Year: 2023
Type: preprint
Abstract: We consider phoretic self-propulsion of a chemically active colloid where solute is consumed at both the colloid boundary and within the bulk solution. Assuming first-order kinetics, the dimensionless transport problem is governed by the surface Damköhler number ${\mathcal{S}}$ and the bulk Damköhler number ${\mathcal B}$. The dimensionless colloid velocity $U$, normalized by a self-phoretic scale, is a nonlinear function of these two parameters. We identify two scenarios where these numbers are linked. When the controlling physical parameter is colloid size, ${\mathcal{S}}$ is proportional to ${\mathcal B}^{1/2}$; when the controlling parameter is solute diffusivity, ${\mathcal{S}}$ is proportional to ${\mathcal B}$. In the limit of small Damköhler numbers, $U$ adopts the same asymptotic limit in both scenarios, proportional to ${\mathcal{S}}$. In the limit of large Damköhler numbers, the deviations of solute concentration from the equilibrium value are restricted to a narrow layer about the active portion of the colloid boundary. The asymptotic predictions of the associated boundary-layer problem are corroborated by an eigenfunction solution of the exact problem. The boundary-layer structure breaks down near the transition between the active and inactive portions of the boundary. The transport problem in that local region partially resembles the classical Sommerfeld problem of wave diffraction from an edge.
Source: arXiv (Cornell University)
Language: English
Topic: Micro and Nano Robotics
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387559201