Magnetic driving of magnetic particles at the liquidair interface.

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Magnetic driving of magnetic particles at the
liquid/air interface.
Particles 90 mm Nickel spherical particles hard
magnets (hysteresis) Magnetic field Hz
H0 sin( 2pf t ) H0 120 Oe Hdc 0-30 Oe
Particles supported by surface tension
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Pattern formation mechanism in ac magnetic field

• dc vertical magnetic field
• repulsion between parallel dipoles
• triangular lattice
• stationary periodic pattern

• ac vertical magnetic field
• rotation of hard magnet particles
• deformation of fluid surface
• chains formed from head to tail dipoles
• dynamic structures

3
Chains, excitation of surface waves, and
self-localization
z
side view
x

• Chains are effective sources of surface waves
• Particles are swept in into the regions of large
  surface oscillations herding
• Depleted particles concentrations ? decreased amp
  of oscillations (self-localization)

top view
y
x
4
.
Magnetic structure of the snake unconventional
magnetism
Hdc 10 Oe
Hdc 2 Oe

• Ferromagnetic order inside segments
• antiferromagnetic order between segments
• zig-zag response on in-plane dc field
• suppression of segments with opposite orientation

5
The tale of the tail

• tail is a powerful engine it pumps a lot of
  water
• flow velocity increases with the frequency
• the snake still does not swim

Velocity field of the tail
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The tug-of-war no swimming
push me pull you effect

• Two powerful jet engines work against each other
• Net effect is zero
• The snake cannot swim

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Symmetry Breaking Onset of Self-Propulsion
Swimming snake
Stream lines One vortex pair dominates
Velocity plot strong jet emanates from the tail
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Why do we care? What are the applications?
Conducting network of particles

• US patent Creation of Conducting Networks of
  Magnetic Particles through Dynamic Self-Assembly
  Process
• US Patent Efficient surface mixing by magnetic
  microparticles

Enhanced interfacial mixing Shown velocity field
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Molecular Dynamics Approach

• Quasi-2D description of fluid shallow water
  equations, however arbitrary Reynolds number
• Particles are suspended at the surface of fluid
• Magnetic moments are tangential to the surface of
  fluid
• Simplified particles-fluid coupling
• Particles are sources of forces on fluid

h
x
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Shallow Water Equations

• Arbitrary Reynolds number
• h-viscosity, g-surface tension
• p magnetic moment of particles (orientation)
• f(r)-shape of the particle
• H0 amplitude of vertical magnetic field

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Particles Forces and Torques

• Dipole-dipole magnetic interactions
• soft core repulsion for small distances
• advection by flow
• alignment by shear flow
• viscous drag forces
• gravity force (sliding down slope of wave)

Magnetic Dipole-Dipole Hamiltonian
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Particles Dynamics

• m,m,I,mp-mass, friction, moment of inertia,
  rotational friction
• Fij,Tij -forces and torques due to
  dipole-dipole magn interaction and soft core
  repulsion
• W,E-vorticity and rate of strain tensor

H0
h
x
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Simulations of a snake excitation of waves
Side view
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Simulations of a snake excitation of waves and
self-assembly
Side view
Top view, stroboscopic sequence