Interdisciplinary Applied Mathematics

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Fd = 6nprv,

where p is the dynamic viscosity and v is the velocity of the particle. Since the inertial effects are negligible, one can assume that the instantaneous velocity of a particle v is proportional to the instantaneous dielectrophoretic force. This results in the dielectrophoretic velocity of a particle given by (Morgan et al., 1999)




ЩК H]V||Erms II


Since the surface area of the particle is proportional to r2,

FIGURE 7.24. A 50 kHz AC electric signal induces electric polarization on human leukemia cells and moves them to the center of four spiral electrodes, while the normal cells are trapped on the electrode surfaces. (Courtesy of P. Gascoyne and X. Wang.)

the dielectrophoretic particle velocity is proportional to the surface area of the particle.

Further examination of equation (7.52) also reveals that the particle velocity is determined by the square of the rms electric field. Therefore,

• dielectrophoresis can be maintained by either DC or AC electric fields.

Positive or negative dielectrophoresis (i.e., motion of particles toward or away from the large electric field gradients) is obtained according to whether Re[K(w)j > 0 or Re[K(w)j < 0. These properties of dielectrophoresis enable highly controlled selective microfluidic particle/cell separation methodologies.

7.6.1 Applications

In the    rest    of    this chapter    we    will    present    various    biomedical and    mi

crofluidic applications of dielectrophoresis. Green and Morgan were the first to    show    that    it    is    possible    to separate    a    population    of nanoparticles

(latex beads    of    93 nm)    into    two    subpopulations    due    to    the    differences in

their dielectrophoretic properties, by using microfabricated electrode arrays (Green and Morgan, 1997). This initiated many applications of separation

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