Hydrodynamic Stokes flow induced by a chemically active patch imprinted on a planar wall

TL;DR

This paper analytically characterizes the complex hydrodynamic flows generated by a chemically active patch on a wall, revealing how flow topology depends on surface chemistry and geometry, aiding interpretation of experimental micropump studies.

Contribution

It provides an analytical model for the flow induced by a chemical patch on a wall, highlighting the flow's dependence on material properties and geometry, which was previously not well understood.

Findings

Flow consists of surface-driven and bulk-driven components with distinct topologies.

Surface-driven flow topology changes qualitatively with surface chemistry contrast.

Flow analysis aids interpretation of tracer drift in experimental micropump setups.

Abstract

Patches of catalyst imprinted on supporting walls induce motion of the fluid around them once they are supplied with the chemical species (``fuel'') that are converted by the catalytic chemical reaction. While the functioning of such chemically active micropumps is conceptually well understood, an in-depth characterization of the induced hydrodynamic flow, and in particular of its possible dependences on parameters such as material properties of the patch and the wall or the geometry of the experimental cell, remains elusive. By using a simple model for the chemical activity of a patch imprinted on a planar wall, we determine analytically the induced hydrodynamic flow in a Newtonian solution that occupies the half space above the wall supporting the patch. This can be seen as an approximation for an experimental-cell geometry with a height much larger than its diameter, the latter, in turn, being much larger than the size of the patch.) The general flow is a linear superposition of a surface-driven and a bulk-driven component; they have different topologies and, generically, each one dominates in distinct regions, with the surface-driven flow being most relevant at small heights above the wall. The surface-driven flows exhibit a somewhat unexpectedly rich behavior, including qualitative changes in the topology of the flow, as a function of the contrast in surface-chemistry (osmotic slip coefficient) between the patch and the support wall. The results are expected to provide guidance for the interpretation of the drift of tracers by the ambient flow, which is the observable usually studied in experimental investigations of chemically active micropumps.