Boyd F. Edwards

A Theoretical and Experimental Study of the Electrophoretic Extraction of Ions from a Pressure Driven Flow in a Microfluidic Device

B. R. Reschke et al. — Fri, 02 Mar 2012 14:21:19 PST

The electrophoretic extraction of ions from a hydrodynamic flow stream is investigated at an intersection between two microfluidic channels. A pressure gradient is used to drive samples through the main channel, while ions are electrophoretically extracted into the side channels. Hydrodynamic restrictors and a neutral coating are used to suppress bulk flow through the side channels. A theoretical model that assumes Poiseuille flow in the main channel and neglects molecular diffusion is used to calculate the extraction efficiency, η, as a function of the ratio, R, of the average hydrodynamic velocity to the electrophoretic velocity. The model predicts complete extraction of ions (η = 1) for R < 2/3 and a monotonic decrease in η as R becomes greater than 2/3, which agrees well with the experimental results. Additionally, the model predicts that the aspect ratio of the microfluidic channel has little effect on the extraction efficiency. It is anticipated that this device can be used for on-line process monitoring, sample injection, and 2D separations for proteomics and other fields.

Long-Period Orbits for Ions in a Periodic Spatiotemporal Potential

J. Vopal et al. — Fri, 02 Mar 2012 14:21:08 PST

Wave Electrophoresis

J. Mease et al. — Fri, 02 Mar 2012 14:20:56 PST

When Are Chiasms Admissible as Evidence?

Boyd F. Edwards et al. — Fri, 02 Mar 2012 14:20:45 PST

Since John Welch’s discovery of chiasmus in the Book of Mormon in 1967, many critics have attempted to show how chiasmus appears in just about every type of literature, from Dr. Seuss to Strangite scripture. This article discusses the authors’ statistical admissibility tests to verify whether a chiasmus in a work shows strong evidence of intentionality by the original author. Their results indicate that certain passages in the Old Testament and in the Book of Mormon show deliberate chiasmus, while Strangite scripture, the Doctrine and Covenants, nursery rhymes, Dr. Seuss, and other works are not intentionally chiastic.

Simultaneous Separation and Detection of Cations and Anions Ion a Microfluidic Device with Suppressed Electroosmotic Flow and a Single Injection Point

B. R. Reschke et al. — Fri, 02 Mar 2012 14:20:36 PST

A rapid and simultaneous separation of cationic and anionic peptides and proteins in a glass microfluidic device that has been covalently modified with a neutral poly(ethylene glycol) (PEG) coating to minimize protein adsorption is presented. The features of the device allow samples that contain both anions and cations to be introduced from a central flow stream and separated in different channels with different outlets—all in the presence of low electroosmotic flow (EOF) imparted by the PEG coating. The analytes are electrophoretically extracted from a central hydrodynamic stream and electrophoretically separated in two different channels, in which pressure driven flow has been suppressed through the use of hydrodynamic restrictors. Having different outlets for the electrophoretic separation channels that are spatially separated from the injection enables coupling with further downstream functionalities or off-chip detection, such as mass spectrometry. A plug of charged analyte is hydrodynamically pumped to the sampling intersection and anions from the plug migrate electrophoretically toward the anode in one channel while cations migrate toward the cathode in the other channel due to suppressed EOF from the PEG coating. The separations presented here required less than a minute to complete and produced average separation efficiencies of up to about 3,500 plates from a separation length of 2 cm. The extraction efficiency of both cations and anions from the hydrodynamic stream is determined experimentally and compared with a previously reported model that was used to determine anion extraction efficiency. The extraction efficiency is determined to be 87% and 98% for the two sample mixtures analyzed, and the values predicted by the model are within 3.5% of the experimental data. It is anticipated that this basic approach for simultaneous separation of anions and cations with reduced EOF will be integrated into larger microfluidic systems because the design provides separate outlets that can feed downstream processes or linked to off-chip detection.

