DIELECTROFORESIS 1915

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The Motion and Precipitation of Suspensoids in Divergent Electric Fields

Herbert A. Pohl

Citation: Journal of Applied Physics 22, 869 (1951); doi: 10.1063/1.1700065

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J O U R N A L

O F

A P P L I E D

P H Y S I C S

V O L U M E 2 2

N U M B E R 7

J U L Y 1915

The Motion and Precipitation of Suspensoids in ivergent Electric Fields

HERBERT A. POHL

*

Naval Research Laboratory, Anacosta, D.

C.

(Received November is, 1950

The motion of suspensoid particles relative to

that

of the solvent resulting from polarization forces pro

duced

by an

inhomogeneous electric field is defined as dielectrophoresis.

t

is analogous to

the

related

phenomenon of electrophoresis, in which motion of suspensoid particles is produced by the action of an

electrostatic field on the charged particles.

From a consideration of theoretical calculations and from experimental observations it is concluded that

the phenomena of dielectrophoresis and dielectro-precipitation can be observed under rather ideal

conditions, though it is ordinarily often difficult to do so because of the presence of the more easily produced

electrophoresis or ion-type migration of charged particles.

The usefulness of die1ectrophoresis (and/or electrophoresis) for removing suspended solid particles from

polymer solutions during analysis is described.

T

HE application of highly inhomogeneous, strong,

electric fields to suspensions of solids or of

liquids in fluids has been found helpful in coagulating

and precipitating finely dispersed material for analysis.

The

phenomenon seen in the relative motion

of

sus-.

pensoid and medium resulting from polarization forces

produced by

an

inhomogeneous electric field is defined

as dielectrophoresis; and when this leads to co

agulation, the process may be called dielectro

precipitation.

Dielectrophoresis does not require ionized particles

but rather depends on asymmetrical induction and

attraction of displacement charges within the particles,

and further that the resultant motions be different for

solvent and

solute. Migration in either alternating or

direct current fields is observed

to

take place. Figure 1

diagrammatically shows the effect of an inhomogeneous

field on a discrete particle lying in the field. The un

equal field force acting on all permanent or induced

dipoles causes them to be constrained to move towards

the region of highest field density.

When the polarizability of the suspensoid is greater

than

the solvent, the asymmetric field forces accelerate

the suspensoid particles more than the solvent, giving

rise to an increased concentration of the suspensoid

near the center of high field strength. The suspensoid

particles are then more prone to collision and coagula

tion. Agglomerations of suspensions may therefore fre

quently be accomplished with this technique using

simple apparatus.

The following equations are included to show the

relative importance of the factors involved. The force

on a small particle in a non-uniform field is expressed

to a good first approximation by

j=PiJE/iJr

(1)

=E E iJE/iJr (2)

=

k-1) EiJE/47riJr= k-1)

iJ(Jtl)/87riJr, (3)

*

Based on research

at

the Naval Research Laboratory, Ana

costa, D. C. Present address:

Du Pont

Experimental Station,

Wilmington, Delaware.

where j=force per unit volume,

P=polarization=EE,

E = field strength, E= proportionality factor of polariza

bility, and k=dielectric constant = 1+ 47rE

The excess force on the suspensoid of dielectric

constant, kl' over that on the solvent

of

dielectric

constant, k2 is

t:.j= EI - E2)iJ(Jtl)/iJr

=

k

l

-

k

)iJ(Jtl)/47riJr. (4)

This relation says that the motion of the suspensoid

under the influence of the inhomogeneous field will be

proportional to the absolute value of the electric field

strength applied, to its divergence,

and

to the differ

ences in dielectric constant of suspensoid and solvent.

The motion will be in the direction of the greatest field

strength and independent of field direction.

The force of the field on the particle will cause mo

tion opposed

by

viscous drag; hence, the force on the

particle is given by

F=

(volume of particle) : j = 4 7 r a 3 ~ j / 3 =

67ra?]v

(5)

using Stoke's equation and assuming spherical par

ticles, giving

v=

2

a

2

~ j / 9 ? ] =

a

2

(k

l

-

k

2

EiJE/187r?]iJr,

(6)

where F=force on the particle, a=radius of particle

in cm, ?]=viscosity of medium in poises, v=velocity

in cm/sec.

In the interesting case of the divergent field formed

in the liquid between two infinitely long concentric

cylinders, we have

E=iJV iJr= 2q/kr,

V

1

- V

2

= (2q/k)

In h/rl),

V

1

- V = (2q/k)ln(r/rt),

iJ(Jtl)/iJr=4q2/rk2,

7)

8)

(9)

10)

where V = potential in statvolts at

r

cm from the center,

V

1

- V

2

=potential in statvolts applied across the elec

trodes,

q=charge

per cm on

the

inner conductor,

k=dielectric constant of the mixture.

869


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870

HERBERT

A.

POHL

v

FIG.

1.

Diagram

of

forces operating on dipoles and suspended

particles in an inhomogeneous electric field.

Dielectrophoresis.

