he focus of this research has been devoted to study the interaction between two or more self-propelled toroidal swimmers in Stokes flow by applying the method of regularized Stokeslets and also study the effect of a nearby wall to the movement of a helical ring by using the method of regurlarized Stokeslets with images. In the study of the interaction between two or more toroidal swimmers, we interpret these as three-dimensional, zero Reynolds number analogues of finite vortex dipoles in an ideal fluid. Then, we examine the stability of relative equilibria that can form for these swimmers when they are initially placed in tandem or abreast. In addition, we examine the dynamics of the torus when a spherical cell body is placed at its center. This gives us an insight into the mechanical role of the transverse flagellum of dinoflagellates. Moreover, we show that the torus with a sphere moves more efficiently than one without. Lastly, we model the transverse flagellum of a dinoflagellate as a helical ring and study the effect of a nearby wall on its movement. The numerical results show that the wall baffles the movement of the helical ring, which is consistent with the phenomenon of sperm accumulation near surfaces. / acase@tulane.edu

Bioinspiration and biomimetics are two increasingly important fields in applied science and mechanics that seek to imitate systems or processes in nature to design improved engineering devices. Here, we are inspired and motivated by microscale internal flow transport phenomena in insect tracheal networks, which are observed to be induced by the rhythmic tracheal wall contractions. These networks have been shown to mange fluid very efficiently compared to current state-of-the-art microfluidic devises. This dissertation presents two versions of a novel bioinspired pumping mechanism that is neither peristaltic nor belongs to impedance mismatch class of pumping mechanisms. The insect-inspired pumping models presented here are expected to function efficiently in the microscale flow regime in a simple channel/tube geometries or a complex network of channels. The first pumping approach shows the ability of inducing a unidirectional net flow by using an inelastic tube or channel with at least two moving contractions. The second pumping approach presents a new concept for directional pumping, namely ``selective pumping in a network.". The results presented here might help in mimicking features of physiological systems in insects and guide efforts to fabricate novel microfluidic devices with improved efficiency. In this study, both theoretical analysis and Stokeslets-meshfree computational methods are used to solve for the 2D and 3D viscous flow transport in several micro-geometries (tubes, channels and networks) with prescribed moving wall contractions. The derived theoretical analysis is based on both lubrication theory and quasi-steady approximations at low Reynolds numbers. The meshfree numerical method is based on the method of fundamental solutions (MFS) that uses a set of singularized force elements ``Stokeslets'' to induce the flow motions. Moreover, the passive particle tracking simulation approach in the Lagrangian frame of reference is also used to strengthen and support our pumping paradigm developed in this dissertation. / Ph. D.

At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.