Growing bubbles rising in line

Over many years the author and others have given theories for bubbles rising in line in a liquid. Theory has usually suggested that the bubbles will tend towards a stable distance apart, but experiments have often showed them pairing off and sometimes coalescing. However, existing theory seems not to deal adequately with the case of bubbles growing as they rise, which they do if the liquid is boiling, or is a supersaturated solution of a gas, or simply because the pressure decreases with height. That omission is now addressed, for spherical bubbles rising at high Reynolds numbers. As the flow is then nearly irrotational, Lagrange’s equations can be used with Rayleigh’s dissipation function. The theory also works for bubbles shrinking as they rise because they dissolve.