Self-Similar Nested Sequences on a Chaotic Attractor for Travelingwave Electrophoresis

Boyd F. Edwards — Fri, 02 Mar 2012 14:20:25 PST

Oscillating electric potentials are applied to interdigitated arrays of cylindrical electrodes above and below a stationary conducting viscous fluid. The phases of these potentials are chosen to produce a longitudinal traveling wave that traps high-mobility ions and partially traps intermediate-mobility ions in periodic and narrowband chaotic attractors with average velocities that are commensurate with the wave speed. Stable periodic attractors have periods up to 101 times the wave period. Incommensurate broadband chaotic attractors are described by one-dimensional iterated contact-angle return maps, which feature self-similar nested sequences that converge geometrically at unstable trapped orbits. Sequences of singular angles and sequences of step transitions are characterized by distinct convergence factors. A criterion for allowed interelectrode orbits is developed. Experiments are suggested to evaluate the applicability of the theory to microfluidic separations.

Traveling-Wave Electrophoresis for Microfluidic Separations

Boyd F. Edwards et al. — Fri, 02 Mar 2012 14:20:15 PST

Models and microfluidic experiments are presented of an electrophoretic separation technique in which charged particles whose mobilities exceed a tunable threshold are trapped between the crests of a longitudinal electric wave traveling through a stationary viscous fluid. The wave is created by applying periodic potentials to electrode arrays above and below a microchannel. Predicted average velocities agree with experiments and feature chaotic attractors for intermediate mobilities.

Fabrication and Performance of a Microfluidic Traveling-Wave Electrophoresis System

K. D. Jo et al. — Fri, 02 Mar 2012 14:20:03 PST

A microfluidic traveling-wave electrophoresis (TWE) system is reported that uses a locally defined traveling electric field wave within a microfluidic channel to achieve band transport and separation. Low voltages, over a range of −0.5 to +0.5 V, are used to avoid electrolysis and other detrimental redox reactions while the short distance between electrodes, 25 μm, provides high electric fields of 200 V cm⁻¹. It is expected that the low voltage requirements will simplify the future development of smaller portable devices. The TWE device uses four interdigitated electrode arrays: one interdigitated electrode array pair is on the top of the microchannel and the other interdigitated electrode array pair is on the microchannel bottom. The top and bottom substrates are joined by a PDMS spacer that has a nominal height of 15 μm. A pinched injection scheme is used to define a narrow sample band within an injection cross either electrokinetically or hydrodynamically. Separation of two dyes, fluorescein and FLCA, with baseline resolution is achieved in less than 3 min and separation of two proteins, insulin and casein is demonstrated. Investigation of band broadening with fluorescein reveals that sample band widths equivalent to the diffusion limit can be achieved within the microfluidic channel, yielding highly efficient separations. This low level of band broadening can be achieved with capillary electrophoresis, but is not routinely observed in microchannel electrophoresis. Sample enrichment can be achieved very easily with TWE using a device with converging electric field waves controlled by two sets of independently controlled interdigitated electrodes arrays positioned serially along the microchannel. Sample enrichment of 40-fold is achieved without heterogeneous buffer/solvent systems, sorptive, or permselective materials. While there is much room for improvement in device fabrication, and many capabilities are yet to be demonstrated, it is anticipated that the capabilities and performance demonstrated herein will enable new lab-on-a-chip processes and systems.

Dynamics of Falling Raindrops

Boyd F. Edwards et al. — Thu, 27 Oct 2011 14:05:48 PDT

A standard undergraduate mechanics problem involves a raindrop which grows in size as it falls through a mist of suspended water droplets. Ignoring air drag, the asymptotic drop acceleration is g/7, independent of the mist density and the drop radius. Here we show that air drag overwhelms mist drag, producing drop accelerations of order 10^-3g. Analytical solutions are facilitated by a new empirical form of the air drag coefficient C = 12R^-1/2, which agrees with experimental data on liquid drops in the Reynolds-number range 10<R<1000 relevant to precipitating spherical drops. Solutions including air drag are within reach of students of intermediate mechanics and nonlinear>dynamics.

