Hydrodynamic Impedance Correction for Reduced-Order Modeling and Real-Time Control of Spermatozoa-Like Soft Micro-Robots for Medicine

Abstract

Hydrodynamic interactions play a key role in the swimming behavior and power consumption of bio-inspired and bio-mimetic micro-swimmers, Cybernetic or artificial alike. As micro-robotic devices, bio-inspired micro-swimmers require fast and reliable numerical models for robust control in order to carry out demanding therapeutic tasks as envisaged for more than sixty 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 altogether. In this scheme, the forces are calculated for a pure fluid resistance, however, at the expense of time-dependent hydrodynamic interaction effects. As a result, the power requirement cannot be predicted accurately although the supply of necessary power is one of the biggest obstacles impeding the micro-robotic efforts. In this study, an analysis 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 required analytical correction and the necessary correction coefficients are based on hydrodynamic impedance analysis via intensive computational fluid dynamics (CFD) models, i.e., the time-dependent solution of 3-dimensional Navier-Stokes equations incorporated with deforming mesh and subject to conservation of mass. The CFD-based model results are then used to extract the correction coefficients with the help of a cost function written based on the hydrodynamic power required to sustain the continuous swimming of selected shape and design. The performance of the corrections embedded in the RFT model is finally validated against the CFD model by means of hydrodynamic power comparisons.