Magnetic microswimmers propelling through biorheological liquid bounded within an active channel

The dynamics of a micro-organism swimming through a channel with undulating walls subject to constant transverse applied magnetic field is investigated. The micro-organism is modeled as self-propelling undulating sheet which is out of phase with the channel waves while the electrically-conducting biofluid (through which micro-swimmers propel) is characterized by the non-Newtonian shear-rate dependent Carreau fluid model. Creeping flow is mobilized in the channel due to the self-propulsion of the micro-organism and the undulatory motion of narrow gapped walls. Under these conditions the conservation equations are formulated under the long wavelength and low Reynolds number assumptions. The speed of the self-propelling sheet and the rate of work done at higher values of rheological parameters are obtained by using a hybrid numerical technique (MATLAB routine bvp-4c combined with a modified Newton-Raphson method). The results are validated through an alternative hybrid numerical scheme (implicit finite difference method (FDM) in conjunction with a modified Newton-Raphson method). The assisting role of magnetic field and rheological effects of the surrounding biofluid on the swimming mode are shown graphically and interpreted at length. The global behavior of biofluid is also expounded via visualization of the streamlines in both regions (above and below the swimming sheet) for realistic micro-organism speeds. The computations reveal that optimal swimming conditions for the micro-organism (i.e., greater speed with lower energy losses) are achievable in magnetohydrodynamic (MHD) environments including magnetic field-assisted cervical treatments.