טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLevchenko Stanislav
SubjectDynamic Simulation of Low-Reynolds-Number Swimmers near
Boundaries
DepartmentDepartment of Chemical Engineering
Supervisor Professor Alexander Leshansky
Full Thesis textFull thesis text - English Version


Abstract

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.