Yield-stress fluids foams: flow patterns and controlled production in T-junction and flow-focusing devices

We study the formation of yield-stress fluid foams in millifluidic flow-focusing and T-junction devices. First, we provide a phase diagram for the unsteady operating regimes of bubble production when the gas pressure and the yield-stress fluid flow rate are imposed. Three regimes are identified: a co-flow of gas and yield-stress fluid, a transient production of bubble and a flow of yield-stress fluid only. Taking wall slip into account, we provide a model for the pressure at the onset of bubble formation. Then, we detail and compare two simple methods to ensure steady bubble production: regulation of the gas pressure or flow-rate. These techniques, which are easy to implement, thus open pathways for controlled production of dry yield-stress fluid foams as shown at the end of this article.