Bubble formation, motion and interaction in a Hele-Shaw cell

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Abstract
We consider the motion of the flattened bubbles which form when air is injected into a viscous fluid contained in the narrow gap between two flat, parallel plates which make up a conventional Hele-Shaw cell, inclined at an angle x to the horizontal. We present a number of qualitative observations on the formation and interaction of the streams of bubbles that appear when air is injected continuously into the cell. The majority of this paper is then concerned with the shape and velocity of rise of single, isolated bubbles over a wide range of bubble size and cell inclination. We compare these results to theories by Taylor & Saffman (1959), and Tanveer (1986). It appears that the bubble characteristics found by an ad hoc speculation in Taylor & Saffman (1959) and by Tanveer (1986) only agree with the experimental results in the limit α → 0, and for large bubble widths (D). For finite values of α, it is necessary to use the measured bubble shape in order to calculate the rise velocity using the more general Taylor & Saffman (1959) formulation. Deviations from these theories for small D can be explained by considering the effects of the detailed flow close to the bubble surface.