Analysis and Modeling of Magnetized Microswimmers: Effects of Geometry and Magnetic Properties

In recent years, much effort has been placed on development of microscale devices capable of propulsion in fluidic environments. These devices have numerous possible applications in biomedicine, microfabrication and sensing. One type of these devices that has drawn much attention among researchers is magnetic microswimmers--artificial microrobots that propel in fluid environments by being actuated using rotating external magnetic fields. This dissertation highlights our contribution to this class of microrobots. We address issues regarding fabrication difficulties arising from geometric complexities as well as issues pertaining to the controllability and adaptability of microswimmers.The majority of research in this field focuses on utilization of flexible or achiral geometries as inspired by microbiological organisms such as sperm and bacteria. Here, we set forth the minimum geometric requirements for feasible designs and demonstrate that neither flexibility nor chirality is required, contrary to biomimetic expectations. The physical models proposed in this work are generally applicable to any geometry and are capable of predicting the swimming behavior of artificial microswimmers with permanent dipoles. Through these models, we explain the wobbling phenomena, reported by experimentalists. Our model predicts the existence of multiple stable solutions under certain conditions. This leads to the realization that control strategies can be improved by adjusting the angle between the applied magnetic field and its axis of rotation. Furthermore, we apply our model to helical geometries which encompass the majority of magnetic microswimmers. We demonstrate the criterion for linear velocity-frequency response and minimization of wobbling motion. One approach to improve the adaptability of swimmers to various environments is to use modular units that can dynamically assemble and disassemble on-site. We propose a model to explain the docking process which informs strategies for successful assemblies. Most studies conducted so far are to elucidate permanent magnetic swimmers, but the literature is lacking on analysis of swimmers made of soft ferromagnetic materials. In this work, we develop a model for soft-magnetic microswimmers in the saturation regime in order to predict the swimming characteristics of these types of swimmers and compare to those of hard-magnetic swimmers

Design and Implementation of Electromagnetic Actuation System to Actuate Micro/NanoRobots in Viscous Environment