Modification of the Eikonal Relation for Chemical Waves to Include Fluid Flow

J. W. Wilder et al. — Thu, 27 Oct 2011 14:05:36 PDT

Propagating wave fronts resulting from autocatalytic chemical reactions have been the focus of much recent research. For the most part, the hydrodynamics resulting from such reactions has been neglected. In this work, a relation is derived for the normal speed of a propagating wave front as a function of the local curvature when fluid motion is allowed. This ‘‘eikonal’’ equation is a generalization of one which was derived in the absence of fluid flow. It is also shown that small variations in the fluid density due to the chemical reaction do not change the form of the relation.

Two-Dimensional Magnetothermal Plumes

D. D. Gray et al. — Thu, 27 Oct 2011 14:05:26 PDT

The physics of the Kelvin body force and the “buoyancy” it creates is explained. It is demonstrated that, under the Boussinesq approximation, the Kelvin buoyancy can be cast in terms of a spatially variable gravity force. Using the boundary layer approximation, closed form and numerical similarity solutions for steady, laminar, two-dimensional plumes driven by the interaction of a line heat source and a non-uniform magnetic field are obtained and discussed.

Mass Distribution on Clusters at the Percolation Threshold

M. F. Gyure et al. — Thu, 27 Oct 2011 14:05:16 PDT

Monte Carlo simulations and a scaling hypothesis are used to study the distribution of blob masses on two-dimensional finite-mass clusters at the percolation threshold. The exponents associated with this distribution function are a combination of backbone and percolation exponents. This work offers insights into the structure and fragmentation properties of percolation clusters in particular, and provides methods applicable to other fractal distribution problems in general.

Exact and Asymptotic Scaling Solutions for Fragmentation with Mass Loss

M. Cai et al. — Thu, 27 Oct 2011 14:05:06 PDT

Exact and asymptotic solutions to a linear rate equation for fragmentation with mass loss are presented. Solutions for spatially discrete random bond annihilation illustrate the mutual exclusiveness of the fragmentation and recession terms in the rate equation. Exact solutions for deterministic equal fragment recession show that continuous mass loss between fragmentation events can be approximated by discrete mass loss during fragmentation events when this mass loss is small. Evidence that continuous and discrete mass loss preclude shattering mass loss, the loss of mass to zero-mass particles due to runaway fragmentation, is presented. General asymptotic scaling forms, general solutions reflecting arbitrary initial conditions, and explicit scaling solutions are derived.

Chemical Wave Propagation in Hele-Shaw Cells and Porous Media

D. A. Vasquez et al. — Thu, 27 Oct 2011 14:04:55 PDT

Chemical waves induce density gradients in fluids which may lead to convection. This paper studies the convective effects on chemical waves propagating in porous media or in fluids confined between two parallel vertical walls. Chemical waves in the iodate–arsenous acid system are modeled with a one variable reaction‐diffusion equation. The fluid flow is modeled using Darcy’s law. A linear stability analysis on convectionless fronts shows a transition to convection. The full nonlinear equations describing the convective front are solved numerically on a vertical slab. Convective fronts propagate faster than convectionless fronts. Near the onset of convection, the fronts are raised on one side of the slab and lowered on the opposite side. Away from the onset, the fronts are raised at the middle of the slab with the opposing sides at the same height.

Cutoff Model and Exact General Solutions for Fragmentation with Mass Loss

J. Huang et al. — Thu, 27 Oct 2011 14:04:43 PDT

Exact solutions are obtained for a linear rate equation for the evolution of the particle mass distribution during fragmentation with mass loss. These involve general power-law dependences on the particle mass for the fragmentation rate, the daughter-mass distribution, and the mass-loss rate. Consumption of bridges joining two or more otherwise disconnected regions leads to fragmentation such as might occur during the combustion of porous charcoal particles. Exact results for mass-loss rates proportional to the particle mass are relevant to random mass-removal processes such as percolation theory. For pure fragmentation without mass loss, a mass cut-off below which no fragmentation occurs is introduced to avoid the unbounded fragmentation rate for small particles in the `shattering' regime, in which the fragmentation rate becomes unbounded for particle masses approaching zero. This cut-off model predicts that, for monodisperse initial conditions in the strong shattering regime, the number of particles whose masses exceed the cut-off mass remains near unity for the duration of the fragmentation process, and then drops quickly to zero. The associated asymptotic behaviour excludes the scaling solution in this regime, but includes the scaling solution otherwise.

