Snap-Off Criteria for Dynamic Flow Conditions in Constricted Circular Capillaries

One of the main mechanisms of emulsion formation in porous media is the snap-off; invasion of the wetting phase flowing adjacent to the pore wall within a constriction mostly occupied by the non-wetting phase, causing breakup into isolated drops of this phase. The current approaches to determine the occurrence of this phenomenon have been formulated for quasistatic flow conditions, where the mechanisms governing the flow are controlled by the geometry of the capillary. However, some studies suggest that the drop breakup does not occur above a capillary number threshold and given a certain viscosity ratio, even if the static breakup criteria are met. In this paper, we extend the current numerical analysis of the capillary number upper limit (Calim), in which the snap-off is inhibited, by considering the effect of viscosity ratio on the dynamics of immiscible two-phase flow through constricted circular capillaries. Based on the results of this study, empirical mathematical expressions that relate the main physical variables of the flow were established as breakup criteria for dynamic flow conditions. The dynamic breakup criteria takes into account, jointly: some aspects of rheology of the two-phase system, such as the viscosity ratio; the dynamic factors of the flow, encapsulated in the local capillary number; and an integral form of the capillary geometry, represented by a parameter that relates both radii and the distance between them.