The navigation of Micro/Nanorobots (MNRs) with the ability to track a selected trajectory accurately holds significant promise for different applications in biomedicine, providing methods for diagnoses and treatments inside the human body. The critical challenge is ensuring that the required power can be generated within the MNR. Furthermore, ensuring that it is feasible for the robot to travel inside the human body with the necessary power availability. Currently, MNRs are widely driven either by exogenous power sources (light energy, magnetic fields, electric fields, acoustics fields, etc.) or by endogenous energy sources, such as chemical interaction energy. Various driving techniques have been established, including piezoelectric as a driving source, thermal driving, electro-osmotic force driven by biological bacteria, and micro-motors powered by chemical fuel. These driving techniques have some restrictions, mainly when used in biomedicine. External magnetic fields are another potential power source of MNRs. Magnetic fields can permeate deep tissues and be safe for human organisms. As a result, magnetic fields’ magnetic forces and moments can be applied to MNRs without affecting biological fluids and tissues. Due to their features and characteristics of magnetic fields in generating high power, they are naturally suited to control the electromagnetically actuated MNRs in inaccessible locations due to their ability to go through tiny spaces. From the literature, it can be inferred from the available range of actuation technologies that magnetic actuation performs better than other technologies in terms of controllability, speed, flexibility of the working environment, and far less harm may cause to people. Also, electromagnetic actuation systems may come in various configurations that offer many degrees of freedom, different working mediums, and controllability schemes. Although this is a promising field of research, further simulation studies, and analysis, new smart materials, and the development and building of new real systems physically, and testing the concepts under development from different aspects and application requirements are required to determine whether these systems could be implemented in natural clinical settings on the human body. Also, to understand the latest development in MNRs and the actuation techniques with the associated technologies. Also, there is a need to conduct studies and comparisons to conclude the main research achievements in the field, highlight the critical challenges waiting for answers, and develop new research directions to solve and improve the performance. Therefore, this thesis aims to model and analyze, simulate, design, develop, and implement (with complete hardware and software integration) an electromagnetic actuation (EMA) system to actuate MNRs in the sixdimensional (6D) motion space inside a relatively large region of interest (ROI). The second stage is a simulation; simulation and finite element analysis were conducted. COMSOL multi-physics software is used to analyze the performance of different coils and coil pairs for Helmholtz and Maxwell coil configurations and electromagnetic actuation systems. This leads to the following.: • Finite element analysis (FEA) demonstrates that the Helmholtz coils generate a uniform and consistent magnetic field within a targeted ROI, and the Maxwell coils generate a uniform magnetic gradient. • The possibility to combine Helmholtz and Maxwell coils in different space dimensions. With the ability to actuate an MNR in a 6D space: 3D as a position and 3D as orientation. • Different electromagnetic system configurations are proposed, and their effectiveness in guiding an MNR inside a mimicked blood vessel environment was assessed. • Three pairs of Helmholtz coils and three pairs of coils of Maxwell coils are combined to actuate different size MNRs inside a mimicked blood vessel environment and in 6D. Based on the modeling results, a magnetic actuation system prototype that can control different sizes MNRs was conceived. A closed-loop control algorithm was proposed, and motion analysis of the MNR was conducted and discussed for both position and orientation. Improved EMA location tracking along a chosen trajectory was achieved using a PID-based closed-loop control approach with the best possible parameters. Through the model and analysis stage, the developed system was simulated and tested using open- and closed-loop circumstances. Finally, the closedloop controlled system was concluded and simulated to verify the ability of the proposed EMA to actuate an MN under different trajectory tracking examples with different dimensionality and for different sizes of MNRs. The last stage is developing the experimental setup by manufacturing the coils and their base in-house. Drivers and power supplies are selected according to the specifications that actuate the coils to generate the required magnetic field. Three digital microscopes were integrated with the electromagnetic actuation system to deliver visual feedback aiming to track in real-time the location of the MNR in the 6D high viscous fluidic environment, which leads to enabling closed-loop control. The closed-loop control algorithm is developed to facilitate MNR trajectory tracking and minimize the error accordingly. Accordingly, different tests were carried out to check the uniformity of the magnetic field generated from the coils. Also, a test was done for the digital microscope to check that it was calibrated and it works correctly. Experimental tests were conducted in 1D, 2D plane, and 3D trajectories with two different MNR sizes. The results show the ability of the proposed EMA system to actuate the two different sizes with a tracking error of 20-45 µm depending on the axis and the size of the MNR. The experiments show the ability of the developed EMA system to hold the MNR at any point within the 3D fluidic environment while overcoming the gravity effects. A comparison was made between the results achieved (in simulation and physical experiments) and the results deduced from the literature. The comparison shows that the thesis’s outcomes regarding the error and MNR size used are significant, with better performance relative to the MNR size and value of the error

Biophysics of Helices: Devices, Bacteria and Viruses

A prevalent morphology in the microscopic world of artificial microswimmers, bacteria and viruses is that of a helix. The intriguingly different physics at play at the small scale level make it necessary for bacteria to employ swimming strategies different from our everyday experience, such as the rotation of a helical filament. Bio-inspired microswimmers that mimic bacterial locomotion achieve propulsion at the microscale level using magnetically actuated, rotating helical filaments. A promising application of these artificial microswimmers is in non-invasive medicine, for drug delivery to tumours or microsurgery. Two crucial features need to be addressed in the design of microswimmers. First, the ability to selectively control large ensembles and second, the adaptivity to move through complex conduit geometries, such as the constrictions and curves of the tortuous tumour microvasculature. In this dissertation, a mechanics-based selective control mechanism for magnetic microswimmers is proposed, and a model and simulation of an elastic helix passing through a constricted microchannel are developed. Thereafter, a theoretical framework is developed for the propulsion by stiff elastic filaments in viscous fluids. In order to address this fluid-structure problem, a pertubative, asymptotic, elastohydrodynamic approach is used to characterise the deformation that arises from and in turn affects the motion. This framework is applied to the helical filaments of bacteria and magnetically actuated microswimmers. The dissertation then turns to the sub-bacterial scale of bacteriophage viruses, ‘phages’ for short, that infect bacteria by ejecting their genetic material and replicating inside their host. The valuable insight that phages can offer in our fight against pathogenic bacteria and the possibility of phage therapy as an alternative to antibiotics, are of paramount importance to tackle antibiotics resistance. In contrast to typical phages, flagellotropic phages first attach to bacterial flagella, and have the striking ability to reach the cell body for infection, despite their lack of independent motion. The last part of the dissertation develops the first theoretical model for the nut-and-bolt mechanism (proposed by Berg and Anderson in 1973). A nut being rotated will move along a bolt. Similarly, a phage wraps itself around a flagellum possessing helical grooves, and exploits the rotation of the flagellum in order to passively travel along and towards the cell body, according to this mechanism. The predictions from the model agree with experimental observations with respect to directionality, speed and the requirements for succesful translocation.This work was funded by the EPSRC (3 years) and the last year was funded by Prof Eric Lauga's grant from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682754 to Prof Eric Lauga)

