M.Sc Thesis | |

M.Sc Student | Levchenko Stanislav |
---|---|

Subject | Dynamic Simulation of Low-Reynolds-Number Swimmers near Boundaries |

Department | Department of Chemical Engineering |

Supervisor | PROF. Alexander Leshansky |

Full Thesis text |

The
main goal of the research was to investigate the dynamics of sphere-based low-*Re
*swimmers in bounded fluid domains by performing numerical simulations**. **In
order to achieve this goal, the research focused on the following objectives:
(i) developing a general tool for numerical simulation of the dynamics of low-*Re
*swimmers near a plane wall; (ii) setting up a case study for a simple model
swimmer composed of just two co-rotating spheres; (iii) comparing the results
with previously reported findings based on far-field theory.

Method of *multipole expansion *(ME) was
used to simulate the dynamics of a swimmer built from spheres near a plain
rigid wall. The ME method is based on Lamb’s exact solution of Stokes equations
of creeping flow in term of spherical harmonics. A direct coordinate
transformation between the spheres’ origin is used calculate the magnitude of
each basis function in order to satisfy the no-slip condition at the boundary
of all spheres. The presence of a plane wall was accounted for by superimposing
the wall-induced image of each basis function. Unlike the far-field
approximation usually adopted to model hydrodynamic interaction with walls, the
ME method can treat arbitrary small separation distances between the swimmer
and the bounding wall and achieve any desired precision by increasing the
number of basis functions retained in the solution.

Applicability of far-field solution was examined and it was found that for swimmers with relatively large distance between the spheres far-field solution estimate of the swimmer velocities is within ~3% error margin at distances larger than two sphere radii from the plane wall. For more compact swimmers, the use of far-field approximation is far less accurate than the ME approach and may even result in non-physical predictions at close proximity to the wall.