Swimming in low reynolds numbers using planar and helical flagellar waves

In travelling towards the oviducts, sperm cells undergo transitions between planar to helical flagellar propulsion by a beating tail based on the viscosity of the environment. In this work, we aim to model and mimic this behaviour in low Reynolds number fluids using externally actuated soft robotic sperms. We numerically investigate the effects of transition between planar to helical flagellar propulsion on the swimming characteristics of the robotic sperm using a model based on resistive-force theory to study the role of viscous forces on its flexible tail. Experimental results are obtained using robots that contain magnetic particles within the polymer matrix of its head and an ultra-thin flexible tail. The planar and helical flagellar propulsion are achieved using in-plane and out-of-plane uniform fields with sinusoidally varying components, respectively. We experimentally show that the swimming speed of the robotic sperm increases by a factor of 1.4 (fluid viscosity 5 Pa.s) when it undergoes a controlled transition between planar to helical flagellar propulsion, at relatively low actuation frequencies.