(268d) Drop Motion and Deformation in Microchannels and Porous Media

Drop motion and deformation are important in emulsion processing, droplet-based microfluidics, and other applications. The use of boundary-integral methods for tracking interfacial motion of an isolated drop at low Reynolds number was pioneered by Rallison & Acrivos, 1978, J. Fluid Mech. 89: 191. In this talk, boundary-integral simulations of the motion of emulsion droplets in porous media and microchannels are presented, with experimental verification for select situations. Droplet trapping in porous media or microchannels with constrictions is observed for drops larger than the pore sizes when the capillary number (ratio of viscous to interfacial forces) is below a critical value, whereas droplets at larger capillary numbers deform more easily and can pass through pores and may even break. The critical capillary number is only weakly dependent on surfactant concentration, but even a small amount of surfactant can substantially reduce the droplet squeezing velocity through pores, due to Marangoni stresses that form along with surfactant concentration gradients (Zinchenko, Gissinger & Davis, 2022, J. Fluid Mech. 953: A21). For drops in long and complex microchannels, a moving-frame boundary-integral method is employed, so that the background flow is determined only once for the entire domain, and then smaller computational domains are used to follow the drop motion (Roure, Zinchenko & Davis, 2023, Phys. Fluids 35: 102013). Both simulations and experiments show that the steady drop velocity in a long, straight channel of constant cross-section decreases as the drop size increases for clean drops of viscosity near that of the suspending fluid, but the opposite trend is observed for drops of relatively low viscosity (Chattopadhyay et al., 2025, J. Fluid Mech. 1009: A61). This latter effect is suppressed by surfactants, due to reduced interfacial mobility. Surfactants can also suppress cross-stream migration of drops for some conditions, but the migration rate of a deformable drop toward the channel center can be enhanced by surfactants under other conditions (Roychowdhury et al., 2025, Phys. Fluids).