On the self-propulsion of an -sphere micro-robot

Abstract

The aim of this paper is to describe the self-propulsion of a micro-robot (or microswimmer) consisting of N spheres moving along a fixed line. The spheres are linked to each other by arms with their lengths changing periodically. We use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that self-propulsion velocity appears (in the main approximation) as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, fourand five-sphere swimmers are calculated.

Hydrodynamic Clustering of Human Sperm in Viscoelastic Fluids

“…The closure equations 5 and 6 can be interpreted via a representation of the sperm as an extended object, consisting of K negligibly small spheres, where is the number of regularised Stokeslets in a single sperm. This is motivated by the commonly used simplification of sphere-linked swimmer models 45 – 47 , noting that the regularised Stokeslets are approximately singular Stokeslets, at least away from the singularity, and similarly Stokeslets are good approximations for spheres away from the very near field of the sphere.…”

Magnetically driven omnidirectional artificial microswimmers

“…The frequency dependence of velocity -initial increase and subsequent decrease -is in qualitative agreement with the predictions of the simple model (Eqs. [1][2][3][4][5]. A more exact numerical simulation of the system, without free parameters, is described in the Appendix and shown by the dashed line in Figure 4.…”

“…The distance then increases with time as Y 5 − Y 5 0 ∼ t where Y 0 is the distance at the onset of the repulsive phase. The particle reaches a distance Y 1 at the end of the repulsive phase, Y 5 1 − Y 5 0 = C/ f , where the constant C depends on the strength and fraction of the repulsive interaction, as well as on hydrodynamic drag. The distance by which the particle moves is then ∆Y = (C/ f +Y 5 0 ) 1/5 −Y 0 .…”

“…The swimmer by Najafi and Golestanian 3 is composed of three linked spheres and swims by periodically yet non-reciprocally changing the lengths of the links. This model has later been extended to a circular swimmer 4 and to larger particle assemblies 5,6 . Another simple model, the so-called pushmepullyou by Avron and co-workers 7 , is made up of two spherical bladders that periodically change their separation and volumes to produce locomotion.…”

Dumbbell micro-robot driven by flow oscillations

“…Studies of different micro-robots by the same method can be found in Vladimirov (2012bVladimirov ( ,c, 2013. In Vladimirov (2012a,d) the same form of TTM resulted in a new asymptotic model and a new equation for the averaged flows generated by acoustic waves and for MHD-flows.…”