Hydrodynamic and Physicochemical Interactions Between an Active Janus Particle and an Inactive Particle

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled. Here we delve into the world of active matter by studying colloidal-sized (100 nm-10 μm) synthetic particle locomotors driven by chemical reactions that occur anisotropically on the particle, creating a slip velocity through self-diffusiophoresis that drives locomotion. Such particle locomotors are a type of Janus particle. Janus particles have many important applications including water decontamination, drug delivery in organisms, and bio-imaging. Many of these applications require the Janus particle to either direct the movement of an inactive (inert) particle (known as cargo) or to navigate around boundaries. We study the process by which a spherical Janus particle driven by self-diffusiophoresis pushes a spherical colloid through a liquid landscape as well as the process by which a Janus particle navigates a spherical fixed obstacle. Neither of these movements involves a tether, an advantage in both cargo transport and Janus particle navigation, but guidance is complicated by the orientation of the active face of the Janus particle relative to the line between the centers of the cargo or obstacle and the Janus particle. We study these systems using models that give numerical solutions for the Janus-cargo and Janus-obstacle systems’ motions. We start by looking at an isolated Janus particle in an infinite solution where we can compare the analytical solutions, derived from the Stokes and continuity equations, with our model’s numerical results. The consistency between the model’s numerical results and the analytical solution is one way we verify the validity of our models. We also verify our models by comparing our results with published works involving (i) two Janus particles moving symmetrically along their line of centers, (ii) an axisymmetric Janus particle-cargo system, and (iii) a Janus particle near a large obstacle. Once our models are verified, we then extend the models to asymmetric Janus particle-cargo pushing motions as well as Janus particle-obstacle situations where the analytical solutions in bispherical coordinates have not been fully solved. There is no published work to compare to these extensions of the model. We create these models with COMSOL Multiphysics, which uses the finite element method (FEM) to find the stresses and the torques on the system. We then use our knowledge that there are no external forces on either particle, or on the obstacle, to determine each particle’s velocity. We conclude for the Janus particle-cargo system that when the two particles are the same size (λ = 1) and the Janus particle is half active, the cargo’s presence has very little influence on the Janus particle’s trajectory and the cargo itself barely moves, unless the system is close to axisymmetric. We also find that for the Janus particle-obstacle system, when the obstacle is five times as large as the Janus particle (λ = 5), with the active side larger than the inactive side on the Janus particle, some trajectories lead to novel hovering and tracking around a spherical object never before seen at a ratio this small