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Motivated by the dynamics of microbubbles in dissolved gas flotationprocesses, we consider theoretically the approach between two shear-freetranslating and growing bubbles. We make use of the lubrication assumption toobtain the thin film flow between the bubbles. We demonstrate that thelubrication force between the bubbles involves two distinct components: oneviscous and one inertial. Both components exhibit weak singular behavior,scaling logarithmically with the ratio of bubble radius to film thickness. Toassess the accuracy of our findings, we compare the obtained solution toresults from Stokes flow and potential flow theory. The comparison demonstratesthat our current results are reliable, provided that we combine the lubricationforces with a constant term that cannot be derived from the lubricationassumption alone. We illustrate the relevance of the solution to determine thedrainage time of a small bubble rising to a free surface, and the drainage rateof expanding bubbles under force-free conditions. Remarkably, our findingsexhibit good agreement with available experimental data.

Viscous and inertial forces between translating and growing bubbles in close proximity