Numerical study of droplet behavior passing through a constricted square channel

Snap-off is a crucial mechanism for drop breakup in multiphase flow within porous media. However, the systematic investigation of snap-off dynamics in constricted capillaries with varying pore and throat heights remains limited. In this study, we conducted three-dimensional simulations of drop behavior in a constricted square capillary with non-uniform depth, employing a color-gradient lattice Boltzmann model. Our analysis encompassed a comprehensive range of parameters, including geometrical factors and physical properties, such as capillary number, initial drop size, viscosity ratio, constriction length, and the presence of soluble surfactants. Depending on these parameters, the drop exhibited either breakup or deformation as it traversed the constriction. Upon snap-off occurrence, we quantified two significant aspects: the snap-off time t̂b, which represents the time interval between the drop front passing the constriction center and the snap-off event, and the volume of the first daughter drop V̂d generated by the breakup mechanism. Consistently, we observed a power-law relationship between t̂b and the capillary number Ca. However, the variation of V̂d with Ca exhibited a more complex behavior, influenced by additional factors, such as the viscosity ratio and the presence of surfactants, which break the linear increase in V̂d with Ca. Notably, the inclusion of surfactants is able to homogenize the volume of the first daughter drop. Through our comprehensive numerical study, we provide valuable insight into the snap-off process in constricted capillaries. This research contributes to the understanding of multiphase flow behavior and facilitates the optimization of processes involving snap-off in porous media.