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Stanford University

Stanford Microfluidics Laboratory

Understanding the Effect of Advective Dispersion on Peak Mode Isotachophoresis

Giancarlo Garcia-Schwarz, Moran Bercovici,
Lewis A. Marshall and Juan G. Santiago

 

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 Ám) 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 axial-average 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 non-uniform 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 one-dimensional analytical model of the focused sample zone where we leverage Taylor-Aris-type 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 left-tailing 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", J. Fluid Mech. 2011, 679, 455-475. (click here for pdf)

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