Unified mobility expressions for externally driven and self-phoretic propulsion of particles

Technologies involving artificial micro-swimmers are advancing for targeted drug delivery, diagnostics, and environmental cleanup, yet face unique challenges in-vivo compared to controlled in-vitro environments. Understanding microswimmer propulsion across different conditions is crucial. The mobility of external and self-propulsion of particles is evaluated by simultaneously solving the solute conservation equation, interaction potential equation, and the Stokes equation with a body force. This method, though accurate, becomes complex, especially at finite interaction length scales. Inspired by Brady JFM (2021), we obtain unified mobility expressions with arbitrary interaction potentials. Firstly, we show that these expressions can recover well-known mobility relationships in external electrophoresis and diffusiophoresis for arbitrary double-layer thickness. Secondly, at the thin interaction length limit, these equations reduce to the slip velocity expressions for spherical microswimmers well-known in active particle literature. Finally, we explore the dynamics of autophoretic ellipsoidal Janus particles, investigating how particle eccentricity, surface heterogeneities, external gradients, and interaction length scales impact their swimming speeds.