Understanding the Effect of Advective Dispersion on Peak Mode ITP
Principal Inverstigators: Juan G. Santiago, Giancarlo Garcia-Schwarz, Moran
Bercovici, Lewis A. Marshall
Isotachophoresis (ITP) is an electrokinetic technique widely used for its ability to focus and
separate ionic molecules. Analytes undergoing ITP focus in a narrow interface (often
~10 µm) of high electric field gradient between a leading (LE) and trailing (TE) electrolyte.
In practice, this electric field gradient results in non-uniform electroosmotic flow, which in
turn generates internal pressure gradients that disperse the focused analyte zone and
greatly reduce ITP sensitivity and resolution. Despite its importance, there has been
surprisingly little research into the underlying physical mechanisms of dispersion in ITP.
Internal pressure gradients due to non-uniform EOF in ITP
In microfluidic systems, EOF is often modeled using a simple slip velocity condition known
as the Helmholtz-Smoluchowski equation. This boundary condition provides a linear
relationship between electroosmotic (EO) slip and local applied electric field. In ITP, axial
electric field gradients needed for analyte focusing cause non-uniform EO slip velocities
and internal pressure gradients, as depicted in Figure 1. Far from the LE-TE interface, local
pressure gradients are uniform and proportional to the difference between local and axialaverage EO velocities. An adverse pressure gradient forms in the TE and a favorable
pressure gradient forms in the LE. The relative magnitude of LE and TE pressure gradients
depends on the location of the ITP interface.
Figure 1: Schematic showing the curvature of the interface between the LE and TE at two
locations along a channel. The parameters LTE and LLE represent the lengths of the TE and
LE zones. Arrow lengths (outside magnified channel) denote the relative strength of the
local electric field in the LE and TE. An axially non-uniform electric field leads to nonuniform EO slip velocities, which results in the formation of favorable and adverse pressure
gradients within the LE and TE zones, respectively. The magnitude of these opposing
pressure gradients is governed by the difference between local and axial-average
electroosmotic velocities and determines the shape of the LE-TE interface.
Modeling dispersion of a focused analyte
We conducted an analytical, numerical, and experimental study of advective dispersion in
ITP. We found that analyte properties contribute greatly to dispersion in ITP. Analytes with
mobility values near those of the TE or LE ions show greater penetration into the TE or LE,
respectively. Local pressure gradients in the TE and LE then locally disperse these zones of
analyte penetration (Figure 2). Based on these observations we developed a onedimensional analytical model of the focused sample zone where we leverage Taylor-Aristype dispersion applied only to the exponential tails of the sample distribution. We
validated our numerical simulations and analytical model with controlled experiments
(Figure 3) and showed that our analytical method is accurate for a broad range of
conditions, including variable analyte mobility, current density, electroosmotic flow
magnitude, and axial position of the ITP interface.
Figure 2: (a) In the absence of advective dispersion (e.g. no EOF), the mobility of the
analyte relative to LE and TE ion mobilities determines the shape of the analyte
distribution. Analytes with mobility approaching the LE or TE exhibit a diffuse tail as a
result of electromigration dispersion. Analyte mobility near TE mobility results in lefttailing analytes (top); analyte mobility near LE mobility results in right-tailing analytes
(bottom). (b) Electromigration couples with advective dispersion to result in further
broadening of the analyte distribution. This effect is only significant when the analyte
distribution exhibits tailing. We show experimental observations with focused Alexa Fluor
488 (symmetric analyte) and Fluorescein (tailing analyte) under strong EOF conditions at
two axial channel locations (channel entrance, blue; channel exit, red). The symmetric
analyte focuses near the center of the interface, and therefore does not experience the
strong dispsersive gradients within the LE and TE zones. In the case of the left-tailing
analyte, when the ITP interface is near the channel exit, a strong pressure gradient in the
TE zone couples with the diffuse exponential tail and results in further broadening.
Figure 3: Experimental data and modeling predictions showing the combined effects of
analyte mobility, dispersion due to EOF, and axial interface position on sample distribution
in a single experiment. Shown together with the experiments are predictions from the
analytical model and simulations. The visualized analyte is Fluorescein and the LE and TE
buffers are 100 mM BisTris-HCl and BisTris-MES, respectively. The analyte’s mobility is
near the TE mobility, which causes it to focus off-center (toward the TE) with respect to the
LE-TE interface. Near the channel entrance (LTE/L = 0.2), the strong pressure gradient in
the TE zone results in strong dispersive broadening of the sample tail into the TE. Near the
channel exit (LTE/L = 0.8), the TE pressure gradient is much weaker, resulting in a 3x
increase in peak signal intensity over the previous case.
Reference
G. Garcia-Schwarz, M. Bercovici, L.A. Marshall, and J.G. Santiago, “Sample dispersion in
isotachophoresis,” Journal of Fluid Mechanics 2011, 679, 455-475.