(17a) A Kernel-Based Unified Framework for Passive and Active Phoretic Spheres

Within a unified framework, we simplify the relationship between the velocities of a phoretic sphere and field distributions by omitting slip velocity calculations and using integral kernels. These kernels calculate the local effects of fields or fluxes on particle dynamics. Both passive and active particles use the same kernel structure, which relies on varying phoretic mobility across the surface. For uniform mobility, the particle translates along the normal vector without rotating. We examine this concept with two examples: a self-phoretic axisymmetric particle in a consistent field gradient and a non-axisymmetric active particle.