Janus particles are a class of artificial swimmers with an anisotropic coverage of catalyst on its surface. This generates a tangential chemical gradient. Solute molecules interact with the particle surface via a short-range potential. The asymmetric distribution of solute molecules gives rise to a tangential pressure gradient near the particle surface. This results in diffusio-osmotic flows in a thin region at the particle surface. The flow inside the thin layer is modeled as an effective slip velocity at the particle scale. This slip results in self-propulsion of a freely suspended particle, even in the absence of externally imposed concentration gradients. Previous studies have shown significant similarity between artificial and biological chemotaxis. Based on the magnitude of Péclet number (ratio of advective to diffusive effects), advective effects can have a moderate effect on the swimming velocity of an artificial swimmer. The current work aims at developing a theoretical framework to capture weak advective effects on the swimming velocity of an active particle under the influence of an external concentration gradient. It can be applied for any active particle with an axisymmetric surface activity distribution. Using Péclet number as a perturbation parameter, we employ a singular perturbation technique along with the method of matched assymptotic expansions to evaluate the concentration field up to $O\left(\mathrm{Pe}\right)$. Using the Lorentz reciprocal theorem, an analytical expression for the translational velocity valid up to $O\left(\mathrm{Pe}\right)$ is obtained. We show $O\left(\mathrm{Pe}\right)$ correction of solute advection always reduces the swimming velocity.

• Received 18 August 2021
• Accepted 4 November 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.124201