Phase-field modeling of bubble growth and flow in a Hele–Shaw cell

A phase-field model is presented for gas bubble growth and flow in a supersaturated liquid inside a Hele–Shaw cell. The flows in the gas and liquid are solved using a two-phase diffuse interface model that accounts for surface tension, interfacial mass transfer, and density and viscosity differences between the phases. This model is coupled with a phase-field equation for interface motion and a diffuse interface conservation equation for gas species transport. The model is first validated for a planar gas layer and a spherical bubble growing in a supersaturated liquid. It is shown that the results converge to the solution of the corresponding sharp interface model in the thin-interface limit. The model capabilities are demonstrated in several examples involving the growth and flow of multiple bubbles, including bubble coarsening and coalescence.