An Analysis of the Swimming Problem of a Singly Flagellated Microorganism in a Fluid Flowing through a Porous Medium

The present work is concerned with the study of the swimming of flagellated microscopic organisms, which employ a single flagellum for propulsion in a fluid flowing through a porous medium. The flow is modeled by appropriate equations and the organism is modeled by an infinite flexible but inextensible transversely waving sheet, which represents approximately the flagellum. The equations of motion are solved subject to the boundary conditions, and expressions for the velocity of propulsion of the microscopic organism are obtained. Certain allied cases involving the viscosity in combination with the effective viscosity of the medium are also investigated. A creeping flow model is also analyzed. Finally, purely from a mathematical standpoint, all cases with large permeability are shown to follow the results of swimming of such organisms in a viscous fluid (discounting the pores).