The passage of a bubble or a drop past an obstruction in a channel

Abstract

The passage of a fluid particle (bubble or a drop) past an obstruction in a rectangular channel is examined by numerical simulation, focusing on the disruption of the wake and the trajectory of the fluid particle. The flow is laminar, and the wake is initially steady. The obstruction is relatively large compared to the height of the channel. The problem is defined by the capillary number (Ca) and the Reynolds number (Re), the density (ηρ) and viscosity (ημ) ratios, and the relative size of the fluid particle (ηd). Simulations of three-dimensional flows are used to examine several combinations of these parameters. The results show that the motion of a drop is nearly independent of the wake downstream of the obstruction, but bubbles may get temporarily trapped in it. Drops also tend to block the background flow, while bubbles may accelerate it. It is found that a bubble of comparable or smaller size than the constriction can pass through the constriction intact without getting trapped. An increase in Ca and Re leads to bubbles passing through the constriction at a faster speed and move further downstream before being caught by the wake. Simulations of two-dimensional flows for a relatively larger range of Ca and Re are performed to obtain a flow regime diagram. The results show that relatively rigid particles (low Ca) tend to be temporarily trapped in the wake, while more deformable particles (higher Ca) pass without being trapped at lower Reynolds numbers but break up at higher Reynolds numbers. The influence of the obstruction geometry is also examined.