Buoyant Bretherton: gravity driven rise of a bubble in a capillary

The pressure driven motion of a bubble in a capillary has long been used to measure fluid flow rates in myriad industrial processes. Advances in microfluidics and small-scale flow applications highlight the importance of the limit when the capillary’s radius is significantly smaller than the capillary length for the fluid of interest, increasing the relative importance of viscous resistance as the bubble moves through the capillary. For buoyancy driven bubble motion, when the bubble is subjected to a constant force, the bubble’s motion is critically dependent on the dynamics of the surrounding liquid film. The absence of quantitative measurements of the liquid film thickness led to contradictory predictions and experimental data for this problem. Here, we present quantitative measurements of the liquid film surrounding the bubble for a liquid with a strong interfacial attraction to the capillary wall. Within the bounds of our measurement, the film thickness reaches a constant value, and the bubble always rises, even for capillary diameters significantly less than the critical value predicted by the theory.