Chromium (III) removal by microporous ion exchanger Amberlite.120 (Na+): kinetic, equilibrium and thermodynamic studies

Cr (III) sorption on microporous strong cation exchanger Amberlite.120 (Na⁺) is studied as a function of time and temperature. The pH changes show the co-sorption of H⁺ ions along with the chromium. The rate constant values for Cr (III) sorption are calculated for both film and particle diffusion processes. However, the particle diffusion is found to be more dominant than the film diffusion. The temperature is found to have a positive effect on both the diffusional processes. The low values of energy of activation also confirm the diffusional nature of the process. Equilibrium data are explained with the help of Langmuir equation. Various thermodynamic parameters (??H, ??S and ??G) for Cr (III) exchange on the resin are calculated. The ??G values are found to be negative, while both the ??H and ??S values obtained are positive.     

Sedimentation of Dispersed Particles and Evolution of Their Distribution Function

As a result of the sedimentation of dispersed particles in channels and ducts, distribution function with respect to the particle sizes changes. Particle sedimentation is affected by the gravitational forces and the diffusional migrations to channel walls. In this article, particle sedimentation in vertical and horizontal channels is investigated depending on Pe and Re_d numbers. Futhermore, new expressions for the calculation of sedimentation velocity depending on the diffusional migrations in turbulent flow were developed. Finally, a distribution function resulting from the particle sedimentaton was suggested. The suggested mathematical expressions were compared with the experimental results given in the literature and a very good aggrement was found.     

Radial diffusion and entrance effects in porous flow-through electrodes

Radial diffusion has two effects on the performance of a flow-through electrode: (a) it may limit the maximum experimentally attainable degree of conversion, and/or (b) the polarization at a certain current output may be lower for smaller than for larger pores. A dimensionless groupwas developed as a criterion of reactant conversion under certain conditions of flow rate, pore diameter and diffusion coefficient. The lengths of both diffusional and hydrodynamic entrance regions are calculated. The ratio between the length of the diffusional entrance region and the electrode thickness is related to the criterion of reactant conversion . It was shown that in all conditions of fully developed laminar flow inside the pores, radial diffusion must be fast with respect to axial convection: hence complete reactant conversion is possible. The effect of radial hydrodynamic dispersion is briefly outlined. It increases the rate of radial mass transfer, hence the degree of conversion and decreases the length of the diffusional entrance region. The length of the hydrodynamic entrance region would normally be much shorter than the diffusional entrance length. They become comparable only when the radial dispersion coefficient is of the same order as the kinematic viscosity of the electrolyte.     

Long‐time relaxations in rubber‐modified polymer systems

Linear and nonlinear viscoelastic properties were measured in the molten state for several model ABS polymers with different rubber particle contents. Linear viscoelastic functions for ABS polymers can be separated in two parts. One is a relaxation associated with the entanglement of matrix SAN chains and the other comes from the particle‐particle interactions of rubber particles. This relaxation depends strongly on the degree of dispersion of rubber particles. The second‐plateau modulus appeared at low frequency with samples in which rubber particles agglomerate. While, the second‐plateau modulus was not observed with samples in which rubber particles are finely dispersed. Matching of AN content between grafted and matrix SAN and optimum graft density form a finely dispersed system. Large deformation relaxation measurements revealed that the damping of ABS polymers having a good dispersion of particles become stronger with an increase in rubber content. This strong damping can be explained by a layered structure. The very long relaxation was found for higher rubber content, when the neighboring grafted SAN chains contact with each other.     

Numerical Analysis of Particle Dispersion Characteristics at the Near Region of Vehicles in a Residential Underground Parking Lot

The study analyzed the transient air flow and particle dispersion at the near region of vehicles under idling conditions in an underground parking lot. It was found that the exhaust jet and particle dispersion behind the vehicles could be treated as a “nearly static” process from 20 seconds after the vehicle started. During the nearly static process, the particle dispersion behind the vehicle could be simplified to be exponentially upward. The particle concentration decreased logarithmically after 0.5 m behind the vehicle. The curvature of the particle streamline behind the vehicle under high exhaust temperature conditions is larger compared with that under low exhaust temperature conditions. When the vehicle exhaust temperature is high enough (318 K or higher in the study), the relationship between time and particle concentration above 3 m remains constant.     

Viscoelastic properties of sterically stabilized nonaqueous dispersions

The viscoelastic properties of a dispersion of poly(vinyl acetate) particles sterically stabilized by poly(2-ethyl hexyl methacrylate) and dispersed in Isopar G have been measured as a function of particle concentration and frequency at ambient temperature.At low particle concentrations, it was found that the loss modulus was larger than the storage modulus, while at high particle concentrations, i.e.,w>0.40, the storage modulus was found to be larger than the loss modulus. This inversion from a viscous to an elastic response as a function of particle concentration is attributable to the change in the configurational entropy of the steric barrier as a result of increasing the concentration of particles in the dispersion.     

Application Relevant Characterization of Aqueous Silica Nanodispersions

This work describes the application relevant characterization of eight commercially available silica powders dependent on dispersing procedure using different instruments: photon correlation spectroscopy, nitrogen adsorption, and particle charge detector. The particle size of silica was found to be different in dispersion from that of all types of fumed silica, where, after proper dispersion, the measured average particle size is similar and much higher than the primary particle size. The different properties of these two silica types will be discussed.     

Ionic melts with waterlike anomalies: thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.     

Pattern formation and morphology evolution in Langmuir monolayers

We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace's equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.     