Dynamics of chiral particles in viscous fluids

Colloidal suspensions --- micron sized particles in a molecular solvent, typically water --- are found everywhere in nature, e.g. milk, and in artificial materials, e.g. paint. The dynamics of colloidal particles are therefore of interest to both academia and industry. The sedimentation of particles in suspensions is relevant in multiple fields, such as its application to the transport and separation of biological particles (viruses, bacteria, etc.). Many classical fluid mechanics studies have looked at the sedimentation, and/or tumbling due to shear, of a single particle, either using analytic methods or, more recently, numerical techniques. By now it is well understood that the particle shape uniquely determines its dynamics, but the precise trajectory and orientational dynamics are only known for a limited set of shapes. This is because, barring the simplest of shapes, the analytic calculations are challenging and often involve reducing approximations. The way chiral particles sediment and behave under shear are still unknown, and in the process of being studied and understood. This is true, in particular, for conditions under which the trajectories of such particles are chiral. In this thesis, therefore, the focus will be on the behaviour of chiral particles suspended in fluids at low Reynolds number --- where the viscosity dominates over the inertia. The dynamics of chiral objects is studied using Resistive Force Theory, which assumes that the body can be partitioned into segments but ignores the hydrodynamic couplings between the parts of the particle. These studies are then compared to a numerical calculation by Palanisamy and Den Otter that accounts for the hydrodynamic interactions using the Rotne-Prager-Yamakawa approximation. For a sedimenting helix, great agreement is found between the analytic and numerical results. Helices, for most initial conditions, sediment performing a superhelical trajectory --- a helical path with the symmetry axis parallel to the direction of gravity --- for which the handedness is opposite to that of the helix. It is also observed that a helix, in an almost horizontal configuration, is either attracted to the horizontal orientation, in which it sediments in a straight line in the direction of gravity, or to trajectories that form an unstable helical-like path. Alternatively, when a helix is in a simple shear flow it travels performing Jeffery-like orbits with a lateral drift perpendicular to the plane of shear. To better understand the result for the helix sedimentation, the settling of L- and C-shapes is also considered. Here it shown that an object does not need to be chiral for its sedimentation trajectory to possess chirality, in agreement with the findings by Krapf et al. Counter-intuitively, it was observed that the result, by Taylor, of a sedimenting rod --- the rod does not reorient --- is not obtained by taking the limit of an L-shape with a vanishing short leg. This is because any minute perturbation away from the rod limit leads to the emergence of a fixed point to the dynamics at infinite time due to orientational couplings in the Grand Mobility Matrix that persist for all perturbations. Thanks to this understanding of simple (chiral) objects, insight was gained into the sedimentation behaviour of a complicated shape: a Möbius strip. This object has a rich state diagram for its settling behaviour, which is strongly dependent on its initial orientation. This diagram, for a single Möbius strip, is portrayed and insight into the identified trends is given. Overall, it was shown that the sedimentation of anisotropic or chiral particles is chiral and future work could include finding analytic expressions to describe these trajectories. Whereas, for a helix in a shear flow, the properties and dependencies of the lateral drift observed can be further studied.

Magnetic Hybrid-Materials

Externally tunable properties allow for new applications of suspensions of micro- and nanoparticles in sensors and actuators in technical and medical applications. By means of easy to generate and control magnetic fields, fluids inside of matrices are studied. This monnograph delivers the latest insigths into multi-scale modelling, manufacturing and application of those magnetic hybrid materials

Magnetic Hybrid-Materials

Externally tunable properties allow for new applications of suspensions of micro- and nanoparticles in sensors and actuators in technical and medical applications. By means of easy to generate and control magnetic fields, fluids inside of matrices are studied. This monnograph delivers the latest insigths into multi-scale modelling, manufacturing and application of those magnetic hybrid materials