Accurate Solutions to Non-Linear PDEs Underlying a Propulsion of Catalytic Microswimmers

Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solutio...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2022-05, Vol.10 (9), p.1503
Main Authors: Asmolov, Evgeny S., Nizkaya, Tatiana V., Vinogradova, Olga I.
Format: Article
Language:English
Subjects:
Anisotropy
Asymptotic methods
Asymptotic series
Boundary conditions
Electric fields
Electric potential
Electrolytes
Exact solutions
Food science
Inhomogeneity
Ion concentration
Ion flux
matched asymptotic expansions
Nernst–Planck–Poisson equations
Particle size
Propulsion
Reynolds number
self-propulsion
Swimming
Thin films
Velocity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solution for ion concentration and electric potential in the inner region is known, the electrostatic problem in the outer region was previously solved but only for a linear case. Additionally, only main geometries such as a sphere or cylinder have been favoured. Here, we derive a non-linear outer solution for the electric field and concentrations for swimmers of any shape with given ion surface fluxes that then allow us to find the velocity of particle self-propulsion. The power of our formalism is to include the complicated effects of the anisotropy and inhomogeneity of surface ion fluxes under relevant boundary conditions. This is demonstrated by exact solutions for electric potential profiles in some particular cases with the consequent calculations of self-propulsion velocities.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10091503