Motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow

This paper determines the pressure-velocity relation of bubble flow in polygonal capillaries. The liquid pressure drop needed to drive a long bubble at a given velocity U is solved by an integral method. In this method, the pressure drop is shown to balance the drag of the bubble, which is determined by the films at the two ends of the bubble. It is found that the drag scales as Ca2/3 in the limit Ca &rarr 0. Thus, the pressure drop also scale as Ca2/3. The proportionality constant for six different capillaries is roughly the same and is about that of circular capillary.