Does Chiasmus Appear in the Book of Mormon by Chance?

Boyd F. Edwards et al. — Thu, 27 Oct 2011 14:04:33 PDT

Chiasmus is an inverted-parallel literary form that was employed by ancient Hebrew biblical writers, among others. An instance of this form, called a “chiasm,” presents two or more literary elements, and then restates them in reverse order. Short chiasms are not uncommon in literature. In some cases, the authors undoubtedly intended to use that form for literary effect (that is, by design); in other cases, the elements fell into that form without author intent (that is, by chance). In 1969, John W. Welch reported his discovery of many-element chiasms in the Book of Mormon,1 which Joseph Smith testified to have translated from plates written anciently by Hebrew descendants.

Onset of Convection for Autocatalytic Reaction Fronts: Laterally Unbounded System

Boyd F. Edwards et al. — Thu, 27 Oct 2011 14:04:23 PDT

The linear stability of exothermic autocatalytic reaction fronts that convert unreacted fluid into a lighter reacted fluid is considered using the viscous thermohydrodynamic equations. For upward front propagation and a thin front, the discontinuous jump in density at the front is reminiscent of the Rayleigh-Taylor problem of an interface between two immiscible fluids, whereas the vertical thermal gradient near the front is reminiscent of the Rayleigh-Bénard problem of a fluid layer heated from below. The problem is also similar to flame propagation, except that here the front propagation speed is limited by catalyst diffusion rather than by activation kinetics. For a thin ascending front and small density changes in a laterally unbounded system, the curvature dependence of the front speed stabilizes perturbations with short wavelengths λ<λ_c, whereas long wavelengths are unstable to convection, indicating that the density discontinuity dominates over thermal gradients. Simple analytical results for the critical wavelength λ_c for onset of convection, the growth rate near onset of convection, and the maximum growth rate are found. Agreement with experiments on iodate–arsenous acid solutions in vertical tubes motivates linear and nonlinear calculations in cylindrical geometries.

Nonaxisymmetric and Axisymmetric Convection in Propagating Reaction-Diffusion Fronts

J. Masere et al. — Thu, 27 Oct 2011 14:04:14 PDT

Observations of steady nonaxisymmetric chemical wave fronts are reported for upward propagation in iodate-arsenous acid solutions within vertical capillary tubes. These observations confirm a recent prediction of hydrodynamic stability theory that the onset of convection in such fronts should be nonaxisymmetric. The nonaxisymmetric waveform reflects the presence of a single convective roll in the vicinity of the moving front.

Convection in Chemical Waves

D. A. Vasquez et al. — Thu, 27 Oct 2011 14:04:03 PDT

We present a theory for the vertical propagation of chemical waves near the onset of convection. Fluid motion, coupled to a standard reaction-diffusion mechanism for chemical wave propagation, determines the speed and shape of the reaction front in a two-dimensional slab. Our model is compared with experiments in capillary tubes. For tilted and horizontal tubes, fluid motion is always present with a corresponding increase in front speed.

Convective Instability of Autocatalytic Reaction Fronts in Vertical Cylinders

D. A. Vasquez et al. — Thu, 27 Oct 2011 14:03:54 PDT

Linear stability analysis predicts that the onset of convection for an ascending autocatalytic reaction front in a vertical cylinder corresponds to a nonaxisymmetric mode. This mode consists of a single convective roll confined to the region near the reaction front, with fluid rising in half of the cylinder and falling in the other half. Experiments show a flat front below the onset of convection and an axisymmetric front well above the onset of convection. New experiments are called for to closely examine the onset of convection in order to test this prediction.