations.

Date received: June 3, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabd-27.