Electroosmotic capillary flow with nonuniform zeta potential

The present work is an analytical and experimental study of electroosmotic flow (EOF) in cylindrical capillaries with nonuniform wall surface charge (zeta-potential) distributions. In particular, this study investigates perturbations of electroosmotic flow in open capillaries that are due to induced pressure gradients resulting from axial variations in the wall zeta-potential. The experimental inquiry focuses on electroosmotic flow under a uniform applied field in capillaries with an EOF-suppressing polymer adsorbed onto various fractions of the total capillary length. This fractional EOF suppression was achieved by coupling capillaries with substantially different zeta-potentials. The resulting flow fields were imaged with a nonintrusive, caged-fluorescence imaging technique. Simple analytical models for the velocity field and rate of sample dispersion in capillaries with axial zeta-potential variations are presented. The resulting induced pressure gradients and the associated band-broadening effects are of particular importance to the performance of chemical and biochemical analysis systems such as capillary electrokinetic chromatography and capillary zone electrophoresis.     

Electroosmotic fluid motion and late-time solute transport for large zeta potentials

Analytical and numerical methods are employed to determine the electric potential, fluid velocity, and late-time solute distribution for electroosmotic flow in a tube and channel at zeta potentials that are not necessarily small. The electric potential and fluid velocity are in general obtained by numerical means. In addition, new analytical solutions are presented for the velocity in a tube and channel in the extremes of large and small Debye layer thickness. The electroosmotic fluid velocity is used to analyze late-time transport of a neutral nonreacting solute. Zero- and first-order solutions describing axial variation of the solute concentration are determined analytically. The resulting expressions contain eigenvalues representing the dispersion and skewness of the axial concentration profiles. These eigenvalues and the functions describing transverse variation of the concentration field are determined numerically using a shooting technique. Results are presented for both tube and channel geometries over a wide range of the normalized Debye layer thickness and zeta potential. Simple analytical approximations to the eigenvalues are also provided for the limiting cases of large and small values of the Debye layer thickness.     

Magnetically immobilized beds for capillary electrochromatography

Fritless packed beds comprised of magnetically responsive octadecylsilane bonded silica particles have been constructed for reversed-phase electrochromatography. The magnetic particles were immobilized in the capillary by applying an external magnetic field transverse to the direction of electroosmotic flow. Being subjected to the interplay of fluid dragging and magnetic forces, the initial loosely packed particle assembly was compacted into a uniform packing structure. The magnetically immobilized beds obtained were used as stationary phases for separation of neutral compounds, with retention behavior and column efficiency similar to those of slurry-packed columns. The results suggest that the magnetic attraction approach to fritless column packing may be used for construction of advanced chip-based chromatography, especially in complex architectures comprising curved and intersecting channels.     

Effects of analyte velocity modulation on the electroosmotic flow in capillary electrophoresis.

Modulation of the electroosmotic flow in capillary zone electrophoresis by modulation of the driving voltage gives rise to a flow profile that changes between laminar and flat profiles. The changing flow profile induces a radial movement of sample species to and from the capillary surface. The induced sample concentration gradient can be monitored by carefully probing the capillary surface. The resulting signal is a derivative of the normal-shaped peak. Derivative-shaped peaks can be observed with cations, but not with anions. Anions are unable to approach the double-layer region and therefore are unaffected by the modulation process.     

Effect of electrical double-layer overlap on the electroosmotic flow in packed-capillary columns

A plug electroosmotic velocity profile is generally assumed to be characteristic of capillary electrochromatography. However, this ideal plug flow may be illusive in some experiments with packed-capillary columns due to overlap of electrical double layers in flow channels. We report here a theoretical analysis of the double-layer overlap effects in packed-capillary columns, which is based on Rice and Whitehead's theory of electroosmotic flow combined with a capillary tube model for porous packing. The results show that the electroosmotic velocity under the influence of double-layer overlap depends strongly on the operating parameters, which increases with the column porosity, the particle diameter, and the electrolyte concentration.     

磁性液体管道流动的数值模拟

通过将磁性液体的磁化曲线用一个反正切函数来模拟，并且将磁场体积力写成Az的函数形式来模拟磁性液体在圆管申的流动。结果表明，圆管内的磁性液体有最大流量时，磁性液体流在靠近永磁附近呈紊流状态流动，在圆管的最右端，大致呈层流状态流动；圆管内的磁性液体净流量为零时，靠近永磁的磁性液体在原地呈激烈的涡旋流动状态．     

