Ph.D Thesis

Ph.D StudentBerman Rotem Sara
SubjectSwimming and Alignment in Low-Reynolds-Number Medium
DepartmentDepartment of Physics
Supervisors PROFESSOR EMERITUS Joseph Avron
PROF. Alexander Leshansky
Full Thesis textFull thesis text - English Version


This work presents mathematical modeling of two problems from fields governed by low Reynolds hydrodynamics, which are the motion of macromolecules inside biological cells and the swimming of microorganisms.

Inspired by the experimental problem of microtubules arrangement arising from molecular motors connections, we solved the problem of flow-driven re-orientation of connected sticks moving in low Reynolds number medium. The molecular motors were modeled by moving connection points and two connection possibilities were considered. Contrary to former works, we showed that in our modeling, the interaction of a motor which advances on two sticks is highly symmetrical and does not lead to sticks arrangement.  However, we found that the alignment of sticks can arise from an interaction which was not considered before, of one motor advancing on one stick and carrying the other. In order to induce alignment, the required properties of the motor are random detachment and a velocity which depends on the angle between the sticks or the sign of the angle change. Going to more complex assemblages, we solved the problem of regular polygons made of connected sticks.

The second part of this thesis is devoted to swimming of short undulating filaments, motivated by the propulsion of C. elegans. We calculated the distance per stroke and efficiency for a sinusoidal swimmer with wide range of wave numbers and amplitudes, employing particle-based algorithm and resistive force theory (RFT). The comparison between the approaches revealed the limit of the RFT applicability, above which inter-filament hydrodynamic interactions become important and the RFT overestimates the advancement of the swimmer and its swimming efficiency. It was found that for the finite sinusoidal swimmer, there are global maxima of distance per stroke and swimming efficiency. The parameters of biological swimmers were compared with the best sine wave gaits, and most of the swimmers proved to be in the range of parameters appropriate for maximizing the efficiency of swimming, but also showing relatively high distance covered per stroke. Concentrating on C. elegans, we calculated its propulsion from the experimental deformation function using the particle-based algorithm, and reached a good agreement with the experimental results. Using this calculation, we were able to compute the propulsion efficiency of the nematode. Compared to the sine wave, both the distance per stroke and the swimming efficiency of C. elegans proved to be much higher, demonstrating the importance of geometric optimization of the spatial beating stroke.