Dynamics of a Gas Bubble in an Inclined Channel at Finite Reynolds Number

Catherine Norman, Northwestern University

The dynamics of a gas bubble rising in an inclined channel are investigated. The solution of this free boundary problem is determined numerically by using a level set method coupled with a finite difference solution of the Navier-Stokes equations. Results are presented as a function of Reynolds number, Bond number and angle of inclination.

Steady solutions are found at small values of both Reynolds and Bond number. In an inclined channel, we find that as these parameters are increased, the bubble will either periodically bounce off of the upper wall or rupture. In a vertical channel with increasing Bond number, the bubble first begins to oscillate periodically and then ruptures. In a vertical channel with increasing Reynolds number, the steady solution will bifurcate to a time periodic, symmetric oscillation as the bubble rises up the channel, but further increase in Reynolds number allows for solutions that are no longer symmetric and oscillate back and forth between the channel walls.

In simulations where the bubble begins along the wall and evolves with a moving contact line, steady solutions are also found. However, large values of Reynolds or Bond number cause the bubble to either detach from the wall or to rupture. Our 2D and 3D results parallel experimental work which shows that there is a critical angle of inclination at which the dynamics change from bouncing bubbles to steady rising bubbles.

Abstract Author(s): Catherine Norman