  An axisymmetric squirmer in a Bingham viscoplastic fluid is studied
numerically to determine the effect of a yield stress environment on
locomotion. The nonlinearity of the governing equations necessitates numerical
methods, which is accomplished by solving a variable-viscosity Stokes equation
with a Finite Element approach. The effects of stroke modes, both pure and
combined, are investigated and it is found that for the treadmill or "neutral"
mode, the swimmer in a yield stress fluid has a lower swimming velocity and
uses more power. However, the efficiency of swimming reaches its maximum at a
finite yield limit. In addition, for higher yield limits, higher stroke modes
can increase the swimming velocity and hydrodynamic efficiency of the treadmill
swimmer. The higher-order odd-numbered squirming modes, particularly the third
stroke mode, can generate propulsion by themselves that increases in strength
as the viscoplastic nonlinearity increases till a specific limit. These results
are closely correlated with the confinement effects induced by the viscoplastic
rigid surface surrounding the swimming body, showing that swimmers in
viscoplastic environments, both biological and artificial, could potentially
employ other non-standard swimming strategies to optimize their locomotion.
