The regularized Stokeslets method applied to the three-sphere swimmer model

TL;DR

This paper demonstrates that the Method of Regularized Stokeslets (MRS) effectively simulates a three-sphere micro-swimmer at low Reynolds number, showing excellent agreement with other methods and analytical solutions, and highlighting its advantages for complex geometries.

Contribution

The study validates the MRS for simulating micro-swimmers, comparing it with established methods and analytical solutions, and discusses its suitability for complex geometries.

Findings

MRS results agree well with lattice Boltzmann and analytical solutions.

MRS is easy to implement and adaptable to complex geometries.

The method is suitable for simulating micro-swimmers at low Reynolds number.

Abstract

We investigate the applicability of the Method of Regularized Stokeslets (MRS) in the simulation of micro-swimmers at low Reynolds number. The chosen model for the study is the well-known three linked spheres swimmer. We compare our results with the lattice Boltzmann method, multiparticle collision dynamics, a numerical solution of the Oseen tensor equation and an analytical solution, all taken from Earl $\textit{et al.}$ [J. Chem. Phys. 126, 064703 (2007)]. The MRS is studied in detail, and our results show an excellent agreement with the lattice Boltzmann method, and with the analytical solution in its range of validity. We conclude that the MRS is well suited for this type of simulation, offering advantages such as being easy to implement and to represent complex geometries. Therefore it presents itself as a suitable candidate for more complex simulations.