M.Sc Thesis

M.Sc StudentFuchs Lanuel
SubjectInvestigation of the Optimal Velocity and Dragging
Efficiency of the Nano Propellers Towing a Passive
DepartmentDepartment of Chemical Engineering
Supervisor PROF. Alexander Leshansky
Full Thesis textFull thesis text - English Version


The locomotion of microorganisms and miniaturized robotic swimmers at the micro and nano scale is governed by low Reynolds number hydrodynamics, where the inertial effects are negligible and the viscous forces dominate the propulsion. The last few decades showed a growing interest in propulsion at micro and nano scales, motivated by both biomedical and engineering problems. Controllable manipulation of nanoscale objects in a viscous environment can promote many areas of nanotechnology due to numerous potential biomedical applications.

The main aim of this theoretical research is to study the optimal cargo towing by a rotating helical filament upon varying the relative size of the propeller and the load and the geometry of the helix. Two potential “towing" designs are considered: (i) rigid attachment of the load and the magnetic helix actuated externally by a rotating magnetic field; (ii)“free axis" attachment inspired by the natural design of bacterial flagella, where the rotation of the helix with respect to the load is powered internally by a motor located at the cargo. Closed form expressions are obtained for the dragging velocity and efficiency under the assumption of negligible hydrodynamic interaction between the propeller and the cargo and unidirectional propulsion along the helical axis. To test the validity of these theoretical predictions the multipole expansion algorithm is used for numerical modeling of cargo towing. This algorithm allows to “build" the propeller and the load from spheres, so that the helix is composed of nearly touching small diameter spheres and the load is modeled as a larger sphere. Finally, the numerical results and the theoretical predictions are compared and discussed.

Finally, a three dimensional dynamics (as opposed to a unidirectional motion along the helical axis) of a rigid magnetic helix actuated externally is considered. The external forcing is modeled as a constant magnetic torque exerted on the helix along some fixed direction. Time integration is performed by constructing a 3D rotation matrix at each instant, and tracking the evolution of the Euler angles in time. The results confirm the experimentally observed “wobbling" behavior of the helix, where the helical axis precess about the direction of externally applied torque depending on the initial orientation of the helix.