Surface conduction in presence of slip is characterized by full Dukhin number, which is given by [1]: Du = 4(1 + m) κL sinh 2 zeζ 2k B T + 2mb L sinh 2 zeζ 4k B T , (1) where m = 2ε(k B T /ze) 2 /(ηD), and D is the ion diffusiv-ity, which is assumed equal for both types of ions. The first term in (1) is the Dukhin number for the no-slip surface, Du b=0 , while the second one, Du b , is due to hy-drodynamic slip. In the Debye-Hückel model zeζ k B T ≪ 1. (2) This restriction (2) allows the simplification: Du b=0 ≈ 4(1 + m) κL zeζ 2k B T 2 , (3) Du b ≈ 2mb L zeζ 4k B T 2. (4) The parameter m ≈ 100/z 2 , and κL ≫ 1 since EDL is thin. Whence Du b=0 ≈ 1/(z 2 κL) ≪ 1 provided the potential is low. For a "slippery part" of Du we evaluate Du b ≈ 0.5b/L if eζ/(k B T) ≈ 0.1, and Du b ≈ 5 · 10 −3 b/L for eζ/(k B T) ≈ 0.01. Therefore for increasing surface charge (potential) and b/L, the conductivity of the diffuse layer can become comparable to the bulk, and surface condition must be considered. The Péclet number, P e = U L/D , in presence of slip can be evaluated as P e = q 2 E t (1 + bκ)L κηD. (5) Typically, electroosmotic velocity is of order is of order micrometers per second for no-slip surfaces [2]. For nano-scale patterns L < 1 µm and typical ion diffusivities D ≈ 10 −6 cm 2 /s this gives P e b=0 < 0.01 ≪ 1. The slip implies a correction factor (1 + bκ) , which suggests that the convective ion transport can safely be neglected only for bκ < 10. Larger values of bκ should relax this standard approximation of small P e. ELECTRO-OSMOTIC VELOCITY IN EIGENDIRECTIONS Longitudinal stripes.-In this configuration only x−velocity component remains, and the Stokes equation takes the form ∂ 2 y + ∂ 2 z u = εκ 2 ψE t (6) We expand surface charge density in a Fourier series, and the potential is then ψ(y, z) = q εκ e −κy + ∞ n=1 q n εξ n e −ξny cos λ n z, (7) where ξ n = κ 2 + λ 2 n , λ n = 2nπ/L , q = q 1 φ 1 + q 2 φ 2 is the mean surface charge, and q n = 2(q 2 − q 1) πn sin πnδ L. (8) The general solution to (6) for u(y, z) has the form u(y, z) = U + ∞ n=1

We present a numerical and experimental study of the effects of ionic strength on electrophoretic focusing and separations. We review the development of ionic strength models for electrophoretic mobility and chemical activity and highlight their differences in the context of electrophoretic separation and focusing simulations. We couple a fast numerical solver for electrophoretic transport with the Onsager-Fuoss model for actual ionic mobility and the extended Debye-Huckle theory for correction of ionic activity. Model predictions for fluorescein mobility as a function of ionic strength and pH compare well with data from CZE experiments. Simulation predictions of preconcentration factors in peak mode ITP also compare well with the published experimental data. We performed ITP experiments to study the effect of ionic strength on the simultaneous focusing and separation. Our comparisons of the latter data with simulation results at 10 and 250 mM ionic strength show the model is able to capture the observed qualitative differences in ITP analyte zone shape and order. Finally, we present simulations of CZE experiments where changes in the ionic strength result in significant change in selectivity and order of analyte peaks. Our simulations of ionic strength effects in capillary electrophoresis compare well with the published experimental data.

We present a comprehensive review and comparison of the methodologies for increasing sensitivity and resolution of capillary electrophoresis (CE) using online transient isotachophoresis (tITP). We categorize the diverse set of coupled tITP and CE (tITP-CE) methods based on their fundamental principles for disrupting isotachophoretic preconcentration and triggering electrophoretic separation. Based on this classification, we discuss important features, advantages, limitations, and optimization principles of various tITP-CE methods. We substantiate our discussion with original simulations, instructive examples, and published experimental results.

We present an experimental study of the effect of pH, ionic strength, and concentrations of the electroosmotic flow (EOF)-suppressing polymer polyvinylpyrrolidone (PVP) on the electrophoretic mobilities of commonly used fluorescent dyes (fluorescein, Rhodamine 6G, and Alexa Fluor 488). We performed on-chip capillary zone electrophoresis experiments to directly quantify the effective electrophoretic mobility. We use Rhodamine B as a fluorescent neutral marker (to quantify EOF) and CCD detection. We also report relevant acid dissociation constants and analyte diffusivities based on our absolute estimate (as per Nernst-Einstein diffusion). We perform well-controlled experiments in a pH range of 3-11 and ionic strengths ranging from 30 to 90  mM. We account for the influence of ionic strength on the electrophoretic transport of sample analytes through the Onsager and Fuoss theory extended for finite radii ions to obtain the absolute mobility of the fluorophores. Lastly, we briefly explore the effect of PVP on adsorption-desorption dynamics of all three analytes, with particular attention to cationic R6G.

Electrokinetic techniques are a staple of microscale applications because of their unique ability to perform a variety of fluidic and electrophoretic processes in simple, compact systems with no moving parts. Isotachophoresis (ITP) is a simple and very robust electrokinetic technique that can achieve million-fold preconcentration 1,2 and efficient separation and extraction based on ionic mobility. 3 For example, we have demonstrated the application of ITP to separation and sensitive detection of unlabeled ionic molecules (e.g. toxins, DNA, rRNA, miRNA) with little or no sample preparation 4-8 and to extraction and purification of nucleic acids from complex matrices including cell culture, urine, and blood. 9-12ITP achieves focusing and separation using an applied electric field and two buffers within a fluidic channel system. For anionic analytes, the leading electrolyte (LE) buffer is chosen such that its anions have higher effective electrophoretic mobility than the anions of the trailing electrolyte (TE) buffer (Effective mobility describes the observable drift velocity of an ion and takes into account the ionization state of the ion, as described in detail by Persat et al. 13). After establishing an interface between the TE and LE, an electric field is applied such that LE ions move away from the region occupied by TE ions. Sample ions of intermediate effective mobility race ahead of TE ions but cannot overtake LE ions, and so they focus at the LE-TE interface (hereafter called the "ITP interface"). Further, the TE and LE form regions of respectively low and high conductivity, which establish a steep electric field gradient at the ITP interface. This field gradient preconcentrates sample species as they focus. Proper choice of TE and LE results in focusing and purification of target species from other non-focused species and, eventually, separation and segregation of sample species.We here review the physical principles underlying ITP and discuss two standard modes of operation: "peak" and "plateau" modes. In peak mode, relatively dilute sample ions focus together within overlapping narrow peaks at the ITP interface. In plateau mode, more abundant sample ions reach a steady-state concentration and segregate into adjoining plateau-like zones ordered by their effective mobility. Peak and plateau modes arise out of the same underlying physics, but represent distinct regimes differentiated by the initial analyte concentration and/or the amount of time allotted for sample accumulation.We first describe in detail a model peak mode experiment and then demonstrate a peak mode assay for the extraction of nucleic acids from E. coli cell culture. We conclude by presenting a plateau mode assay, where we use a non-focusing tracer (NFT) species to visualize the separation and perform quantitation of amino acids. Video LinkThe video component of this article can be found at https://www.jove.com/video/3890/ Protocol Physics of ITPITP forms a sharp moving boundary between ions of like charge. The technique can be per...