Flexible paramagnetic membranes in fast precessing fields

Abstract

Elastic membranes composed of paramagnetic beads offer the possibility of assembling versatile actuators operated autonomously by external magnetic fields. Here we develop a theoretical framework to study shapes of such paramagnetic membranes under the influence of a fast precessing magnetic field. Their conformations are determined by the competition of the elastic and magnetic energies, arising as a result of their bending and the induced dipolar interactions between nearest neighbors beads. In the harmonic approximation, the elastic energy is quadratic in the surface curvatures. To account for the magnetic energy we introduce a continuum limit energy, quadratic in the projections of the surface tangents onto the precession axis. We derive the Euler-Lagrange equation governing the equilibria of these membranes, as well as the corresponding stresses. We apply this framework to examine paramagnetic membranes with quasiplanar, cylindrical, and helicoidal geometries. In all cases we found that their shape, energy, and stresses can be modified by means of the parameters of the magnetic field, mainly by the angle of precession.

Janus magnetoelastic membrane swimmers

“…We remain o = 0.5 t À1 (B1760 s À1 ), and all production simulations run at least 1.7 Â 10 6 timesteps (1.7 Â 10 3 t). Similar to the FvK number, the relative strength between magnetic energy and bending energy can be characterized by a dimensionless quantity called magnetoelastic parameter, 56,83…”

Locomotion of magnetoelastic membranes in viscous fluids

“…If the precession is slow (ω < ω c ), the membrane has enough time to rotate completely parallel to the precession axis and will adopt new configurations due to elastic buckling. How the membrane buckles depends on the magnetoelastic parameter [26], Γ = M L 2 /κ, which characterizes the ratio between the membrane's magnetic and bending energies, where M is the magnetic modulus, and L 2 is the membrane area. If the magnitude of Γ is very small (Γ 1) or very large (Γ 1), we observe hard disk behavior because bending distortions become impossible due to mechanical stiffness or due to unfavorable magnetic interactions, respectively.…”

Spontaneous deformation of flexible ferromagnetic ribbons induced by Dzyaloshinskii-Moriya interaction

“…So far the magneto-sensitive elastomers [12][13][14][15][16][17] are the most studied magnetically responsive flexible materials. The magnetic properties of elastomers are determined by the long range dipole-dipole interaction [18][19][20][21] which results in the relatively large scale of the geometrical deformations. It is well known that organic, organic-inorganic hybrid, and molecule-based magnets exhibiting different types of magnetic ordering [22][23][24][25][26][27][28][29] and some of them can keep ferromagnetic order even for a room temperature [30].…”