Dimensionless Analyses of Liquid-Liquid-Liquid Three-Phase Flow Patterns in a Confined Microchannel

The flow pattern transition of a liquid-liquid-liquidthree-phase flow in a confined microchannel has been ascertained bysystematic numerical simulations with a volume of fluid-continuumsurface force (VOF-CSF) model. Three typical flow patterns of theliquid-liquid-liquid three-phase flow can be distinguishedby the flow field structures, namely, plug, slug, and blocked-slug.Further, the effects of the key dimensionless numbers on the quantitativetransition laws of flow patterns are intensively investigated. Itis found that the transition from plug to slug is only determinedby the capillary number of the outer phase. However, as for the transitionfrom slug to blocked-slug, it can be significantly regulated by thecoupling of all involved dimensionless numbers. In addition, to revealthe underlying mechanisms of flow pattern transition, the force fieldcharacteristics have been thoroughly discussed. The results indicatethat, in plug flow, the Laplace pressure force acting on the outerinterface is dominant. Once the pressure differential force and shearforce together acting on the outer interface overcome the Laplacepressure force, the flow pattern of the slug emerges. As the pressuredifferential force and the shear force acting on the inner interfaceincrease, the flow pattern falls into the blocked-slug because ofan enhanced hindering effect of the inner interface on the deformationof the outer interface. The results offer a theoretical guide forprecisely controlling the liquid-liquid-liquid three-phaseflow behaviors to fulfill the process intensification of microfluidsin a confined microchannel.