Moving Boundary Method Research Articles

Electric Field-assisted Fine Finishing of Brittle Materials Using Electrophoresis Phenomenon

Electrophoresis-polishing method, it is one of the methods of “Field-assisted Fine Finishing (FFF)”, has been developed recently, in which charged grains suspended in liquid move to an electorode under an applied potential. Present paper focuses on effect of electrophoresis current yielded by the movement of the charged grains in liquid under the applied potential. Effect of grain concentration of CeO2 and ZrO2 fine abrasives on the electrophoresis-polishing both of BK7 glass and silicon wafer is examined experimentally. It is found thatζ-potential of CeO2 and ZrO2 fine abrasives dispersed into liquid are measured by moving boundary method on simple setup using the electrophoresis phenomenon of the charged grains, on which the electrical double layer is conducted. The result of examinations presents controllability by the applied potential and independence for grain concentration. Polishing setup is able to give the polishing pressure to the work piece on the unwoven polisher made of polymer. Experimental results show that the stock removal increases with increasing the applied potential. Concerning the increase of stock removal in the conditions of high concentration of grain, influence of the electrophoresis current is discussed relating with the flow of polishing compound.

On iontophoretic delivery enhancement: ionization and transport properties of lidocaine hydrochloride in aqueous propylene glycol

The ionization and transport properties of lidocaine hydrochloride (LidHCl) in aqueous propylene glycol (PG) containing 20% PG by weight was studied by means of electrical precision conductometry. For drug concentrations exceeding about 1.7 mM a slight formation of LidH +Cl − ion-pairs is indicated; ion-pair association constant, K p=1.73 (molar scale). A two variable analysis of the experimental data yielded K a=1.5×10 −8 for the acid dissociation constant of LidH +, i.e. p K a=7.82, and the limiting ionic conductivity, λ o(LidH +)=21.73 cm 2 S mol −1. To enable evaluation of single ion conductivities the proton transport number of HCl in the present solvent mixture was determined using the moving boundary method.

Proton mobilities obtained by the moving boundary method and an empirical equation in capillary electrophoresis

Proton mobilities obtained by the moving boundary method and an empirical equation in capillary electrophoresis

Comparisons of the mobilities of salt ions obtained by the moving boundary method and two empirical equations in capillary electrophoresis

The actual mobilities of some small salt ions with high charge intensities, such as Cl −, K +, Na +, Ba 2+, SO 4 2− and La 3+, calculated using two empirical equations., μ act = μ 0exp(−0.77 √ zI) [valid for z ≥ 2 and 0.001mol/l ≤ I ≤ 0.1mol/I] and μ act = μ 0exp(−0.5 z 1.78 √ I) [valid for I ≤ 0.001mol/l], are compared with the actual mobilities determined by the moving boundary method (here, μ act and μ 0 are the actual and absolute mobilities, respectively, z is the charge of the ion, I the ionic strength). The results show that, (i) under the given conditions both of the empirical equations are valid for small ions with high charge intensities as well as large ions with low charge intensities, (ii) the former is also valid for multivalent ions of ionic strength I ≤ 0.001mol/l, (iii) the latter also applies to monovalent ions of ionic strength 0.001mol/l≤ I≤ 0.1mol/1. Thus, the two equations can be expressed as a single equation: μ act = μ 0exp(− η√ zI) [used for I ≤ 0.1mol/l, and if z = 1, η = 0.5,or if z ≥ 2, η = 0.77].

Numerical analysis in oscillating flow considering orientation of porous media regenerator

Numerical analyses were performed to investigate the characteristics of regenerator in oscillating flow by using moving boundary method and Darcy model. In this work, periodic adiabatic boundary condition was suggested as the boundary condition of adiabatic part so that the effects of the thermal inertia of the wall could be considered. In carrying out numerical analyses, two models were applied and compared. One called isotropic model has the same thermal conductivity in radial and axial directions within a porous media. The other called aeolotropic model has different conductivity in each directions. Isotropic model could not show the advantage of energy reduction which needs to maintain constant wall temperature difference between heater and cooler. But aeolotropic model could simulate the reduction of energy consumption.

