Self-diffusiophoretic colloidal propulsion near a solid boundary

Abstract

Self-propelled, chemically powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing, and cargo transport. Although applications can require precise navigation and onboard steering mechanisms, here we examine by calculation how locomotors through their hydrodynamic interaction can navigate along a boundary. We adopt an engine model consisting of a spherical Janus colloid coated with a symmetrical catalyst cap, which converts fuel into a product solute. The solute is repelled from the colloid through a repulsive interaction, which occurs over a distance much smaller than the swimmer radius. Within this thin interaction layer, a concentration difference develops along the surface, which generates a pressure gradient as pressure balances the interaction force of the solute with the surface. The pressure gradient drives a slip flow towards the high concentration, which propels the particle oppositely, away from product accumulation (self-diffusiophoresis). To study boundary guidance, the motion near an infinite no-slip planar wall that does not adsorb solute is obtained by analytical solution of the solute conservation and the Stokes equations using bispherical coordinates. Several regimes of boundary interaction unfold: When the colloid is oriented with its cap axisymmetrically facing the wall, it is repelled by the accumulation of solute in the gap between the swimmer and the wall. With the cap opposite to the wall, the swimmer moves towards the wall by the repulsion from the solute accumulating on the cap side, but very large caps accumulate solute in the gap, and the motor stops. For oblique approach with the cap opposite to the wall and small cap sizes, the swimmer is driven to the wall by accumulation on the cap side, but rotates as it approaches the wall, and eventually scatters as the cap reorients and faces the wall. For a swimmer approaching obliquely with a larger cap (again facing away from the wall), boundary navigation results as the accumulation of product in the gap suppresses rotation and provides a normal force, which directs the swimmer to skim along the surface at a fixed distance and orientation or to become stationary. We also demonstrate how gravity can force transitions between skimming and stationary states.