Theory of Ferromagnetic Microswimmers

Abstract

SummaryThis paper considers the dynamics of a microscale swimmer based on two magnetic beads that are elastically coupled together. A time-varying external magnetic field is imposed that has two principal effects: one is to exert a torque on the magnetic beads. The second is to change the orientation of the magnetic field dipoles in one or both beads, depending on their ferromagnetic properties. This then creates an attraction or repulsion between the two dipoles. The combination of dipole attraction/repulsion, moderated by the elastic coupling, and torque gives motions that are not generally time-reversible and can lead to unidirectional swimming, that is persistent motion in one direction, in a Stokes flow regime.The equations of motion for the swimmer are set up using a Lagrangian formulation and supplemented by equations giving the dipole orientation of the magnetic fields of the beads in the external field. The equations are non-dimensionalised and key parameters determined. Numerical simulations reveal a number of regimes which are studied using simplified models and multiple scale analysis. Approximate thresholds are obtained above which the swimmer moves in a closed path, and below which the orientation is 'trapped' giving unidirectional motion. Three mechanisms for such trapping are isolated and discussed.

Emergent propagation modes of ferromagnetic swimmers in constrained geometries

“…Building on our previous work, 18,19 we consider a swimmer composed of two spherical ferromagnetic beads of different size joined by a spring within a rotating elliptical magnetic field ( fig. 1).…”

“…[9][10][11][12][13][14][15][16][17][18][19] Magnetic actuation enables propulsion to be controlled wirelessly without affecting biological viability, an essential requirement of many biomedical applications, with the added benefit that the magnetic field also determines the direction of motion. Simple magnetic attraction of particles can be effective, but requires the magnetic field to have both a strong magnitude and gradient, so this solution is only viable when the particles are close to the magnetic poles (e.g.…”

“…[14][15][16][17] Our group proposed a third strategy based on two ferromagnetic particles with differing size and magnetic anisotropies, connected by an elastic link. 18,19 Experimental demonstration of a prototype magneto-elastic swimmer can be found in the supplementary material of reference 19. This breaks time-reversal symmetry via the combined actions of the structural asymmetry, the torque induced by an oscillating applied field and of the interaction between the ferromagnetic particles, which alternates between repulsion and attraction due to reversal of the magnetically softer particle during the field cycle.…”

Flexible mechanism of magnetic microbeads chains in an oscillating field

“…[6][7][8][9][10][11] Magnetic actuation enables motion of the magnetic micro devises to be controlled wirelessly without affecting biological viability but with the extra benefit that the direction of motion can be determined by the field. 12,13 One of the challenges in proposing the micro devices to move in the low-Reynolds-number regime should be that a microswimmer must deform without structural instability in a way that is not invariant under time-reversal.…”

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

“…Studies of micro-robots represent a flourishing modern research topic that strives to create a fundamental base for modern applications in medicine and technology, see Purcell (1977), Becker, Koelher & Ryder (2003), Najafi & Golestanian (2004), Dreyfus et al (2005), Chang et al (2007), Earl et al (2007), Alouges, DeSimone & Lefebvre (2008), Golestanian & Ajdari (2008, 2009, Leoni et al (2009), Alexander, Pooley & Yeomans (2009), Gilbert et al (2010) and Lauga (2011). The simplicity of the geometry represents the major advantage in studies of micro-robots (in contrast with the extreme complexity of self-swimming micro-organisms, e.g.…”