Mathematical model describing gradient focusing methods for trace analytes

The problem of gradient focusing for concentrating trace analytes is considered. Variation of buffer viscosity, conductivity, and possibly also the zeta-potential results in a focusing point where the electrophoretic velocity is balanced by the electroosmotic flow (EOF) and where the sample concentrates. The axial inhomogeneity also results in an induced pressure gradient that alters the EOF profile and therefore causes Taylor dispersion. The coupled hydrodynamics and transport problem leading to the achievement of a steady state is studied in the context of the lubrication approximation: all variations in the axial direction take place over a length scale very much larger than the characteristic channel width. A single length scale sigma(m) and a single time scale tau is found to completely determine the dynamics of the evolution close to the focusing point. Using appropriate scaled variables, the time evolution of the concentration profile near equilibrium can be described by an inhomogeneous advection diffusion equation that is free of all parameters. Explicit formulas are deduced for the location of the peak centroid and its width as a function of time. A simple graphical method is proposed for optimizing the performance of the system when some tunable external parameters are available.     

Pore-scale dispersion in electrokinetic flow through a random sphere packing

The three-dimensional velocity field and corresponding hydrodynamic dispersion in electrokinetic flow through a random bulk packing of impermeable, nonconducting spheres are studied by quantitative numerical analysis. First, a fixed bed with interparticle porosity of 0.38 is generated using a parallel collective-rearrangement algorithm. Then, the interparticle velocity field is calculated using the lattice-Boltzmann (LB) method, and a random-walk particle-tracking method is finally employed to model advection-diffusion of an inert tracer in the LB velocity field. We demonstrate that the pore-scale velocity profile for electroosmotic flow (EOF) is nonuniform even under most ideal conditions, including a negligible thickness of the electrical double layer compared to the mean pore size, a uniform distribution of the electrokinetic potential at the solid-liquid interface, and the absence of applied pressure gradients. This EOF dynamics is caused by a nonuniform distribution of the local electrical field strength in the sphere packing and engenders significant hydrodynamic dispersion compared to pluglike EOF through a single straight channel. Both transient and asymptotic dispersion behaviors are analyzed for EOF in the context of packing microstructure and are compared to pressure-driven flow in dependence of the average velocity through the bed. A better hydrodynamic performance of EOF originates in a still much smaller amplitude of velocity fluctuations on a mesoscopic scale (covering several particle diameters), as well as on the microscopic scale of an individual pore.     

Fritless packed columns for capillary electrochromatography: separation of uncharged compounds on hydrophobic hydrogels

A novel column is described that does not require frits to keep packing material within a capillary. A continuous bed is prepared in situ in aqueous solution by radical copolymerization of N-isopropylacrylamide and 2-acrylamido-2-methylpropanesulfonic acid (the resultant gel is denoted poly(AMPS-co-IPAAm). N,N'-Methylenebisacrylamide is used for cross-linking. On the application of an electrical field, electroosmotic flow (EOF) is developed in the bed along the capillary, where fluid propulsion would be otherwise difficult to achieve. The resultant EOF transports neutral compounds through the column without forcing the gel out of the capillary. Examination of the fluid motion in the continuous bed using a video microscope system and an image processor shows a relatively flat flow profile of EOF. The bed functions as the stationary phase for reversed-phase capillary electrochromatography (CEC). This new approach is an alternative to packed capillary columns which have been used previously in CEC. A high efficiency is obtained for a steroid which is separated on a 4.0% total monomer concentration (T), 10.0% degree of cross-linking (C), and 10.0% mole fraction of AMPS in the total monomer (S), poly(AMPS-co-IPAAm) column. A mixture of polyaromatic hydrocarbons is separated on a 6.9% T, 5.8% C, and 5.5% S poly(AMPS-co-IPAAm) column. The capacity factor of benzo[a]pyrene increases from 0.63 to 1.91 as the acetonitrile content in a Tris-boric acid buffer is decreased from 45 to 30% (v/v). The run-to-run RSD of analyte migration time is less than 0.73%, and the day-to-day RSD is acceptable. Potential benefits of this approach are also mentioned.     

Investigation of transverse oscillation method

Conventional ultrasound scanners can display only the axial component of the blood velocity vector, which is a significant limitation when vessels nearly parallel to the skin surface are scanned. The transverse oscillation (TO) method overcomes this limitation by introducing a TO and an axial oscillation in the pulse echo field. The theory behind the creation of the double oscillation pulse echo field is explained as well as the theory behind the estimation of the vector velocity. A parameter study of the method is performed, using the ultrasound simulation program Field II. A virtual linear-array transducer with center frequency 7 MHz and 128 active elements is created, and a virtual blood vessel of radius 6.4 mm is simulated. The performance of the TO method is found around an initial point in the parameter space. The parameters varied are: flow angle, transmit focus depth, receive apodization, pulse length, transverse wave length, number of emissions, signal-to-noise ratio (SNR), and type of echo-canceling filter used. Using an experimental scanner, the performance of the TO method is evaluated. An experimental flowrig is used to create laminar parabolic flow in a blood mimicking fluid, and the fluid is scanned under different flow-to-beam angles. The relative standard deviation on the transverse velocity estimate is found to be less than 10% for all angles between 50 degrees and 90 degrees. Furthermore, the TO method is evaluated in the flowrig using pulsatile flow, which resembles the flow in the femoral artery. The estimated volume flow as a function of time is compared to the volume flow derived from a conventional axial method at a flow-to-beam angle of 60 degrees. It is found that the method is highly sensitive to the angle between the flow and the beam direction. Also, the choice of echo canceling filter affects the performance significantly.     

