SWIMMING OF A SINGLY FLAGELLATED MICROORGANISM IN A MAGNETOHYDRODYNAMIC SECOND-ORDER FLUID

Magnetic swimming is rapidly attracting interest in biomedical engineering applications. In the present work, we study the swimming of a singly flagellated microorganism propelling in an electrically-conducting magnetohydrodynamic (MHD) viscoelastic second-order fluid. The singly flagellated microorganism is modeled by a transversely waving infinite flexible sheet. The method of successive approximation is employed up to second-order in the amplitude of oscillation of the waving sheet. It has been shown that the velocity induced by a transversely waving infinite flexible sheet in a viscoelastic second-order fluid decreases with the elastic property for all the values of the Reynolds number. The solution reveals that the magnetic parameter (relating the relative influence of magnetic body force and viscous force effects) increases the propulsion for small Reynolds number and reduces it with high Reynolds number. The influence of magnetic field is therefore variable depending on the inertial effect. Comparisons with the literature demonstrate the generality of the proposed approach which allows errors included in previous formulations to be corrected. The present results may be, in principle, taken as a benchmark for computational modeling of magnetic swimming in viscoelastic fluids of relevance to green energy and magnetic biomedical procedures.