Combining Eqs. 8) and 9) and substituting in

Eq. (6), we get

v=a

2

(k

1

2

) V

1

-

V

2

)2j1811 ?)r

In(r2/rl)'

11)

In

a system, e.g., where

11

=

10

mils=

1.27X lQ-2

em,

2=5

em,

and

V l- V

2

=1()o1

volts=33.3 statvolts, and '1=1Q-2 poise (tolu

ene, etc.), we have

12)

E.g.,

i a= 101 =

10-

8

em,

r=

1 em, k

1

k

2

i= 108

as for a graphite

or Ni sol

in

toluene, then

we

have

V= 55 10-

3

)2108= 0.055 em/sec,

which is a reasonably determinable velocity in the laboratory.

However, for a very

fine

suspension of particles

of

not too

different dielectric constant we might observe, e.g., where

a=

11'

= 10-

4

em,

r=

1 em,

k

l

- k

2

i=

10; as for a polymer suspended in

toluene:

v=55(1Q-4)210=5.5X10-

6

em/sec, which is in the order

of

magnitude of diffusional velocities.

The

migration in this case

would be quite difficult to observe.

A calculation due to

J.

A. Wheeler of the time re

quired to sweep out a cell by dielectrophoresis is given

below:

dt=dr/ ar/at) =dr/v=const rdr,

13)

since

rlr.

Hence, the time in seconds is

t sec) 911 ?)r4[ln(r/rl)]2/2a

2

(k

1

2

)

(V1- V

2

. (15)

E.g., in the above apparatus [see Eq. (12)J,

we

have

t

,4/220a

2

kl- k

2

.

For the case

of

the graphite or

Ni

sol described,

t=

103108/220103=4.55 sec, which is a reasonably short experi

mental period.

For

the polymer suspension described

t= lQ410

4

/22010=4.55

I )o1 sec=

12.6 hr.

In the absence of disturbing influences such as con

vection, the weight, w, of material migrating to the

central electrode in time,

t,

will be

W=c vol. swept out)=ch(1I r,2)i

hence, we have,

W = hca[(V1 V

2)/ln(r2/rl)][211 (k1-

k

2

)/?)]lt

1

,

where c=conc of sol in grams/cm

3

, h=height of cylin

drical cell, and rt=radius swept clean in time t.

At this point it is well to sum up our expectations

about the occurrence of dielectrophoresis and compare

it with the related phenomenon

of

electrophoresis.

Dielectrophoresis, arising because

of

the tendency

of

matter to become polarized

and

move into regions

of highest field strength,

1.

Produces motion

of

the particles in which the direction of

motion is independent

of

the direction of the field; Le., either dc

or ac voltages can be employed.

2.

Should be observable most readily in relatively coarse sus

pensions (e.g., particle diameter

~ 2 1 )

3.

Requires highly divergent fields. No motion should be ob

served in the nondivergent field between centers of parallel plates.

4. Requires relatively high

field

strengths, e.g., 10,000 v across

a 5-cm cell.

5.

Would be most apparent in fluids of

low

viscosity (thin

liquids, gases).

6. Generally requires a large difference in dielectric constant

between solvent and

s o l u t ~ . g .

(k

l

- k

2

)

>

10-100.

7.

Will deposit weights

of

sol in direct proportion to the voltage

applied in equal times of deposition.

Electrophoresis, arising from the electrostatic attrac

tion

of

charged electrodes for charged particles,

1.

Produces motion of the particles in which the direction of the

motion is dependent on the direction

of

the field. Reversal of the

field reverses the direction

of

travel. Care must be taken in the

application of this rule for distinction between electro- and

dielectrophoresis as motion

of

charged particles towards a sharp

electrode can occur even in alternating fields of high strength

because of the occurrence of partial rectification effects making

the applied alternating voltage cause predominantly direct current.

For

example, a milky

20

percent suspension

of

Hycar rubber in

methyl ethyl ketone was readily precipitated to form a thick

adherent coat on parallel electrode plates 5 cm apart by dc

but

not

by

ac voltage

of 2000

to

6000

v. This shows the suspension

to consist mainly of charged particles capable of deposition fol

lowing electrophoresis. The suspension was also precipitated

at

the wire

of

the wire and sheet pair

by

either dc or 6O-cycle ac

voltage as above. The latter observation by itself might

at

first

sight be considered as caused by dielectro-precipitation; however,

the further consideration shows this cannot be the case as the

dielectric constant of the medium (18.4) exceeds

that

of the sus

pended particles

ca

15). This leaves deposition following electro

phoresis as the more probable explanation with the assumption

that partia l rectification of the ac occurred.

2. Is

observable with particles of any molecular size.

3. Operates in either divergent or uniform fields.

4. Requires relatively

low

voltages.

5. Requires relatively small charges per unit volume

of

the

particles.


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S U S P E N S O I D S

IN D I V E R G E N T E L E C T R I C F I E L D S

871

With these guides for examination of particle motion

in electric fields, it is instructive to examine some of

the experimental facts available. Hatschek and Thorne

l

studied nickel sols in anhydrous toluene in which rubber

acted as a protective colloid.

