Marangoni effects on the motion of an expanding or contracting bubble pinned at a submerged tube tip (original) (raw)

1999, Journal of Fluid Mechanics

This work studies the motion of an expanding or contracting bubble pinned at a submerged tube tip and covered with an insoluble Volmer surfactant. The motion is driven by constant flow rate Q into or out of the tube tip. The purpose is to examine two central assumptions commonly made in the bubble and drop methods for measuring dynamic surface tension, those of uniform surfactant concentration and of purely radial flow. Asymptotic solutions are obtained in the limit of the capillary number Ca→0 with the Reynolds number Re=o(Ca−1, non-zero Gibbs elasticity (G), and arbitrary Bond number (Bo). (Ca=μQ/a2σc, where μ is the liquid viscosity, a is the tube radius, and σc is the clean surface tension.) This limit is relevant to dynamic-tension experiments, and gives M→∞, where M=G/Ca is the Marangoni number. We find that in this limit the deforming bubble at each instant in time takes the static shape. The surfactant distribution is uniform, but its value varies with time as the bubble are...