Electroviscous sphere-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged spherical particle and a charged plane wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from Cox's general theory [R.G. Cox, J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential and electroviscous flow field. It is a priori assumed that the double layer thickness surrounding each charged surfaces is much smaller than the particle size. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the sphere are explicitly determined analytically for small particle-wall distances, but low and intermediate Peclet numbers.     

Primary electroviscous effect in a dilute suspension of charged mercury drops

The standard theory of the primary electroviscous effect in a dilute suspension of charged spherical rigid particles in an electrolyte solution (Watterson, I. G.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1115) is extended to cover the case of a dilute suspension of charged mercury drops of viscosity eta(d). A general expression for the effective viscosity or the electroviscous coefficient p of the suspension is derived. This expression tends to that for the case of rigid particles in the limit of eta(d) --> infinity. We also derive an approximate analytical viscosity expressions applicable to mercury drops carrying low zeta potentials at arbitrary kappaa (where kappa is the Debye-Hückel parameter and a is the drop radius) and to mercury drops as well as rigid spheres with arbitrary zeta potentials at large kappaa. It is shown that the large-kappaa expression of p for rigid particles predicts a maximum when plotted as a function of zeta potential. This result for rigid particles agrees with the exact numerical results of Watterson and White. It is also shown that in the limit of high zeta potential the effective viscosity of a suspension of mercury drops tends to that of uncharged rigid spheres given by Einstein's formula (Einstein, A. Ann. Phys. 1906, 19, 289), whereas in the opposite limit of low zeta potential the effective viscosity approaches that of a suspension of uncharged liquid drops derived by Taylor (Taylor, G. I. Proc. R. Soc. London, Ser. A 1932, 138, 41).     

The electroviscous force between charged particles: beyond the thin-double-layer approximation

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95-112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye-Hückel approximation.     

Electroviscous cylinder-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle-wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.     

Primary Electroviscous Effect with a Dynamic Stern Layer: Low kappaa Results

The classical treatments of the primary electroviscous effect show important discrepancies with respect to the experimental data. A possible better agreement may be found if the contribution of the ions adsorbed on the Stern layer, which can move tangentially near the particle surface, is taken into account. This contribution has been incorporated into the Watterson-White theory. A study of the influence of the Stern-layer parameters on the primary electroviscous coefficient has been made. Copyright 2000 Academic Press.     

The primary electroviscous effect,free solution electrophoretic mobility,and diffusion of dilute prolate ellipsoid particles (minor axis = 3 nm) in monovalent salt solution

The principal objective of the present work is the modeling of the primary electroviscous effect of charged prolate ellipsoid models of low axial ratio. Other transport properties examined include (free solution) electrophoretic mobilities and translational diffusion constants. A numerical boundary element method is employed to solve the coupled Poisson, low Reynolds number Navier-Stokes, and ion transport equations. The methodology is first applied to the primary electroviscous effect of spheres with a centrosymmetric charge distribution and excellent agreement with independent theory is obtained. Specific model studies are also carried out for prolate ellipsoid models with axial ratios less than 4 and a minor axis equal to 3 nm. Most studies are carried out in aqueous NaCl solution (2 to 50 mM) at 20 degrees C for a range of different particle charges, although limited results are also presented in LiCl and KCl solution. The primary electroviscous effect for weakly charged prolate ellipsoids is smaller than that of a sphere under similar conditions. These studies are also carried out at high absolute particle charge. A comparison is made between the primary electroviscous effect and electrophoretic mobilities of prolate ellipsoids and corresponding spherical models.     

The electroviscous effect in ethylcellulose latex suspensions. Effect of ionic strength and correlation between theory and experiments

 This article describes an experimental and theoretical investigation of the so-called primary electroviscous effect, i.e., the increase in suspension viscosity due to the existence of an electrical double layer around the particles. By measuring the viscosity of ethylcellulose latex suspensions, the electroviscous coefficient, the quantity measuring the effect, was estimated for different concentrations of 1-1 electrolyte in the dispersion medium. These data were compared with the predictions of Watterson and White's model, using the zeta potential of the particles deduced from electrophoretic mobility measurements. It was found that the theory considerably underestimates the effect. In an attempt to improve the agreement between data and predictions, the model was generalized to include the possibility (dynamic Stern layer) that ions in the inner part of the double layer have nonzero mobility. The general theory, however, predicts even lower values of the electroviscous coefficients, thus increasing the separation between calculated and measured electroviscous coefficients. A careful analysis of the ionic concentrations and velocity profiles with and without dynamic Stern layer corrections can account for this fact, but leaves unsolved the problem of the large discrepancies found in the theoretical explanation of the strength of the electroviscous effect. Received: 19 October 1999/Accepted: 17 December 1999     

