Mathematical Modelling of Flagellated Microswimmers

Abstract

The motion of a flagellated microorganism in a free space based on specifying the space-time shape of its centreline is studied. To solve the governing Stokes equations subject to non-slip boundary conditions on the microorganism body, a computational algorithm based on the finite element method is proposed. Results of computations on meshes of various density, domains of various sizes, and the solution of the benchmark problem of flow around the Stokes sphere used for verification are presented. Using the Lighthill–Gueron–Liron theory, a semi-analytical solution of the same problem of motion of a flagellated microorganism in which the corresponding coefficients of viscous drag are found by additional test computations is obtained. It is shown that the theory and the results of direct numerical simulation are in good agreement.