Electrokinetic Dispersion in Capillary
Electrophoresis
A “Taylor” dispersion-type model is developed for the electrokinetic
dispersion coefficient of a solute in capillary electrophoresis that
accounts for the effects of Poiseuille andlor electro-osmotic flow of the
elutant for the case of low potential. The expression obtained for the
height equivalent of a theoretical plate is compared with experimental
results reported in the literature for the case of neutral, nonretained
solutes propelled by electro-osmotic flow. The results further reveal
some interesting and somewhat unexpected interactions of the electro-
osmotic and Poiseuille components of the elutant flow. Superposition of
Poiseuille flow on the natural electro-osmotic flow allows greater
freedom in the choice of elutant velocity, without necessarily increasing
the dispersion. In fact, it results in lower dispersion under some
conditions. Optimum flow conditions are obtained for minimizing the
plate height or, equivalently, for maximizing the Peclet number.
Ravindra Datta
Veerabhadra R. Kotamarthi
Department of Chemical and
Biochemical Engineering
University of Iowa
Iowa City, IA 52242
Introduction
Capillary electrophoresis (CE), also sometimes called capil-
lary zone electrophoresis (CZE) or high-performance capillary
electrophoresis (HPCE), is a new analytical technique that
offers the advantages of rapid analysis with excellent resolution
of complex biochemical mixtures. The development of CE has
generated much excitement since conventional electrophoretic
devices are slow and involve manually intensive methodologies.
The slow speed in conventional electrophoresis techniques is a
result of the traditional use of low electric field strengths
(dV/dz - 1 kV/m), coupled with inherently small values of
electrophoretic mobilities (ui - lo-’ m2/V - s) of solutes. Use of
high-voltage gradients in electrophoresis has so far been limited
by heat transfer considerations since effective heat transfer is
crucial to avoid loss of zone resolution because of natural
convection, and also the possible denaturation of heat-sensitive,
biologically-active compounds. Capillary electrophoresis over-
comes this limitation by using very small-diameter capillaries
(25- 100 hm ID and wall thickness -200 hm), typically 50-100
cm long, that provide largexurface area to volume ratio for
effective heat dissipation. This allows the use of extraordinarily
high electric fields strengths, of the order of 20-30 kV/m, which
Correspondence concerning this paper should be addressed lo R. Datta
results in very efficient separation of complex, closely-related
species in a relatively short time period (10-30 minutes). The
currents generated are usually less than 200 pA, corresponding
to a power dissipation of less than 5 W in the capillary.
The history of the development of CE is described by
Compton and Brownlee (1988). Mikkers et al. (1979) first used
a 200 pm ID Teflon tube for free-flow electrophoresis with
high-voltage drops and obtained efficient separations with unprec-
edented plate heights of less than 10 pm. Soon thereafter,
Jorgenson and Lukacs (1981) utilized 75 hm ID borosilicate
glass capillary and successfully separated dansyl amino acids
obtaining plate heights of only a few pm. Since then, research on
CE has proliferated and the technique has also been extended to
other electrophoresis modes such as isotachophoresis, capillary
gel electrophoresis, micellar electrokinetic capillary chromatog-
raphy, and capillary isoelectric focusing. Many reviews have
appeared on the subject (e.g., Jorgenson, 1987; Ewing et al.,
1989), even though the field is still in its infancy. Tehrani and
Day (1989) have provided a summary of the performance
characteristics of CE in comparison with conventional gel
electrophoresis and high-pressure liquid chromatography.
The most common capillary material now used in CE is fused
silica, although glass and Teflon have also been used. The silanol
groups on the silica capillary walls acquire a negative charge,
with positive counter-ions in the aqueous electrolyte buffer.
These hydrated counter-ions are attracted to the cathode and,
916 June 1990 Vol. 36, No. 6 AIChE Journal

therefore, give rise to an electro-osmotic flow toward the
cathode. The electro-osmotic flow thus generated can be quite
substantial in CE because of the use of high electric field
strengths and is, in fact, utilized in CE for the elutant flow
instead of the conventional pressure-driven flows. Further, since
the electro-osmotic velocity profile is considerably flatter than
that in Poiseuille flow, it also results in reduced hydrodynamic
dispersion. Unfortunately, however. there is no easy way to
control the electro-osmotic flow in an open capillary for a given
field strength, apart from capillary surface modifications. This
imposes a severe limitation in the choice of elutant velocity
which, of course, is easily controlled with conventional pumping
in rival analytical techniques such as HPLC.