Cell models for the primary electroviscous effect

The primary electroviscous effect in a nondilute suspension of charged spherical particles is studied by means of cell models. The governing equations are derived, and then analytic results are obtained by restricting attention to the limit of thin double layers, small Hartmann and Peclet numbers, and small potentials. Previous work has assumed that the velocity at the outer boundary of the cell is identical to the imposed flow, as proposed by Simha (J. Appl. Phys. 1952, 23, 1020). Results with this boundary condition are compared against those predicted when the tangential shear stress on the outer boundary is assumed to be unperturbed, as proposed by Happel (J. Appl. Phys. 1957, 28, 1288). Both the hydrodynamic and electroviscous contributions to the effective viscosity are smaller with the Happel boundary condition, showing that such cell models offer a range of predictions and should be used with caution.     

Primary electroviscous effect in a moderately concentrated suspension of charged spherical colloidal particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernández, F. J.; Gómez-Merino, A. I.; García-Sánchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials zeta at the particle volume fraction phi < or = 0.3 for the case of nonoverlapping double layers, that is, at kappaalpha > 10 (where kappa is the Debye-Hückel parameter). A simple approximate analytic expression for p applicable for particles with large kappaalpha and arbitrary zeta is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi < or = 0.3, where the relative error is negligible for kappaalpha > or =100 and even at kappaalpha = 50 the maximum error is approximately 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.     

An experimental test of Booth's primary electroviscous effect theory

The primary electroviscous effect has been investigated in dilute suspensions of titanium oxide (anatase), the viscosities of which were measured by means of a capillary viscometer with automatic timing. The linear relation between viscosity and solids volume fraction was first determined at the isoelectric point of the particles when the particles are uncharged, and the electroviscous contribution to the intrinsic viscosity was then determined at other values of pH. Booth's theory (Proc. R. Soc. London Ser. A203, 533 (1950)) agrees well with the experimental results when the particle zeta potential is small and the double layer is thin (kappa alpha approximately 7.3), but agreement is poor when the double layer is thick (kappa alpha approximately 0.6).     

The primary electroviscous effect of prolate silica sols

The intrinsic viscosity and the dynamic mobility of four silica sols have been measured as a function of the ionic strength. It was found that intrinsic viscosity decreased with increasing ionic strength, which we attribute to the primary electroviscous effect. The geometry and the charge of the particles were fitted using experimental viscosity, light scattering, and dynamic mobility data, where the intrinsic viscosity measured at the highest ionic strength for a given sol was used as input data in our analysis. Further, the boundary element (BE) method was used to calculate the primary electroviscous effect and electrophoretic mobility of charged prolate ellipsoids. These calculations were then compared with experimental data, and the primary electroviscous effect was subtracted from the intrinsic viscosity at a given ionic strength, which led to a slightly altered geometry of the particles. This revised geometry was used as input data using the BE method, and the procedure was repeated iteratively until agreement was obtained at high ionic strength. In general, good agreement between theory and experiment was found.     

Electroviscous effects on pressure-driven flow of dilute electrolyte solutions in small microchannels

A fundamental understanding of the flow characteristics of electrolyte solutions in microchannels is critical to the design and control of microfluidic devices. Experimental studies have shown that the electroviscous effect is appreciable for a dilute solution in a small microchannel. However, the experimentally observed electroviscous effects cannot be predicted by the traditional theoretical model, which involves the use of the Boltzmann distribution for the ionic concentration field. It has been found that the Boltzmann distribution is not applicable to systems with dilute electrolyte solutions in small microchannels because it violates the ion number conservation condition. A new theoretical model is developed in this paper using the Nernst equation and the ion number conservation, instead of the Boltzmann distribution, to obtain the ionic concentration field. The ionic concentration field, electrical potential field, and flow field in small microchannels are studied using the model developed here. In order to verify this model, the model-predicted dP/dx (applied pressure gradient) Re (Reynolds number) relationship is compared with the experimentally determined dP/dx approximately Re relationship. Strong agreement between the model predictions and the experimental results supports this model.     

