Orbits, Spirals, and Trapped States: Dynamics of a Phoretic Janus Particle in a Radial Concentration Gradient

A long-standing goal in colloidal active matter is to understand how gradients in fuel concentration influence the motion of phoretic Janus particles. Here, we present a theoretical description of the motion of a spherical phoretic Janus particle in the presence of a radial gradient of the chemical solute driving self-propulsion. Radial gradients are a geometry relevant to many scenarios in active matter systems and naturally arise due to the presence of a point source or sink of fuel. We derive an analytical solution for the Janus particle's velocity and quantify the influence of the radial concentration gradient on the particle's trajectory. Compared to a phoretic Janus particle in a linear gradient in fuel concentration, we uncover a much richer set of dynamic behaviors including circular orbits and trapped stationary states. We identify the ratio of the phoretic mobilities between the two domains of the Janus particle as a central quantity in tuning their dynamics. Our results provide a path for developing optimum protocols for tuning the dynamics of phoretic Janus particles and mixing fluid at the microscale. In addition, this work suggests a method for quantifying the surface properties of phoretic Janus particles, which have proven to be challenging to probe experimentally.