DUNCAN ARTHUR MACINNES, FOREMOST AMERICAN ELECTROCHEMIST

Duncan Arthur Macinnes, one of the worlds outstanding electrochemists, was born in Salt Lake City, Utah, on Marah 3l, l885, and died on September 23, 1965. He graduated from the University of Utah with a bachelor of science degree in chemical engineering in 1907 and obtained a Ph.D. degree in chemistry from the University of Illinois in 1911. He held positions mainly at M.I.T and the Rockefeller Institute for Medical Research. His most important contributions deal with the determination of transference numbers by the moving boundary method, development of the glass electrode, and experimental confirmation of the Debye-Hllakel Theory.

Design of Unity Feedback Control Systems Based on the Method of Inequalities.

In this paper, we develop a computer-aided control system design based on the method of inequalities proposed by Zakian. First, for single-input single-output unity feedback systems, we give a simple pole-zero placement algorithm that can prevent specified pole-zero cancellation. Then this algorithm is used to develop a computer-aided design (CAD) system based on the method of inequalities. As a parameter search algorithm, we use Rosenbrock's moving boundary method. For efficient parameter search, we propose a simple modification of the algorithm, which takes account of the role of the tuning parameters. Since the developed CAD system is written as m-tiles of MATLAB, it can be widely used on various computers, from personal computers to workstations. A design example is presented to illustrate the effectiveness of the proposed CAD system.

Quantitative measurement of lipoprotein surface charge by agarose gel electrophoresis.

The electrophoretic mobilities of low density lipoprotein (LDL) and six pure proteins in a 0.5% agarose gel have been compared to literature electrophoretic mobility values determined by the Tiselius moving boundary method. There is a strong correlation (r = 0.99) between the electrophoretic mobilities determined by the two techniques. The electrophoretic behavior of charged particles smaller than very low density lipoproteins (VLDL) is not markedly perturbed by a 0.5% agarose matrix, and variations in mobility primarily reflect differences in particle valence and density of surface charge. Application of electrokinetic theory to derive protein and lipoprotein net charges from the electrophoretic mobilities in agarose yields a quantitative delineation of lipoprotein electrophoretic migration patterns wherein the beta mobility region comprises a surface potential range of -4.5 to -7.0 mV; the pre-beta region a range of -7.0 to -10.5 mV; the alpha mobility region a range of -10.5 to -12.5 mV and the serum albumin region a range of -12.5 to -14.0 mV. Because protein conformation and charge are critical in metabolic regulation, the agarose gel electrophoresis technique provides a valuable analytical tool that should help to elucidate further details of the structure-function relationships of serum lipoprotein particles.

Cone Breakthrough Time for Horizontal Wells

Summary Recovery from an oil zone underlying a gas cap, overlying an aquifer, or sandwiched between gas and water can be improved by repressing the coning problem through horizontal-well drainage. Literature methods to predict coning behavior are limited to steady-state flow conditions and determination of the critical rate. The results in this paper are based on new semianalytical solutions for time development of a gas or water cone and of simultaneous gas and water cones in an anisotropic infinite reservoir with a horizontal well placed in the oil column. The solutions are derived by a moving-boundary method with gravity equilibrium assumed in the cones. For the gas-cone case, the semianalytical results are presented as a single dimensionless curve (time to breakthrough vs. rate) and as a simple analytical expression for dimensionless rates > ⅓. For the simultaneous gas- and water-cone case, the results are given in two dimensionless sets of curves: one for the optimum vertical well placement and one for the corresponding time to breakthrough, both as functions of rate with the density contrast as a parameter. The validity of the results has been extensively tested by a general numerical simulation model. Sample calculations with reservoir data from the Troll field and comparison with test data from the Helder field demonstrate how the theory can be used to estimate the time to cone breakthrough and its sensitivity to the uncertainties in reservoir parameters.

