Hydrodynamics-mediated trapping of micro-swimmers near drops

The swimming characteristics and dynamics of a model micro-swimmer (force dipole) near a clean, and a surfactant covered drop, are investigated. We report the critical trapping radius, the basin of attraction, and the trapping time distribution, of deterministic and stochastic swimmers, as a function of the swimmer’s dipole strength, the viscosity ratio, and the dimensionless surface viscosity. We find that addition of surfactant greatly reduces the critical trapping radius for low values of swimmer dipole strength, viscosity ratio, and dimensionless surface viscosity. The basin of attraction though, remains at O(1) swimmer body length for all combinations of viscosity ratio and dimensionless surface viscosity. A dynamical system analysis, for deterministic swimmers, reveals the existence of saddle points in the phase-space, for all cases where swimmers can get trapped. Although swimmer escape is possible via diffusive motion, we find that even in this case, addition of surfactant increases the interface-retention times by ~ 5-25%. It is seen that all effects of surfactant addition saturate rapidly with increase in the surface viscosity.