Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross‐sectional area. We develop a quasi‐1D model based on local cross‐sectional area averaging of the equations describing unsteady, multispecies, electromigration‐diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross‐section; and we include chemical equilibrium calculations for weak electrolytes, Taylor–Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid–base equilibrium constants. To solve the quasi‐1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high‐resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross‐sectional area channels. We also show that our simulations of ITP in variable cross‐sectional area channels have very good quantitative agreement with published experimental data.     

Compact adaptive-grid scheme for high numerical resolution simulations of isotachophoresis

In a previous publication we demonstrated a fast simulation tool for solution of electrophoretic focusing and separation. We here describe the novel mathematical model and numerical algorithms used to create this code. These include the representation of advection–diffusion equations on an adaptive grid, high-resolution discretization of the equations (sixth order compact), a new variational-based approach for controlling the motion of grid points, and new boundary conditions which enable solution in a moving frame of reference. We discuss the advantages of combining a high-resolution discretization with an adaptive grid in accurately resolving sharp interfaces in isotachophoresis, and provide verification against known analytical solutions and comparison with prevailing exiting numerical algorithms.     

High-sensitivity detection using isotachophoresis with variable cross-section geometry

We present a theoretical and experimental study on increasing the sensitivity of ITP assays by varying channel cross-section. We present a simple, unsteady, diffusion-free model for plateau mode ITP in channels with axially varying cross-section. Our model takes into account detailed chemical equilibrium calculations and handles arbitrary variations in channel cross-section. We have validated our model with numerical simulations of a more comprehensive model of ITP. We show that using strongly convergent channels can lead to a large increase in sensitivity and simultaneous reduction in assay time, compared to uniform cross-section channels. We have validated our theoretical predictions with detailed experiments by varying channel geometry and analyte concentrations. We show the effectiveness of using strongly convergent channels by demonstrating indirect fluorescence detection with a sensitivity of 100 nM. We also present simple analytical relations for dependence of zone length and assay time on geometric parameters of strongly convergent channels. Our theoretical analysis and experimental validations provide useful guidelines on optimizing chip geometry for maximum sensitivity under constraints of required assay time, chip area and power supply.     

Tunable Bidirectional Electroosmotic Flow for Diffusion‐Based Separations

We present a new concept for on‐chip separation that leverages bidirectional flow, to tune the dispersion regime of molecules and particles. The system can be configured so that low diffusivity species experience a ballistic transport regime and are advected through the chamber, whereas high diffusivity species experience a diffusion dominated regime with zero average velocity and are retained in the chamber. We detail the means of achieving bidirectional electroosmotic flow using an array of alternating current (AC) field‐effect electrodes, experimentally demonstrate the separation of particles and antibodies from dyes, and present a theoretical analysis of the system, providing engineering guidelines for its design and operation.     

Eigenvalue inequalities in an embeddable factor

We provide a characterization of the possible eigenvalues of the sum of two selfadjoint elements of a II factor which can be embedded in the ultrapower of the hyperfinite II factor.

     

Normal boundary dilations and rationally invariant subspaces

The first named author was supported by grants from the National Science Foundation.     

Hydrolytic cleavages of 7-nitro-2-phenyl-1,2-benzisoxazol-3-one. Evidence for the occurrence of a benzidine-like rearrangement of N,O-diphenylhydroxylamines

Preparation of the title compound 1 is described. Its treatment with base caused hydrolysis of the amide bond and subsequent benzidine-like rearrangement to give 4′-amino-3-carboxy-4-hydroxy-5-nitrobiphenyl (4) . Acid treatment caused cleavage of the nitrogen-oxygen bond and rearrangement to 7-nitro-3-phenylbenzoxazol-2-one (6) .     

Synthesis of polymers with isolated thiophene–arylidene–thiophene chromophores for enhanced and specific electron/hole transport

The synthesis of nine new polymers intended for future use in light‐emitting diodes is described. The polymers consist of alternating units of thiophene–arylidene–thiophene chromophores and saturated silicon‐containing spacers. The arylidene moieties include benzene‐1,4‐, 2,5‐dimethoxybenzene‐1,4‐, naphthalene‐1,4‐, anthracene‐9,10‐, pyridine‐2,5‐, pyridine‐2,6‐, N‐methylcarbazole‐3,6‐, 1,3,4‐oxadiazole‐2,5‐, and 4,4′‐dimethyl‐2,2′‐bithiazole‐5,5′‐. The syntheses involved dibromination of the central arene followed by Suzuki or Kumada cross‐coupling reactions with two thiophene units. Subsequent dilithiation and reaction with dihalosilylalkanes provided the polymers. Their optical properties, including ultraviolet–visible absorption and emission in solution, were comparable to those of the parent monomer units, and they possessed the physical characteristics of macromolecules. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 872–879, 2001