The motion of a long bubble in polygonal capillaries at low capillary numbers.

摘要

The motion of a long bubble in various regular-polygonal and rectangular capillaries is solved by a singular perturbation method in the limit Ca ;An integral force balance on the moving bubble and its surrounding liquid reveals for the first time the existence of a contact-line drag. The force balance also determines the liquid pressure required to balance the drag. The drag arises predominantly from the thin film near the bubble ends, and therefore is not affected by capillary corners. Due to film rearrangement, the drag at the back end increases with L;The liquid pressure drop across the moving bubble drives liquid through the capillary corners at a higher velocity than the bubble. For a given liquid flow, longer bubbles experience larger pressure drops and therefore move faster than short bubbles. This coupling between bubble velocities and bubble lengths has not been previously reported and is confirmed by experimental results.;In the inner viscous problem, a lubrication equation governs the profiles of the thin film deposited on the capillary wall by the moving bubble. Numerical and analytic solutions show that the deposited film is nonuniform in the cross-stream direction and rearranges in the downstream direction. For bubble lengths L