This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas-liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel.

We report a study of the capillary pinching of a gas bubble by a wetting liquid inside a pinched channel. The capillary pinching induces very reproducible bubbling, at a very well-defined frequency. There are two regimes associated with drip and jet bubbling. In the latter, we show that highly monodispersed bubbles are formed by our pinched channel. The dynamics of the bubble formation also shows two distinct regimes: a long-duration elongation of the air bubble and a rapid relaxation of the interface after interface breakup. The slow regime depends on the flux imposed and the channel geometry. The rapid deformation dynamic regime depends very weakly on the boundary conditions. Scaling arguments are proposed in the context of the lubrication approximation to describe the two regimes.