Locomotion with a wavy cylindrical filament in a yield-stress fluid

A yield stress is added to Taylor's (1952, Proc. Royal Soc. , 211 225-239) model of a microscopic organism with wavy cylindrical tail swimming through viscous fluid. Viscoplastic slender-body theory employed for the task, generalising existing results Bingham fluid Herschel–Bulkley constitutive model. Numerical solutions are provided over range two key parameters problem: wave amplitude relative wavelength, and number which describes strength stress. supplemented discussions various limits problem in analytical progress possible. If sufficiently small, material inevitably dominates flow; resulting ‘plastic locomotion’ speeds that depend strongly on gait, can, some cases, even be negative. Conversely, when large, becomes possible at speed, swimmer sliding or burrowing along its centreline relatively high efficiency.