聚电解质溶液性质的研究 Ⅰ.在无外加盐存在下聚电解质溶液的粘性行为

实验测定了磺化聚砜钠盐在无外加盐存在下在二甲基甲酰胺溶液中的粘性行为,提出了一个新的经验公式: η_(sp)/C=D+A/(1+BC~n)用以描述聚电解质溶液的比浓粘度与浓度的依赖关系。利用经验式对我们及Fuoss等的实验数据进行处理时,所得结果是满意的。用“电粘滞效应”和聚离子链伸展效应对经验式进行了讨论。     

Electronic spectra and crystal field analysis of energy levels of Ho3+ in HoF6(3-)

The electronic absorption spectra of single crystals of Cs(2)NaHoF(6) have been recorded in the spectral region between 4700 and 42000 cm(-1) at temperatures down to 10 K. The structure in the (5)I(8) → (5)I(J) (J = 7-4), (5)F(J) (J = 5-1), (5)S(2), (5)G(J) (J = 4-6), (3)K(J) (J = 7, 8) transitions has been analyzed and assigned. The emission spectra (5)S(2) → (5)I(J) (J = 6-8) and (5)G(4) → (5)I(J) (J = 5-7), (5)F(5) have also been recorded at 10 K for crystals of Cs(2)NaHoF(6) and partly also for samples of Cs(2)NaHoF(6):Yb(3+). The spectra comprise magnetic dipole zero phonon lines and electric dipole allowed one-phonon vibronic sidebands. From the detailed interpretation of the emission and absorption spectra, aided by a clear understanding of the vibrational behavior of the HoF(6)(3-) moiety and by magnetic dipole intensity calculations, a data set of 59 energy levels spanning 17 multiplet terms was derived. Crystal field calculations were then performed using a 4f(10) basis, as well as including the configuration interaction with a p-electron configuration. The latter calculation, which employed 14 parameters, gave better agreement with experiment and the mean deviation was 13.5 cm(-1). A comparison with the energy level fittings for Cs(2)NaHoCl(6) has been included. The crystal field parameters for the fluoro- and chloro-systems followed empirically predicted ratios.     

The primary electroviscous effect of polystyrene latexes

An investigation on the primary electroviscous effect of polystyrene latexes has been made. Capillary viscometers of Ubbelohde type have been used. The comparison of the results obtained with the theories allow us to conclude that the effect is underestimated for low electrolyte concentrations. We suggest that this underestimation is due to an additional surface conductance into the electric double layer. This interpretation is consistent with previous studies on electrophoretic mobility of the same system.     

Modeling and analysis of vacuum membrane distillation for the recovery of volatile aroma compounds from black currant juice

A vacuum membrane distillation (VMD) model has been developed and validated with experimental data. The model consists of an extended transport model for the VMD process and is able to predict the effects of concentration and temperature polarization on the overall process performance. To validate the model, first it was tested with few experimental case studies from literature [S. Bandini, G.G. Sarti, Heat and mass transport resistances in vacuum membrane distillation per drop, AIChE J. 45 (7) (1999) 1422–1433; K.W. Lawson, D.R. Lloyd, Membrane distillation. I. Module design and performance evaluation using vacuum membrane distillation, J. Membr. Sci. 120 (1996) 111–121; A.M. Urtiaga, G. Ruiz, I. Ortiz, Kinetic analysis of the vacuum membrane distillation of chloroform from aqueous solutions, J. Membr. Sci. 165 (2000) 99–110]. Then the VMD model has been validated with experimental data collected from the recovery of aroma compounds from black currant [R.B. Jørgensen, A.S. Meyer, C. Varming, G. Jonsson, Recovery of volatile aroma compounds from black currant juice by vacuum membrane distillation, J. Food Eng. 64 (2004) 23–31]. In this work, recovery of 12 characteristic volatile aroma compounds from black currant juice has been studied. The simulated results from the VMD model, in terms of aroma concentration in the permeate have been compared with those obtained from laboratory experiments. The validated model has been used to study the effects of various process and membrane parameters on the concentration factor. The physical properties of various aroma compounds have been predicted using group contribution method as a function of temperature.     

A STUDY OF THE PRIMARY ELECTROVISCOUS EFFECT IN PYREX GLASS SUSPENSIONS.