Electroosmotic flows in microchannels with finite inertial and pressure forces

Emerging microfluidic systems have spurred an interest in the study of electrokinetic flow phenomena in complex geometries and a variety of flow conditions. This paper presents an analysis of the effects of fluid inertia and pressure on the velocity and vorticity field of electroosmotic flows. In typical on-chip electrokinetics applications, the flow field can be separated into an inner flow region dominated by viscous and electrostatic forces and an outer flow region dominated by inertial and pressure forces. These two regions are separated by a slip velocity condition determined by the Helmholtz-Smoulochowski equation. The validity of this assumption is investigated by analyzing the velocity field in a pressure-driven, two-dimensional flow channel with an impulsively started electric field. The regime for which the inner/outer flow model is valid is described in terms of nondimensional parameters derived from this example problem. Next, the inertial forces, surface conditions, and pressure-gradient conditions for a full-field similarity between the electric and velocity fields in electroosmotic flows are discussed. A sufficient set of conditions for this similarity to hold in arbitrarily shaped, insulating wall microchannels is the following: uniform surface charge, low Reynolds number, low Reynolds and Strouhal number product, uniform fluid properties, and zero pressure differences between inlets and outlets. Last, simple relations describing the generation of vorticity in electroosmotic flow are derived using a wall-local, streamline coordinate system.     

Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model

Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al₂O₃-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.     

Development of an Electroosmotic Pump Using Nanosilica Particle Packed Capillary

High-pressure electroosmotic pumps (EOPs) operate on the principle that electroosmotic flow (EOF) can be generated through a packed-bed capillary by applying an electric field through it. In this paper, a novel packed-bed EOP design using nanosilica particles is described. The packed-bed capillary was fabricated using a capillary of 5 cm x 530 mum i.d. close packed with silica particles having an average particle size of 20-30 nm. The flow rates, pressures and pressure/flow rate (P-Q)characteristics, electric properties of the pump and the influence of phosphate buffer concentration on the pump were carefully studied. By increasing the pressure, decreasing the applied voltage, and the electric current, the thermodynamic efficiency was about 1%-2% for inorganic buffers and 3%-5% for organic solvents or their mixture without ions.     

Electrosmotic mobility and conductivity in columns for capillary electrochromatography.

Columns employed so far in capillary electrochromatography (CEC) contain both a packed and an open segment with concomitant changes of the electric field strength and the flow velocity at the interface of the two segments in such duplex columns. To take this into account in measuring, processing, and interpreting CEC data, a framework is presented for the evaluation of the conductivity ratio and the interstitial electrosmotic flow (EOF) mobility and their usage as tools for characterizing CEC columns. This is illustrated by experimental data obtained from measurement of the current and the EOF in capillary columns packed with different stationary phases. The current data yielded the ratio of the conductivities of the packed and open segments that has been shown to be useful for the evaluation of the porosity and tortuosity. It is assumed that these important packing characteristics are the same for the flow of current and for the flow of the bulk mobile phase in the CEC column. The EOF mobility in such duplex columns is defined in two different ways. The apparent mobility, which is widely reported at present, is obtained from the length of packed segment, the migration time, and the overall electric field strength. On the other hand, the actual mobility is obtained after taking into account the porosity and tortuosity of the packing as well. Thus, the actual mobility is made independent of the porosity and tortuosity and therefore can be useful to estimate the zeta potential for characterizing the packing surface. Measurements of both the apparent and actual electrosmotic mobilities for a number of different columns have shown that the apparent and actual mobilities are significantly different in their magnitude. For this reason, it is recommended that, instead of the apparent EOF mobility, the actual mobility is used for the characterization of the packing in CEC columns.     

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

Numerical and analytical study of rotating flow in an enclosed cylinder under an axial magnetic field

Summary. A numerical and analytical study of the steady laminar flow driven by a rotating disk at the top of an enclosed cylinder, having an aspect ratio H/R equal to 1, filled with a liquid metal, and submitted to an axial magnetic field B, is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. In the absence of a magnetic field, the numerical method is validated via a comparison with experimental data; the latter was found to be in good agreement with the predictions. In the presence of a magnetic field, the analytical velocity profiles under the rotating disk and on the bottom wall obtained for a high value of the magnetic interaction parameter N are in excellent agreement with those obtained by numerical simulations. The effect of the top, bottom and vertical walls' conductivity on the flow is studied and found to be an important parameter in the control of the flow.     