As

electrodes, they used

small parallel plates having sharp edges. They observed

equal quantities of precipitate forming

at

each elec

trode, with considerable rubber present n the pre

cipitate. The

sol

precipitated in quantities proportional

to the first power

of the applied voltage during equal

times. This, they concluded, was a principal reason for

interpreting the results as electrophoretic and not di

electrophoretic, since they expected first-power de

pendence in the first and second-power dependence in

the second instance. The present theory indicates that

first power dependence on voltage for the weight de

posited would be expected for cells of cylindrical sym

metry, an approximation of the field at the sharp edge

of the parallel sheet electrodes.

Hatschek and Thorne found several contradictory

phenomena in their interesting study. For one, alter

nating potential did not cause coagulation (migration

was

not

studied) as did static voltage in their large

apparatus,

an

observation which led them to interpret

the phenomenon in this instance to be electrophoresis.

On the other hand, in a smaller cell used

on

their

microscope stage they observed the particles in the

middle of the field between two narrow parallel plates

to be unaffected by the field. Further, particles away

from the exact middle, which were caused to migrate

under the influence

of

the field, did not reverse their

direction of travel on changing the field direction. The

last two observations cannot easily be explained as

electrophoresis but can easily be interpreted as typical

examples

of

dielectrophoresis.

t

would seem that both

electrophoresis and dielectrophoresis were being ob

served in their experiments despite their conclusion that

only electrophoresis was present.

Soyenoff2

noted the coalescence of coal dust in

toluene occurring at over 5000 volts/em to be equally

effective by dc or ac voltage. This he attributed to

dielectric pohtrization, remarking

that

any sus

pensoid body of higher conductivity or dielectric con

stant

than the medium

is

caused) to move toward the

region of highest field intensity.

Reising,S in a study of the migration of pigment

particles in paint vehicles observed in several cases

that roughly equal quantities

of

precipitate collected

on his relatively narrow electrodes. He used static

voltages. Whether or

not

this is an instance of dielectro

phoresis is not certain from the descriptions given.

1 E. Hatschek and P. C. L. Thorne, Kolloid-Z. 23, 1 (1923).

2

B

C. Soyenoff, J. Phys. Chern. 35, 2993 (1931).

S J. A. Reising, Ind. Eng. Chern. 29, 565 (1937).

Winslow' produced rotary migration and alignment

of elongated semiconducting particles suspended in

media

of

low dielectric constant (e.g., moist silica gel

particles suspended in kerosene), and also observed

migration of particles under the influence of field gradi

ents. The latter seems describable as dielectrophoresis.

Studies in our laboratory have been concerned prin

cipally with the use of dielectrophoretic technique to

aid in polymer analysis. t proved difficult, e.g., to

remove carbon-black filler from polyvinyl chloride

samples by other means such as filtration or centrifuga

tion;

but

removal was rapidly and simply accomplished

in a powerful, divergent electric field.

For

example, a

one-gram sample of the polymer sample was taken up

in 50 ml of di-isopropyl ketone with the aid

of

gentle

heating, then placed in the coagulation cell. The cell

consisted of a Petri dish of c lO-cm diameter containing

the electrodes. A lO-mil tungsten wire formed the

central electrode and dipped vertically into the liquid.

A band

of

tinfoil 8 rum high resting on the inner wall

of the cell formed the outer electrode. A high voltage,

either dc or ac

of

10,000 volts, was then applied.

The

liquid immediately underwent considerable action, small

ripples formed, and the carbon particles underwent

rapid migration toward the central wire to form a

coating. The solution

of

polymer became water clear in

a few minutes of what was very likely dielectro-pre

cipitation and was then removed for further analysis.

Similar results were obtained with polyvinyl chloride

polyvinyl acetate copolymers .When parallel plates,

with carefully rounded edges to avoid high field gradi

ents, were used instead of the wire and sheet combina

tion, no precipitation was observable with either dc or

ac. This adds confirmation to the conclusion

that

di

electrophoresis occurred under these conditions.

Similar results were obtained with suspensions of

coal dust or of charcoal dust in toluene.

t is concluded

that

the phenomenon

of

dielectro

phoresis can be observed, though it is often difficult

to do so because of the presence of the more easily

produced electrophoresis or ion-type migration of

charged particles. Calculations of the magnitudes of the

effects of various variables on

it

show

that

dielectro

phoresis, to be observed, requires rather ideal condi

tions. A number of experiments are cited as examples

of

these conclusions. The usefulness

of

dielectrophoresis

and/or electrophoresis) for polymer analysis

is

de

scribed.

The

author wishes to acknowledge the many helpful

suggestions

and

criticisms made by Drs. Maurice B.

Hall, Harold F. Ring, and John A. Wheeler.

4 W.

M. Winslow, J. App\. Phys. 20, 1137 (1949).


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DIELECTROFORESIS 1915