Ferrofluid Pump for Lab-on-a-Chip Technology
| • | Research addresses thermal limitations of conventional electric motors. |
| • | Develop finite element models of magnetocaloric pumping. |
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Identify
fluid flow characteristics (pressures and flow rates) as a function
of heat source and external magnetic field.
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Motivation
The overall objective of this proposed project is to demonstrate magnetocaloric pumping, ferrofluid flow based on externally applied magnetic and thermal fields, on a proof-of-principle lab-on-a-chip (LOC) microfluidic system. The relevance of this project to the Department of Energy (DOE) is the potential for developing new materials and technologies that enable microfluidic pumping for future man-portable LOC systems. The specific advantage of this approach to microfluidic pumping, in comparison to existing technologies, is that the proposed approach requires no moving mechanical parts, no high voltage source, and is based solely on external magnetic and thermal fields.
Comparison of Ion-Drag and Magnetocaloric Pump
One
of the more successful field-effect approaches to microfluidic pumping is
based on the principle of ion drag. The basic principle of operation is somewhat
similar to the magnetocaloric pump. Electrical forces can be produced in highly
insulating gases and liquids by injecting charged particles and using an electric
field to pull them through the fluid. The motion of the particles is retarded
by friction, and momentum is imparted to the fluid. Thus, the ion-drag effect
can be used to pump or accelerate fluid, much the same way that nanoparticles
are used to pump or accelerate the fluid in the magnetocaloric pump. Equation
(1) expresses the pressure differential 
to
the temperature dependent magnetization (M(T)) of the particles. H is the
externally applied magnetic field intensity and 
is
the permeability of free space.
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(1) |
Equation
(2) expresses the pressure differential ,
based on the Maxwell stress tensor, between two electrodes where 
is the material permittivity and E is the externally applied electric field.
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(2) |
Ahn
and Kim describe a microfluidic ion drag pump with staged pumping chambers,
much like we have described above for the magnetocaloric LOC pump. With a
maximum electric field of 1.3e6 V/m, using ethyl alcohol,
the maximum theoretical operating pressure is approximately 180 Pa resulting
in a flow rate of 32 
in
their chambers which closely correlates to their experimental results. Care
must be taken at high voltages to minimize water, else electrolysis of the
water results. Comparing Eqs. (1) and (2), it is possible to compare
pressure gradients using the two methodologies. It is not unreasonable to
expect magnetic fields, H, on the order of 2e5 A/m using conventional
rare earth materials located adjacent to the channels. Assuming the ferrofluid
has the permeability of air, and magnetic saturation on the order of 300 Gauss,
we expect maximum pressure gradients on the order of 6 kPa. This is close
to what we have verified in the laboratory on 3 mm diameter cylindrical
chambers. One clear advantage of the ion drag approach is the compactness
of the electrodes and ease of cascading as done by Ahn and Kim. In addition,
Culbertson has shown how the same principle can be used for gating flow as
well. This research will address the scaling of the magnetocaloric effect
to verify this approach as a viable technique for pumping fluids on the LOC
scale. Please see Ferrofluid Field Induced Flow for a description of ferrofluids,
their synthesis, and the mechanism for field induced flow.
Constitutive
Relationships for Magnetocaloric Pump
Magnetocaloric effect couples magnetic, thermal, and fluid dynamic fields to generate field induced fluid flow at the LOC scale.
For fluid dynamics, we use Navier-Stokes to express the inertial and viscous behavior of the fluid.
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(3) |
For use conservation of energy to model the heat transfer from the heat source to the fluid.
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(4) |
We assume a fixed magnetic field so we use a magnetostatic model to express the magnetic field.
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(5) |
The pressure gradient in Eq. (3) is based on the fluid stresses due to the magnetic field.
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(6) |
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u
is fluid velocity, n is viscosity, r is density, P is pressure, B is
magnetic field, M is magnetization intensity, A is magnetic vector potential,
m is permeability, Q is heat source, T is temperature,
 is
specific heat, k is thermal conductivity. |