Another significant advantage of CE as compared with
conventional electrophoresis techniques is that, provided a
solute does not have strong coulombic or adsorptive interaction
with the capillary surface, anionic, cationic and neutral species
can be efficiently separated in a single run. The reason for this is
that under typical conditions electro-osmotic mobility, u,, is
considerably greater than the electrophoretic mobility, I(,, of
most species. Thus, even without the aid of any pressure-driven
flow, the electro-osmotic flow generated is sufficiently strong to
carry most species, regardless of their charge, toward the
cathode. This allows the sample to be introduced at the anode
end of the capillary and the separated zones to be detected near
the cathode end, with the order of appearance being cationic,
neutral and finally anionic species. Separation of protein mix-
tures with CE has proved to be more difficult, and substantial
peak broadening and tailing is encountered. This difficulty arises
as a result of the tendency of proteins to adsorb strongly on most
capillary surfaces (Lauer and McManigill, 1986). The protein-
wall interaction can be substantially reduced by appropriate
surface treatment. Substances used for surface modifications
include methyl cellulose, polyethylene glycol, and polyacryl-
amide. However, such surface modifications concomitantly
reduce the electro-osmotic flow as well. In such cases, pressure/
gravity driven flows may be unavoidable to elute the species. The
use of nonaqueous media in CE appears to be promising for
some applications and may also require pressure-driven flows.
The objective of this paper is to provide a theoretical model
for the electrokinetic dispersion in CE for the general case
involving Poiseuille and electro-osmotic elutant flow. The disper-
sion coefficient is labeled “electrokinetic” to emphasize the
combined effects of motion and electrical phenomena. It will be
shown that a combination of electro-osmotic and Poiseuille flows
not only allows greater freedom in the choice of appropriate
elutant velocity. but under certain conditions, can actually
provide substantially lower zone spreading. A brief overview of
the other causes of zone spreading is provided next before
describing the model.
Causes of zone spreading in free-flow electrophoresis
According to Wieme (1 979, dispersion in free-flow electro-
phoresis occurs for the following reasons:
0 Axial diffusion is, of course. unavoidable and represents the
minimum possible spreading.
Joule heating, which is generated uniformly throughout the
liquid volume but removed only at the capillary surface, results
in a radial temperature profile that reduces the fluid viscosity
and density in the warmer central parts of the capillary. This
also increases the electrophoretic mobility (by about 2% per “C)
as well as the electro-osmotic mobility, since both of them are
inversely related to the viscosity, as shown in Eqs. 12 and 18,
respectively. Thus, the species velocities are higher in the central
portion of the capillary, resulting in zone spreading.
Sample overloading can result in zone spreading and distor-
tion. If the applied sample is concentrated, its conductivity and
pH could be quite different from those of the elutant, leading to
a local distortion of the electric field and hence resulting in zone
spreading.
.Any sorptive interaction of the solute with the capillary
surface can substantially contribute to dispersion.
“Microheterogeneity,” is., any deviations in size, sha
and/or change of the migrating species can cause zone spread-
ing.
.Spreading can also be caused if a migrating species pos-
sesses different states that are rapidly interconvertible. This is
called “electro-diffusion.”
Gravitational effects, due to any density differences between
the fluid and the applied sample, can cause dispersion.
Elutant flow velocity profile by virtue of lamiinar flow caused
by pressure difference or gravity and/or electro-osmotic flow
results in dispersion.
This paper is concerned only with the last factor, the effect of
laminar and/or electro-osmotic flow velocity profile on the
electrokinetic dispersion. Martin and Guiochon (1984) and
Martin et al. (1985) analyzed zone broadening caused by
electro-osmotic flow and suface adsorption in capillary liquid
chromatography. They considered the case of low t potential
and approximated the electro-osmotic velocity profile by empiri-
cal expressions, which were then used in the theory developed by
Golay (1958) and Aris (1959) to obtain plate height. They
concluded that electro-osmotic flow provides lower zone spread-
ing than pressure-driven flow, but the difference becomes small
as the capacity factor of the stationary phase becomes large.
at
Theoretical Model
Consider a straight cylindrical capillary of diameter d, and
length L shown in Figure 1. The capillary is connected between
two reservoirs of an electrolyte buffer, and a constant voltage.
gradient is applied across it. In addition, a pressure gradient and
a gravity component in the axial direction may exist in general.
The sample to be separated is introduced as a pulse at z = 0.
The species migrate at different rates under the influence of the
electric field, resulting in separation, and are eluted and detected
at I - L.
c
I vo
“L
+ ++++--
(9- - ++ + +++--
‘YO
Figure 1. Capillary electrophoresis.
AIChE Journal June 1990 Vd. 36, No. 6 917