# Dielectrophoresis

*Written by Kevin Tian, AP 225, Fall 2011*
--Ktian 18:33, 5 December 2011 (UTC)

At its very essence, Dielectrophoresis (DEP) is the force that arises from the interaction of a dielectric particle's *dipole* and the *spatial gradient of an electric field*. This phenomenon differentiates itself from Electrophoresis (EP) which instead comes from interactions of a particles *charge* with a *uniform electric field*. Since the particle has to be only dielectric for this effect to manifest itself, essentially any particle will experience this force under the right conditions. However the strength of the force depends on various parameters, including the electrical properties of the medium and particle. Since the electric field need not be static, a time varying sinusoidal field can introduce a dependency of frequency as well.

One of the primary reasons interest has been revived in DEP has been its ability to allow for the manipulation of particles on the (sub) micron scale. A few examples have been given in the additional reading section.

## Contents

## Phenomenological Definition

The term 'Dielectrophoresis' was first coined by H.A. Pohl in 1951, who performed some experiments involving small plastic particles suspended in dielectric fluid. It was found that these particles would move in response to any nonuniform AC/DC electric field. The word itself originates combines two aspects of the phenomenon; the interaction involves an (induced) dipole in a *dielectric* material and the greek suffix for migration, *-phoresis*. The intention was to emphasize the force exerting itself by virtue of the polarizability of a particle.

The basic phenomenological bases of Pohl's definition, which are widely cited as defining features of the DEP force, are the following [1][2]:

- Particles experience DEP force only when the electric field is nonuniform.
- The DEP force does not depend on the polarity of the electric field and is observed with both AC and DC excitation.
- Particles are attracted to regions of stronger electric field when their permitivity exceeds that of the suspension medium permitivity.
- Particles are repelled from regions of stronger electric field when medium permitivity exceeds that of particle permitivity.
- DEP is most readily observed for particles with diameters ranging from approximately 1-1000<math>\mu m</math>

Though we must note that there do exist higher order multi-poles that can contribute to a force, practically speaking the DEP term dominates (for the most part). The reason for the last constraint can be observed with a reasonable order of magnitude estimate for both upper bound (limited by gravitational forces)

## DEP Force

One can obtain a closed form for a DEP force by a relatively straightforward derivation by making the following assumptions:

- Uniform spherical particle
- Linearly polarized sinusoidal electric field
- Medium permitivity and conductivity remain constant over all frequencies of concern (no dielectric losses)

In general the following is true: <math>\mathbf{F}=(\mathbf{p} \cdot \nabla) \mathbf{E}</math>. By applying the above we get the time average DEP Force [2]:

<math>\left \langle \mathbf{F}_{DEP} \right \rangle = 2 \pi \epsilon_m R^3 Re[\tilde{K}(\omega)] \cdot \nabla |\mathbf{E}|^2</math>

Where R is the radius of the particle and <math>\epsilon_m</math> is the permitivity of the medium. The Clausius-Mossotti (CM) factor, <math>Re[\tilde{K}(\omega)]</math> embodies the frequency dependence of the time averaged force. For <math>\tilde{\epsilon}_m , \tilde{\epsilon}_p</math> representing the complex permitivity for the medium and particle respectively...

<math>\tilde{K}(\omega) = {{\tilde{\epsilon}_p - \tilde{\epsilon}_m } \over {\tilde{\epsilon}_p} + 2 \tilde{\epsilon}_m}</math>, where we note that <math> \tilde{\epsilon} = \epsilon + {{\sigma} \over {j \omega}} </math>

We note that the CM factor can range between -0.5 and +1.0. For the regime where the CM factor < 0, we have what we call negative DEP (nDEP), as observed in the 4th point in our phenomenalogical definition above. For CM factor > 0 we have positive DEP (pDEP), which is likewise described by the 3rd point above.

## References

See also: Dielectrophoresis in Charged interfaces from Lectures for AP225.

[1] Wikipedia on Dielectrophoresis

[2] Jones,Thomas B. "Electromechanics of Particles". Cambridge: Cambridge University Press, 1995. Print.

## Additional Readings

K.A. Brown and R.M. Westervelt. "Proposed triaxial atomic force microscope contact-free tweezers for nanoassembly", Nanotechnology (2009), 20 385302.

E. Fabbri et al. "Levitation and Movement of Tripalmitin-Based Cationic Lipospheres on a Dielectrophoresis-Based Lab-on-a-Chip Device", Wiley InterScience (online), June 2 2008. DOI 10.1002/app.28413. <www.interscience.wiley.com>

T.P.Hunt et al. "Integrated circuit/microfluidic chip to programmably trap and move cells and droplets with dielectrophoresis", Lab on a Chip (2008), 8-1, 81-87.

## Keyword in references:

A Microfabrication-Based Dynamic Array Cytometer

Dielectrophoretic registration of living cells to a microelectrode array

Modified Dielectrophoresis: Motion of objects in AC fields from FIXED dipole moments