Hydrodynamics-mediated trapping of micro-swimmers near drops

In this paper, we investigate the swimming characteristics and dynamics of a model micro-swimmer in the vicinity of a clean drop, and of a surfactant covered drop. We model the swimmer as a force dipole and utilize the image-singularity system to study the dynamical behavior of the swimmer. Motivated by bacterial bio-remediation of insoluble hydrocarbons (HCs) released during oil spills, we report the 'trapping characteristics' - critical trapping radius, basin of attraction and trapping time distribution - of deterministic and stochastic swimmers, as a function of viscosity ratio, and dimensionless surface viscosity. We find that addition of surfactant reduces the critical trapping radius of a drop by similar to 30%. The basin of attraction though, is not affected acutely for any combination in the parameter space of viscosity ratio and surface viscosity. We also carry out a dynamical system analysis of our problem, for deterministic swimmers, to clarify the aforementioned concepts. For hydrodynamics combined with diffusion based motion, we note increments ranging from similar to 5-25% in the interface-retention times of surfactant-laden drops, as compared to clean drops. These differences occur for low values of surface viscosity, and saturate rapidly as the surface viscosity increases. With potential applications in bioremediation, our results highlight the importance of considering dispersant-addition in oil spills involving insoluble hydrocarbons.