Motion and deformation of a bubble in a Hele-Shaw cell

We theoretically and experimentally study the propagation of approximately circular pancake-shaped bubbles in a Hele-Shaw cell under a uniform background flow at low Reynolds number. Bubble motion and deformation are determined by an interplay between the Hele-Shaw viscous pressure, the pressure drop due to the thin films surrounding the bubble, and the capillary pressure due to the in-plane curvature of the bubble boundary. Numerical, asymptotic and experimental results indicate that, with all other parameters constant, the in-plane aspect ratio of the bubble varies nonmonotonically with its size. The model is also extended for buoyancy-driven bubbles in inclined or vertical channels.