Hydrodynamics of Helical Swimmers in Low-Reynolds-number Flow

Abstract

In medical engineering, microrobots offer the potential for targeted therapy through minimally invasive surgical procedures. However, realizing this vision requires further advancements in microfluidics to enhance the robots’ propulsion efficiency and their adaptation to the complex in vivo environment. This thesis aims to investigate, through numerical simulations combined with experimental methods, the effects of free surfaces and walls on the thrust generated by a helical swimmer, as well as its motion and trajectory when driven by a magnetic field. The method of regularized Stokeslets (MRS) is a convenient numerical approach to simulating very-low-Reynolds-number fluid flow. Based on the original image system for a wall, a new image system for a free surface under the framework of the method of regularized Stokeslets (IMRS) has been derived. This research focuses on an investigation into the often-neglected influence of a free surface on the thrust produced by a rotating helix. Numerical simulations evaluate the impact of a free surface on the thrust. Findings show that the thrust generated by a rotating helix is highly sensitive to the distance and the direction of the boundary. This phenomenon arises from alterations in shear stress near the helix due to the free surface and the reduction in nearby fluid to be accelerated. Since no relevant experimental studies were found, the author conducted experiments to validate his numerical results. This thesis investigates the wobbling phenomenon of a magnetic-field-driven helix through numerical simulations. This wobbling motion is attributed to the asymmetric geometry of the helix. This assumption is demonstrated by a numerical simulation of a magnetic-field-driven double helix, revealing that it exhibits no wobbling regardless of geometry factors and magnetization angle. The dependency of wobbling angle on geometric factors and magnetization of the helix is quantified. An optimal magnetization angle that minimizes the steady wobbling angle is identified. Finally, based on the simulation, it is found that the wall effects play a crucial role in affecting the magnetic-field-driven helical swimmer. The presence of a wall alters the steady wobbling state for a single helix, and the double helix is no longer immune to wobbling under these conditions. The study of the impact of a free surface not only shows the importance of a free surface on the thrust of a rotating helix, but also offers an effective method to evaluate it. The optimal magnetization angle reduces the wobbling angle without changing the geometry of the helix, and a double helix avoids the wobbling issue without compromising propulsion efficiency, which could serve as a new and promising model for micro-medical robots.

Date of Award	23 May 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	David Apsley (Main Supervisor) & Shan Zhong (Co Supervisor)