Gas bubble with a moving contact line rising in an inclined channel at finite Reynolds number

The dynamics of a gas bubble with a moving contact line rising in an inclined channel is 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 (Re), Bond number, and the angle of inclination. Steadily rising bubbles are found for small values of both the Reynolds and Bond number. With increasing Reynolds number, the steady solution first bifurcates to a time periodic oscillation, and then the numerical results imply period doubling. Large values of Reynolds or Bond number cause the bubble to either detach from the wall or to rupture.