Autophoresis of a Janus particle near a planar wall: a lubrication limit

Abstract

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the extreme near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the near-contact limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the capsize determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

Figures (5)

• Figure 1: Schematic illustration of a spherical Janus particle with radius $a$ near a planar wall.
• Figure 2: Translational velocity in the $z$-direction of a freely-suspended Janus particle near a wall as a function of the parameter $\Phi = \phi/\epsilon^{1/2}$. The dotted curve corresponds to the original configuration, in which the particle has a large active cap and a small inert face, with the inert face oriented toward the wall. The dashed curve corresponds to the complementary configuration, where the particle has a small active cap and a large inert face, with the active cap oriented toward the wall. The velocity for a fully active particle (solid line) was obtained by yariv2016wallyariv2017boundary.
• Figure 3: Schematic illustration of a spherical Janus particle of radius $a$ near a planar wall. The particle is tilted by a small angle $\psi$ about the $y$-axis relative to the wall.
• Figure 4: (a) Translational velocity in the $x$-direction of a slightly tilted, freely-suspended Janus particle near a wall, plotted as a function of the parameter $\Phi = \phi/\epsilon^{1/2}$. (b) Angular velocity around the $y$-axis of a slightly tilted, freely-suspended Janus particle near a wall, plotted as a function of the parameter $\Phi = \phi/\epsilon^{1/2}$.
• Figure 5: Schematic illustration of a slightly tilted Janus particle of radius $a$ near a planar wall, indicating the direction of its motion. For all values of $\Phi = \phi / \epsilon^{1/2}$, the particle translates in the positive $x$- and $z$-directions. In contrast, the direction of rotation depends on $\Phi$: (left) for $\Phi \gtrsim 4.6$, the particle rotates counterclockwise, whereas (right) for $\Phi \lesssim 4.6$, it rotates clockwise.