Dynamics of a sphere with inhomogeneous slip boundary conditions in Stokes flow

TL;DR

This paper analyzes how inhomogeneous slip boundary conditions affect the resistance and dynamics of a sphere in low Reynolds number flow, providing explicit calculations for complex shapes like Janus particles.

Contribution

It introduces a perturbation approach to model inhomogeneous slip effects on spherical particles in Stokes flow, including resistance tensors and specific dynamics of hemispherical inhomogeneous spheres.

Findings

Inhomogeneous slip acts as a radial deformation to first order.

Full resistance tensors for inhomogeneous spheres are derived.

Dynamics of Janus particles with inhomogeneous slip are explicitly calculated.

Abstract

The dynamic resistance of a sphere with a general inhomogeneous slip boundary condition is analysed in Newtonian unbounded uniform flow at low Reynolds number. The boundary condition is treated as a perturbation to a homogeneous sphere, assuming that the slip length magnitude b is much smaller than the sphere radius a. To first order, the effect of inhomogeneous slip is the same as that of a radial deformity of magnitude b. Full resistance tensors are presented and the dynamics of a hemispherical inhomogeneous sphere, such as a Janus particle, are explicitly calculated.