Squirming in viscoplastic fluids

An axisymmetric squirmer in a Bingham viscoplastic fluid is studied numerically to determine the effect of a yield stress environment on locomotion. 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 at moderate yield limits. These results show that swimmers in viscoplastic environments, both biological and artificial, could potentially employ other non-standard swimming strategies to optimize their locomotion.