Abstract
For a sperm-cell-like flagellated swimmer in an unbounded domain, several numerical models of different fidelity are considered based on the Stokes flow approximation. The models include a regularized Stokeslet method and a three-dimensional finite-element method, which serve as the benchmark solutions for several approximate models considered. The latter include the resistive force theory versions of Lighthill, and Gray and Hancock, as well as a simplified approximation based on computing the hydrodynamic forces exerted on the head and the flagellum separately. It is shown how none of the simplified models is robust enough with regards to predicting the effect of the swimmer head shape change on the swimmer dynamics. For a range of swimmer motions considered, the resulting solutions for the swimmer force and velocities are analysed and the applicability of the Stokes model for the swimmers in question is probed.
Highlights
Flagellated microswimmers are cells or micrometre-sized robots that swim by moving appendages called flagella
We study the motion of a single sperm cell in an infinite domain to address three issues: (i) the accuracy of approximating swimming as the linear superposition of the dynamics of separate body-parts versus a full-body description, (ii) the accuracy of modelling swimming with the resistive force theory (RFT), which is one of the possible approximations based on the above superposition that ignores long-range hydrodynamical interactions, and (iii) the validity of the quasisteady and inertia-less assumption for swimming at the micro-scale, where the quasi-steady hypothesis entails assuming that the flow instantaneously adapts to the body deformations
Despite this extensive prior research on the zero-Reynolds number propulsion of flagellated microorganisms, a systematic comparison of RFT, which can be seen as an abridged version of slender body theory (SBT), and a direct solution of the Stokes equation in the case of a realistic, flexible flagellum of a sperm cell [12] with and without fully accounting for non-local hydrodynamic effects of the head/flagellum interaction, has not been performed yet
Summary
Flagellated microswimmers are cells or micrometre-sized robots that swim by moving appendages called flagella. Later studies that focused on the dynamics of such swimmers close to no-slip and/or free-slip boundaries generally adopted a boundary element method approach [30,31,32] Despite this extensive prior research on the zero-Reynolds number propulsion of flagellated microorganisms, a systematic comparison of RFT, which can be seen as an abridged version of SBT, and a direct solution of the Stokes equation in the case of a realistic, flexible flagellum of a sperm cell [12] with and without fully accounting for non-local hydrodynamic effects of the head/flagellum interaction, has not been performed yet.
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