DIELECTROPHORETIC ARCHITECTURES - Bio-Inspired and Nanoscale Integrated Computing - page 156

5.1. INTRODUCTION TO DIELECTROPHORESIS

Let us first begin with a discussion of the phenomenon of dielectrophoresis itself.
Following Pohl's seminal work on the subject [6], we first calculate the strength of
the dielectrophoretic force on a particle and then consider the consequences of
dielectrophoresis in media with different electromagnetic responses.

5.1.1. The Dielectrophoretic Effect
Dielectrophoresis is the net force experienced by a dielectric object in a nonuni-
form electric field. This effect exists because the dipole charges q induced at

characteristic locations r 7 are subject to different values of the electric field E e (r),
as shown in Figure 5.1.
There is no net force in a homogeneous electric field, so we can expand,

7

* e ð r þ Þ¼ * e ð r Þþð *

*

Þ * e ð r Þþ O ð L 2

r Þ:

For particles that are small relative to the characteristic length of a field gradient,
the net force is given by

* ¼ *

þ * þ ¼ q ð * e ð * þ Þ * e ð * ÞÞ ¼ ð q *

*

Þ * e ¼ð * r

*

Þ * e : r

Under vector transformation,

*

*

Þ * e ¼r

*

* e Þð * e r

* *

* e Þ * e ðr

*

¼ð * ð * Þ * * * r ðr Þ:

* e ¼ 0, and for a dielectric that is isotropically, linearly, and homo-
geneously polarizable, * ¼ v

*

Since r

a * e for body volume v and tensor polarizability

^ ^ a , the

force reduces to

1
2 v

2

*

*

ð * * e Þð *

*

að * e r

*

Þ * e ¼

* * e

Þ * ¼ v ¼r r ^ ^ ar :

Notably, the above dielectrophoretic force is invariant under field inversion.

E e ( r )

L = r

+ −

r

−

− q + q

Figure 5.1. Schematic of dielectric particle in inhomogeneous field.