An experimental investigation on the electrokinetic phenomenon known as primary electroviscous effect is described for suspensions of Pyrex glass, a highly charged and well known material. By means of an automatic method, the viscosity of the suspensions is measured for different volume fractions of solids, at various electrolyte concentrations and pH values. These measurements allow the estimation of the electroviscous coefficient, p. The electrophoretic mobility was determined for the same systems and zeta potential calculated from these experimental data in order to carry out the comparison between the measured values of p and different theoretical predictions. A qualitative agreement between theory and experiment was found in many cases, but the rigorous theories seem to systemmatically underestimate the experimental p values. The reasons for this disagreement are discussed in addition to the general trends of the electrokinetic behaviour of Pyrex glass.     

Electroviscous effect on the streaming current in a pH-regulated nanochannel

Accurate and rapid estimation of the streaming current in nanochannels is crucial for the development of the nanofluidics based power generation apparatus. In this study, an analytical model is developed for the first time to examine the electroviscous effect on the streaming current/conductance in a pH-regulated nanochannel by considering practical effects of multiple ionic species, surface chemistry reactions, and the Stern layer. Predictions from the model are in good agreement with the experimental results of the streaming conductance in silica nanochannels available in the literature. The electroviscous effect could have a significant reduction of ca. 30% in the streaming conductance at medium pH and low salt concentration.     

High magnetic exchange coupling constants: a density functional theory based study of substituted schlenk diradicals

The Schlenk diradical has been known since 1915. After a detailed experimental work by Rajca, its magnetic nature has remained more or less unexplored. We have investigated by quantum chemical calculations the nature of magnetic coupling in 11 substituted Schlenk diradicals. Substitution has been considered at the fifth carbon atom of the meta-phenylene moiety. The UB3LYP method has been used to study 12 diradicals including the original one. The 6-311G(d,p) basis set has been employed for optimization of molecular geometry in both singlet and triplet states for each species. The singlet optimization has led to the optimization of the broken-symmetry structure for 10 species including the unsubstituted one. This development makes it possible to carry out further broken symmetry calculations in two ways. The triplet calculation has been done using 6-311++G(d,p) basis set and the optimized triplet geometry in both procedures. The broken symmetry calculations have used the optimized geometries of either the triplet states or the broken symmetry solutions. The first method leads to the prediction of electron paramagnetic resonance (EPR) compatible magnetic exchange coupling constant (J) in the range 517-617 cm(-1). A direct optimization of the broken symmetry geometry gives rise to a lower estimate of J, in the range of 411-525 cm(-1) and compatible with macroscopic Curie studies. The calculated J for the unsubstituted Schlenk diradical is 512 cm(-1) that can be compared with 455 cm(-1) estimated by Rajca. In both cases, introduction of groups with +M and +I effects (Ingold's notation) decreases the J value from that for the unsubstituted Schlenk diradical while -I and -M groups at the same position increases J. These trends have been explained in terms of Hammett constants, atomic spin densities, and dihedral angles.     

Experimental and chemical kinetic modeling study of 3-pentanone oxidation

Shock tube ignition delay times have been measured for 3-pentanone at a reflected shock pressure of 1 atm (±2%), in the temperature range 1250-1850 K, at equivalence ratios of 0.5-2.0 for O(2) mixtures in argon with fuel concentrations varying from 0.875 to 1.3125%. Laminar flame speeds have also been measured at an initial pressure of 1 atm over an equivalence ratio range. Complementary to previous studies [Pichon S., Black, G., Chaumeix, N., Yahyaoui, M., Simmie, J. M., Curran, H. J., Donohue, R. Combust. Flame, 2009, 156, 494-504; Serinyel, Z.; Black, G.; Curran, H. J.; Simmie, J. M. Combustion Sci. Tech., 2010, 182, 574-587], laminar flame speeds of 2-butanone have also been measured, and relative reactivities of these ketones have been compared and discussed. A chemical kinetic submechanism describing the oxidation of 3-pentanone has been developed and detailed in this paper; rate constants for unimolecular fuel decomposition reactions have been treated for falloff in pressure with nine-parameter fits using the Troe Formulism. Both compounds treated in this work may be used as fuel tracers, thus further ignition delay time measurements have been carried out by adding 3-pentanone to n-heptane in order to test the effect of the blend on ignition delay timing. It was found that the autoignition characteristics of n-heptane remained unaffected in the presence of 15% 3-pentanone in the fuel, consistent with results obtained using acetone and 2-butanone [Pichon S., Black, G., Chaumeix, N., Yahyaoui, M., Simmie, J. M., Curran, H. J., Donohue, R. Combust. Flame, 2009, 156, 494-504; Serinyel, Z.; Black, G.; Curran, H. J.; Simmie, J. M. Combustion Sci. Tech., 2010, 182, 574-587].