Hydrodynamic Impedance of Bacteria and Bacteria‐Inspired Micro‐Swimmers: A New Strategy to Predict Power Consumption of Swimming Micro‐Robots for Real‐Time Applications

Abstract

Power supply is one of the key issues with bio-inspired micro-robots for therapeutic applications. There have been different approaches to predict the hydrodynamic behavior of such systems, most of which are based on the low-Reynolds-number approximation of the surrounding flow field, also known as the Stokes flow. However, it has been long debated that the Stokes-flow approach without corrections for hydrodynamic interactions is inadequate in explaining the dynamics of a particle, even a blunt sphere, following a non-trivial path subject to spatial and temporal variations. A cargo being towed by a rotating helical tail presents an even more complicated problem which can only be appreciated by numerical solutions of time-dependent Navier-Stokes equations incorporated with rigid-body dynamics. In this study, such a solution scheme is presented for the six degrees of freedom motion of both bacteria and bacteria-inspired micro-robots, swimming in backward or forward direction. Furthermore, the analysis is extended to characterize the impedance coefficients via parameterized wave geometry. Thus, it is demonstrated that the resistive force theory can be improved to predict time-dependent fluid resistance acting on bio-inspired micro-swimmers via hydrodynamic impedance-based corrections, allowing accurate calculation of required power to achieve desired actuation strategies.

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

“…It should be noted that there will be no contribution of the binormal component as it is parallel to the z-axis. This phase information is found to be a function of time for helical wave propagation [44] and a very similar analysis will be carried out here to ascertain the time-dependent characteristics of this phenomenon for planar wave propagation. However, the reduced-order mathematical model articulated thus far considers the velocity kinematics and omits the hydrodynamic interactions between the head and the tail.…”

“…[23,24,[41][42][43][44] The Re number is defined as Re = 0.01 for the results presented in this work. As a result, the scaling Reynolds number becomes Re = 2π fρD body 2 /μ, the reciprocal of which will be used to define the dimensionless dynamic viscosity of the domain (t), which is a common practice for micro-hydrodynamic analysis of such micro-swimmers.…”

“…[23,24,[41][42][43][44] The Re number is defined as Re = 0.01 for the results presented in this work. [44] Simulations were carried out for three full periods, although the analysis was carried out for the interval between the time stamps t = t ramp and t = t. The CFD simulations are carried out by a commercial finite element method (FEM) package [45] and the domain (t) is discretized by second-order Lagrangian tetrahedral elements with a numerical degree of freedom of 300.000 on each simulation.…”

“…[44] Here the focus will exclusively be on the deforming tail. The resistance matrix B, for a bio-inspired micro-swimmer composed of single head and single tail, can be decomposed into two 6 × 6 matrices that are calculated separately, that is, B = B head + B tail , decoupling the two objects in the analysis.…”

Tek Mıknatıs aracığılı ile bir Manyetotaktik Bakterinin Adaptif Manevra Kontrolü için Bağımsız Eklem Kontrol Simulasyonları

“…Here, one can obtain the accelerations at the first three joints using the aforementioned equations. Next, using the low Reynolds (Re) number assumption and resistive force theory (RFT) (Purcell, 1977;Keller and Rubinow, 1976;Tabak, 2018), the equation of motion for the last three DOFs are written as follows:…”