Wall effects on self-diffusiophoretic Janus particles: a theoretical study

We present a theoretical investigation of the self-diffusiophoresis of a class of two-faced, two-dimensional Janus particles propelled by the production of gradients in the concentration of a solute diffusing into a surrounding fluid at zero Reynolds and Peclet numbers. Those concentration gradients produce a tangential boundary slip resulting in translation and rotation of the particle, as a consequence of the fact that it is free of both force and torque. The model Janus particles studied here have piecewise constant surface mobilities and surface activities over two faces. An isolated circular Janus particle is studied first and its speed of locomotion in free space is found analytically. Confinement effects are then investigated by placing such a Janus particle near a straight no-slip wall. The governing nonlinear dynamical system is found in explicit form. It is used to study how the geometry, location and orientation of the particle relative to the wall affect its motion. It is found that if the particles do not hit the wall in finite time they are eventually repelled away from it.