Ferrofluid Flow and Spin Profiles in Alternating and Traveling Magnetic
Ferrofluid Flow and Spin Profiles in Alternating and Traveling Magnetic Fields
National Science Foundation
Jan. 15, 2000 - Dec. 31, 2003
Analysis and measurements have shown anomalous behavior of ferrofluids
in AC magnetic fields, whereby in a rotating magnetic field the ferrofluid
can be pumped but the flow direction can reverse as a function of magnetic
field amplitude, frequency, and direction. This anomalous behavior is investigated
using the governing fluid mechanical linear and angular momentum conservation
equations including nonsymmetric viscous and Maxwell stress tensors.
Here we examine a simple case where applied magnetic field components along
and transverse to the duct axis are spatially uniform and vary sinusoidally
with time. In the uniform magnetic field the magnetization characteristic
depends on fluid spin velocity but does not depend on fluid flow velocity.
The magnetization force density along the duct axis is zero while the magnetic
torque density is non-zero as magnetization and magnetic field are not collinear due to a magnetic relaxation
time constant as well as due to spatially varying fluid spin velocity. The
governing linear and angular momentum conservation equations then require
non-symmetric fluid viscous and Maxwell stress tensors. Ferrofluid behavior
in AC magnetic fields offer an excellent experimental system to examine
this unusual type of coupled electro-mechanical system.
The governing equations are integrated to solve for flow and
spin velocity distributions for zero shear spin viscosity as a function
of magnetic field strength, phase, frequency, and direction along and transverse
to the duct axis; as a function of pressure gradient along the duct; vortex
viscosity; dynamic viscosity; and ferrofluid magnetic susceptibility. Analytical
solutions for simple limiting cases are given especially focusing on the
case when the effective dynamic viscosity that depends on magnetic field
strength can be made positive, zero or negative. Negative effective dynamic
viscosity may explain the observed flow reversals while simple approximate
theory for the transition point where the effective viscosity goes through
zero predicts an infinite flow and spin velocity in response to a pressure
gradient. The shear coefficient of spin viscosity, nonlinear effects, and
flow instabilities most likely limits the fluid mechanical response to remain
large but finite. Numerical integrations show the highly non-linear and
multi-valued solutions for flow and spin velocities when the shear spin
viscosity coefficient is zero.
References and Links:
- Zahn, M. and D.R. Greer, "Ferrohydrodynamic Pumping in Spatially Uniform
Sinusoidally Time-Varying Magnetic Fields," Journal of Magnetism and Magnetic
Materials, 149, No. 1, pp. 165-173, August, 1995.
- Zahn, M. "Magnetizable Fluid Behavior with Effective Positive, Zero, or
Negative Dynamic Viscosity," Indian Journal of Engineering and Material
Sciences, Vol. 5, pp. 400-410, December 1999.
- Zahn, M. and L.L. Pioch, "Ferrofluid Flows in AC and Traveling Wave Magnetic
Fields with Effective Positive, Zero, or Negative Viscosity," accepted for
publication in the Journal of Magnetism and Magnetic Materials, 1999.
- Pioch, L., "Ferrofluid Flow & Spin Profiles for Positive and Negative
Electric Viscosities," MIT M.Eng. thesis, May, 1997.
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