Bubble growth by injection of gas into viscous liquids in cylindrical and conical tubes

The effect of partial confinement on the shape and volume of bubbles generated by injection of a constant flow rate of gas into a very viscous liquid is studied numerically and experimentally. Numerical solutions of the Stokes equations for the liquid and the evolution equation for the surface of a bubble, and experiments with two different liquids, show that cylindrical and conical walls concentric with a gas injection orifice in the horizontal bottom of the liquid may strongly affect the shape and volume of the bubbles, and can be used to control the size of the generated bubbles without changing the flow rate of gas. A well-known scaling law for the volume of the bubbles generated by injection of a high flow rate of gas in a very viscous unconfined liquid is extended to take into account the presence of cylindrical or conical walls around the injection orifice.