Micron scale robots going inside our body and curing various ailments is a technolog¬ical dream that easily captures our imagination. However, with the advent of novel nanofabrication and nanocharacterization tools there has been a surge in the research in this field over the last decade. In order to achieve locomotion (swim) at these small length scales, special strategies need to be adopted, that is able to overcome the large viscous damping that these microbots have to face while moving in the various bod¬ily fluids. Thus researchers have looked into the swimming strategies found in nature like that of bacteria like E.coli found in our gut or spermatozoa in the reproductive mucus. Biomimetic swimmers that replicate the motion of these small microorganisms hold tremendous promise in a host of biomedical applications like targeted drug delivery, microsurgery, biochemical sensing and disease diagnosis. In one such method of swimming at very low Reynolds numbers, a micron scale helix has been fabricated and rendered magnetic by putting a magnetic material on it. Small rotating magnetic fields could be used then to rotate the helix, which translated as a result of the intrinsic translation rotation coupling in a helix. The present work focussed on the development of such a system of nanopropellers, a few microns in length, the characterization of its dynamics and velocity fluctuations originating from thermal noise. The work has also showed a possible application of the nanopropellers in microrheology where it could be used as a new tool to measure the rheological characteristics of a complex heterogeneous environment with very high spatial and temporal resolutions. A generalized study of the dynamics of these propellers under a rotating field, has showed the existence of a variety of different dynamical configurations. Rigid body dynamics simulations have been carried out to understand the behaviour. Significant amount of insight has been gained by solving the equations of motion of the object analytically and it has helped to obtain a complete understanding, along with providing closed form expressions of the various characteristics frequencies and parameters that has defined the motion. A study of the velocity fluctuations of these chiral nanopropellers has been carried out, where the nearby wall of the microfluidic cell was found to have a dominant effect on the fluctuations. The wall has been found to enhance the average level of fluctuations apart from bringing in significant non Gaussian effects. The experimentally obtained fluctuations has been corroborated by a simulation in which a time evolution study of the governing 3D Langevin dynamics equations has been done. A closer look at the various sources of velocity fluctuations and a causality study thereof has brought out a minimum length scale below which helical propulsion has become impractical to achieve because of the increased effect of the orientational fluctuations of the propeller at those small length scales. An interesting bistable dynamics of the propeller has been observed under certain experimental conditions, in which the propeller randomly switched between the different dynamical states. This defied common sense because of the inherent deterministic nature of the governing Stokes equation. Rigid body dynamics simulations and stability analysis has shown the existence of time scales in which two different dynamical states of the propeller have become stable. Thus the intrinsic dynamics of the system has been found to be the reason behind the bistable behaviour, randomness being brought about by the thermal fluctuations present in the system. Finally, in a novel application of the propellers, they have been demonstrated as a tool for microrheological mapping in a complex fluidic environment. The studies done in this work have helped to develop this method of active microrheology in which the measurement times are orders of magnitude smaller than its existing counterparts.

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.