Dispersion in a two-zone packed tube: An extended Taylor’s analysis

Taylor’s classical analysis for scalar dispersion in a single phase fluid flow is rigorously generalized for an instantaneous release of scalar substances into a fully developed flow through a long tube of two zones distinctively packed with porous media. A formulation for the dispersion is presented by cross-sectionally averaging the concentration transport equations and introducing a closure model for the concentration deviation terms produced in the averaging procedure. The velocity distribution of the flow through the tube is derived, with existing solution for a single zone tube flow included as a special case. Corresponding dispersivity is analytically determined, and Taylor’s well-known result for a single phase flow in a single-zone tube is recovered by setting corresponding parameters as unity. The effects of relevant parameters on both velocity profile and Taylor dispersivity are illustrated.     

Generalised vortex motion of compressible fluid with and without magnetic field and suction

The laminar boundary layer over a stationary infinite disk induced by a rotating compressible fluid is considered. The free stream velocity has been taken as tangential and varies as a power of radius, i.e. v_∞ ˜ r⁻ⁿ. The effect of the axial magnetic field and suction is also included in the analysis. An implicit finite difference scheme is employed to the governing similarity equations for numerical computations. Solutions are studied for various values of disk to fluid temperature ratio and for values of n between 1 and −1. In the absence of the magnetic field and suction, velocity profiles exhibit oscillations. It has been observed that for a hot disk in the presence of a magnetic field the boundary layer solutions decay algebraically instead of decaying exponentially. In the absence of the magnetic field and suction, the solution of the similarity equations exists only for a certain range of n.     

Gradient elution in capillary electrochromatography

In analogy to pressure-driven gradient techniques in high-performance liquid chromatography, a system has been developed for delivering electroosmotically driven solvent gradients for capillary electrochromatography (CEC). Dynamic gradients with submicroliter per minute flow rates are generated by merging two electroosmotic flows that are regulated by computer-controlled voltages. These flows are delivered by two fused-silica capillary arms attached to a T-connector, where they mix and then flow into a capillary column that has been electrokinetically packed with 3-μm reversed-phase particles. The inlet of one capillary arm is placed in a solution reservoir containing one mobile phase, and the inlet of the other is placed in a second reservoir containing a second mobile phase. Two independent computer-controlled, programmable, high-voltage power supplies (0-50 kV) [Formula: see text] one providing an increasing ramp and the other providing a decreasing ramp [Formula: see text] are used to apply variable high-voltage potentials to the mobile phase reservoirs to regulate the electroosmotic flow in each arm. The ratio of the electroosmotic flow rates between the two arms is changed with time according to the computer-controlled voltages to deliver the required gradient profile to the separation column. Experiments were performed to confirm the composition of the mobile phase during a gradient run and to determine the change of the composition in response to the programmed voltage profile. To demonstrate the performance of electroosmotically driven gradient elution in CEC, a mixture of 16 polycyclic aromatic hydrocarbons was separated in less than 90 min. This gradient technique is expected to be well-suited for generating not only solvent gradients in CEC but also other types of gradients, such as pH and ionic strength gradients, in capillary electrokinetic separations and analyses.     

Electrokinetic stacking injection of neutral analytes under continuous conductivity conditions

In capillary electrokinetic chromatography, neutral analytes can be injected by electroosmotic flow directly from a sample matrix into a separation buffer containing an electrokinetic vector with an opposite mobility. Analytes are injected at the velocity of electroosmotic flow but are retained at the interface of the sample matrix co-ion and separation buffer micelle zones as analyte/micelle complexes. A simple electrokinetic chromatography system containing sodium dodecyl sulfate as the micellar agent with borate as the buffering electrolyte included in the separation buffer and in the sample matrix to provide continuous conductivity was investigated. Concentrations of the micelle, methanol, and borate in the separation buffer were explored to increase maximum injection length of neutral analytes. Reducing the analyte velocity in the separation buffer without substantially decreasing the velocity of the analyte during injection from the sample vial allowed greatly extended sample plug injection lengths. It is presently possible to inject sample solvent volumes equivalent to approximately 7 effective capillary lengths (180 cm) with a 50-microm-i.d. capillary (24.5 cm effective capillary length), total volume of sample injection approximately 3.5 microL Equations describing the injection process and maximum injection lengths for this mode of stacking in electrokinetic capillary chromatography are introduced. The result of this work leads to a postulated generalization of electrokinetic stacking injection maximums for electrophoretic processes, and the concept of orthogonal analyte stacking/injection systems is discussed.