Transference numbers for NaCl in a 60 wt.% ethanol–water mixture at 25 °C

Transference number values for both ions of NaCl in a 60 wt.% ethanol–water mixture were determined by the moving boundary method at 25 °C. These values, after the volume and the solvent corrections had been applied, were optimized by dividing them by their sum at each concentration studied and the Tbest values obtained. From the analysis of these best values against C(NaCl) three different regions of behaviour were clearly defined. In region I only the presence of free ions and ionic pairs were considered and the transference number values were fitted by using the classical Fuoss–Onsager and Pitts equations and Barthel and Perie's equations, based on a chemical model. From these treatments a limiting value (〈T0+〉= 0.43613) was obtained. Region II starts with an abnormal and sudden rising of the transference number value of Na+ ion constituent which was justified by considering the formation of the triple ions Na2Cl+ and NaCl–2. An estimation of the concentration of these species was made. When C(NaCl) is made sufficiently large, this abnormal behaviour ends (and also region II) which was interpreted as a consequence of the formation of the Na2Cl2 species. Finally, ionic limiting conductance values [λ0(Na+)= 18.98 and λ0(Cl–)= 24.53 Ω–1 cm2 mol–1] were determined.

Ion mobilities in DMF-water mixtures at 25�C

Densities and viscosities of mixtures of N,N-dimethylformamide (DMF) with water at 25°C have been determined. Limiting equivalent conductances of cesium chloride, potassium chloride, potassium bromide and potassium thiocyanate in these solvent mixtures at 25°C are presented together with corresponding values of ion association constants and distance of closest approach parameters. The transference number of the potassium ion has been determined in solvent mixtures ranging from 0 to 0.75 mol fraction in DMF in water at 25°C. The conductimetric Hittorf method has been used for both potassium bromide and potassium chloride in solutions of up to 0.496 mole fraction of DMF. For solutions of potassium thiocyanate in 0.5 and 0.75 mole fraction in DMF the cationic transference number has been determined using the moving boundary method. Stokes radii have been evaluated. Transport properties are examined in relation to-solvent properties such as composition, dielectric constant, excess volume of mixing and free volume.

Transference number measurements in aqueous solutions at 25.degree.C. 3. Lithium bromide

Transference numbers for aqueous solutions of LIBr at 25 °C are determined by employing the direct moving-boundary method. Due to the hygroscopic character of this electrolyte, the value of the concentration for each of the solutions studied, with Its most probable error included, is obtained from its experimental density. The corrected ionic transference numbers are optimized on the basis of their sum which must equal 1 at each concentration. From the “best” transference numbers thus obtained, Cbest values are calculated which allow the direct determination of experimental values for such transference numbers that would be coincident with these best ones. The extrapolation to zero concentration of these transference numbers is done by using the 1963 Fuoss and Onsager equation and from such limiting values, T±°, the limiting equivalent conductance for the lithium Ion, Is also obtained. The density-concentration relationship found for these aqueous solutions of LIBr is also presented. © 1987, American Chemical Society. All rights reserved.

Transport Numbers in Molten Aluminum Chloride‐1‐Methyl‐3‐Ethylimidazolium Chloride Mixtures

The transport numbers of 1‐methyl‐3‐ethylimidazolium (MEI+), , and Cl− ions were measured in equimolar and melts of and 1‐methyl‐3‐ethylimidazolium chloride (MEICl). The moving boundary method and a modified Hittorf method were used. The external transport numbers of the three ions in the equimolar melt were , , and 0, respectively. As mole fraction decreases, the transport number for decreases, while that for Cl+ increases and that for MEI+ remains the same. The internal transport number of the MEI+ relative to Cl as the reference is .

Temperature Effect on Transference Numbers for KCl in Ethanol–Water Mixtures

Abstract Cation-transference numbers were determined by the moving boundary method for 0.02 mol dm−3 KCl in 5-, 10-, 15-, 20-, and 30 mol% ethanol–water mixtures at 15 and 35 °C. The cation-transference number has a maximum around 10 mol% of ethanol at each temperature studied, and becomes larger with decreasing temperature in the solvent of the same composition. From the temperature dependence of the transference number, the differences in the activation energy of transport between K+ and Cl− ions were estimated, and it was found that the activation energy of the K+ ion is less than that of the Cl− ion and the difference becomes larger in the range of 5–20 mol% of ethanol. These results are discussed in terms of structural effects and ion-solvent interactions.

Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids

Equations of motion are given that are suitable for setting up non-equilibrium momentum fluxes in molecular fluids. In a recent article Marechal and Ryckaert have pointed out that equilibrium time correlation functions depend on whether the stress is measured in a centre of mass or atomic representation. In non-equilibrium simulations of molecular systems, a corresponding ambiguity arises between perturbations applied to the individual atoms and perturbations applied to the centres-of-mass of the molecules. I use linear response theory to demonstrate the equivalence of the non-equilibrium equations of motion with the equilibrium correlation functions, for small strain rates. I also show that the two sets of equations of motion produce identical trajectories in the low-frequency limit. In this limit the equations of motion are equivalent to the Lees-Edward's method, but at finite frequencies the moving boundary method is incorrect.

A method of determining the diffusion coefficient

It is proposed to determine the diffusion coefficient by the moving boundary method, without using a solution of the diffusion equation, by studying the finishing stage of boundary movement in appropriate coordinates, which take account of the symmetry and characteristic dimensions of the system.

A revision of the transference numbers of CsCl in water at 25°C

Transference numbers for CsCl in water at 25°C at concentrations of 0.02, 0.04, 0.06 and 0.10 equiv·dm −3 were measured by the moving boundary method, comparing them against the data from the available literature. Because transference numbers for both ions were measured in each concentration, optimum values, T opt, were calculated. By applying theoretical equations, T vs C, to these optimum values, the limiting transference numbers, T 0, were determined. From these T 0 values the ionic limiting conductance for caesium ions was obtained and compared with the values derived from studies by other authors.

Pressure Effect on Transference Numbers for KCl in Ethanol–Water Mixtures at 25 °C

Abstract Cation transference numbers for 0.02 mol dm−3 KCl in 0-, 5-, 10-, 15-, 20-, and 30-mol% ethanol–water mixtures were determined by the moving boundary method at 25 °C up to 1500 kg cm−2 (1 kg cm−2=0.9807×105 Pa). The cation transference number, t+, initially increases with increasing ethanol content up to 10–15 mol% and then decreases at all the pressures studied. In water and ethanol–water mixtures below 20 mol%, t+ at the definite solvent decreases with increasing pressure. The decreasing rate becomes smaller as the ethanol content increases, and the tendency is reversed finally at 30 mol%. To account for the variation of t+ with solvent composition and pressure, specific interactions between the ions and solvent have been taken into consideration.

Transference numbers and conductance in concentrated copper(II) chloride solutions at 25°C

Transference numbers in concentrated copper(II) chloride solutions at 25°C are obtained by (i) a modified moving boundary method using other solutions to isolate both electrodes from the CuCl2 solution, and (ii) the e.m.f. method using cells with transference with gaseous chlorine electrodes. Conductance and density measurements are also reported. The transference results support the more recent Russian work against the earlier measurements of Denham; there is no evidence of negative cation constituent transference numbers, and it is concluded that anionic chloro complexes are not a major constituent of the concentrated solutions. In this respect copper(II) chloride differs from the halides of cadmium and zinc.

Transference numbers and phenomenological transport coefficients for concentrated aqueous hydrochloric acid solutions at 25�C

The transference numbers of HCl in water at 25°C have been determined up to 8 mol-kg−1 by using cells with transference. The problem of the solubility of AgCl from Ag/AgCl electrodes was avoided by employing dilute chlorine gas/iridium electrodes for T H and hydrogen gas/platinum electrodes for T Cl . The sums of the independently measured T H and T Cl values never differed from unity by more than 0.9%. The cation constituent transference number of HCl was also measured at 1M by the recently modified moving boundary method, but at higher concentrations the Soret effect produced unacceptably large current dependences. Combination of these transference numbers with literature conductances, diffusion coefficients and activity coefficients led to a new set of phenomenological transport coefficients l ij . The resulting curve for l12/c vs. c behaves more normally than did the curve based on previous transference numbers.