Hydrodynamic Impedance Correction for Reduced-Order Modeling of Spermatozoa-Like Soft Micro-Robots

Abstract

Hydrodynamic interactions play a key role in the swimming behavior and power consumption of bio-inspired and biomimetic micro-swimmers, cybernetic or artificial alike. Bio-inspired robotic micro-swimmers require fast and reliable numerical models for robust control in order to carry out demanding therapeutic tasks as envisaged for more than 60 years. The fastest known numerical model, the resistive force theory (RFT), incorporates local viscous force coefficients with the local velocity of slender bodies in order to find the resisting hydrodynamic forces, however, omitting the induced far-field. As a result, the power requirement cannot be predicted accurately. The question of predicting and supplying the necessary power is one of the obstacles impeding the micro-robotic efforts. In this study, a novel strategy is proposed to improve the RFT-based analysis, particularly for spermatozoa and spermatozoa-inspired micro-swimmers with elastic slender tails, in order to present a practical solution to the problem. The postulated analytical improvement and the associated correction coefficients are based on hydrodynamic impedance analysis of the time-dependent solution of three-dimensional (3D) Navier-Stokes equations incorporated with deforming mesh and subject to conservation of mass.