LAUSR

We numerically study the deformation and breakup of a surfactant-laden liquid drop immersed in another immiscible liquid flowing through a single pore with curvilinear boundaries using a conservative phase-field lattice Boltzmann method. Our results show that, compared to pure drops, surfactant-laden drops are prone to break, generating small satellite drops due to a non-uniform distribution of surfactant at the drop interface and a decrease in interfacial tension. As the surfactant concentration increases, it becomes increasingly challenging to maintain the stability of the drop, as higher surfactant concentrations result in a lower interfacial tension, thereby enhancing drop breakage. To provide a guideline on drop breakup conditions when it moves through a curved pore space, we present a map of the Weber number (We) vs the Reynolds number (Re), outlining the critical boundary beyond which drops break for surfactant-laden drops (at dimensionless bulk concentrations ψb=0.1 and 0.2) at Re ranging from 0.26 to 2.51. We theoretically explain this critical relationship for drop breakage by balancing the shear force and the surface tension force acting on the drop. We further investigate the combined effect of the viscosity ratio and channel confinement ratio (defined as the ratio between the channel depth and drop diameter) on drop breakup. We find that less viscous drops in a more confined channel are prone to breakage. The channel confinement ratio has a dominant effect on drop breakage since viscous drops with a high surfactant load do not break when the channel is not confined.