Effective velocity and effective dispersion coefficient for finite-sized particles flowing in a uniform fracture

In this work we derive expressions for the effective velocity and effective dispersion coefficient for finite-sized spherical particles with neutral buoyancy flowing within a water saturated fracture. We considered the miscible displacement of a fluid initially free of particles by another fluid containing particles of finite size in suspension within a fracture formed by two semi-infinite parallel plates. Particle spreading occurs due to the combined actions of molecular diffusion and the dispersive effect of the Poiseuille velocity profile. Unlike Taylor dispersion, here the finite size of the particles is taken into account. It is shown that because the finite size of a particle excludes it from the slowest moving portion of the velocity profile, the effective particle velocity is increased, while the overall particle dispersion is reduced. A similar derivation applied to particles flowing in uniform tubes yields analogous results. The effective velocity and dispersion coefficient derived in this work for particle transport in fractures with uniform aperture are unique and ideally suited for use in particle tracking models.     

Stability of films with nanoparticles

Numerous products (such as paints, inks, foods, and beverages) and processes (such as coating, coagulation, sedimentation, lubrication, and paper-making) depend on the stability of the liquid films separating the dispersed phase from the continuous phase in the presence of nanoparticles or surfactant micelles. Nanoparticles exhibit a tendency to form ordered layers (i.e., stratification) and particle in-layer structures in these thin films at a sufficiently high concentration, resulting in a structural force that stabilizes the dispersion. The dispersion stability depends on the film size and the nanoparticle concentration.     

Advective flow in a sludge floc

The interior of sludge floc is highly heterogeneous, while the large pores in the floc control the advective flow. This work for the first time numerically details fluid flow and mass transfer processes in pores of activated sludge floc. The dimensionless permeabilities and mass dispersion coefficients were contoured against pore size ratio and the floc Reynolds number. With a pore size less than 20% of the floc size, the commonly adopted homogeneous model overestimates the floc permeability, and pore velocity is less than 2% of the bulk velocity. This is particularly true for flocs with low porosity. Although the convective flux is low, the dispersive mass transfer rate can be much higher than the diffusional rate, attributable to the strong Taylor dispersion effect. The three-dimensional pore structures in waste activated-sludge floc were identified using confocal laser scanning microscope (CLSM) images. Large pores were used to numerically estimate the permeability and dispersion coefficient for these pores. The permeability and the dispersion coefficient of the tortuous pores can be one order of magnitude lower than those for the equivalent straight pores. Besides the dispersion effect, the pore tortuosity appeared as the most important geometrical factor retarding the advective flow in the sludge pores. In addition, the small side pores connected to the large pore had only a mild effect on the flow process, and can be neglected in analysis.     

Analysis of Interactions between the Epidermal Growth Factor Receptor and Soluble Ligands on the Basis of Single‐Molecule Diffusivity in the Membrane of Living Cells

We present a single‐molecule diffusional‐mobility‐shift assay (smDIMSA) for analyzing the interactions between membrane and water‐soluble proteins in the crowded membrane of living cells. We found that ligand–receptor interactions decreased the diffusional mobility of ErbB receptors and β‐adrenergic receptors, as determined by single‐particle tracking with super‐resolution microscopy. The shift in diffusional mobility was sensitive to the size of the water‐soluble binders that ranged from a few tens of kilodaltons to several hundred kilodaltons. This technique was used to quantitatively analyze the dissociation constant and the cooperativity of antibody interactions with the epidermal growth factor receptor and its mutants. smDIMSA enables the quantitative investigation of previously undetected ligand–receptor interactions in the intact membrane of living cells on the basis of the diffusivity of single‐molecule membrane proteins without ligand labeling.     

Contribution of axial dispersion to band spreading in perfusion chromatography

A new interpretation of the band spreading data in perfusion chromatography is proposed by investigating the relative importance of axial dispersion in perfusive beds. Elution chromatography of proteins (bovine serum albumin and lysozyme) under non-retained conditions on two kinds of reversed-phase perfusive supports (POROS R1/H and POROS R2/H), which have different pore structures, were carried out to obtain the axial dispersion data. The Knox equation and some empirical correlations for dispersion coefficients in porous media were applied to correlate the experimental data. The influences of particle properties, solute molecular sizes and flow velocity on the dispersion coefficient were elucidated. Axial dispersion was recognised to be the main contributor to peak broadening in perfusion chromatography. The dependence of the height equivalent to a theoretical plate on flow-rate was found to be the result of the velocity dependence of the axial dispersion. The dispersion coefficient in a perfusive column can be well represented both by a power-law relationship and a correlation derived based on stochastic theory. Pursuant to these, it was found that pore size distribution of the perfusive particles and solute molecular size are important parameters, which influenced the dispersion results significantly.     

Electrorotation of leaky-dielectric and conducting microspheres in asymmetric electrolytes and angular velocity reversal

We consider the central problem of polarizable and leaky-dielectric uncharged spherical particle freely suspended in an unbounded nonsymmetric binary electrolyte, which is forced by an ambient time-harmonic uniform electric field. Under the assumption of a “weak field,” we employ the linearized standard electrokinetic model of binary electrolytes to account for such anion/cation asymmetry. A simplified generalized asymmetric dipole-term approximation, valid for a dielectric/conducting microsphere, is analytically derived for an arbitrary Debye scale and for any mismatch between ion diffusivities and valances. A two-peak unified dispersion spectrum covering all range of practical frequencies (KHz to MHz), is found for the case of a rotating electric field (ROT). The angular velocity of a free polarized particle is composed of dielectrophoretic contribution, resulting from the electrical torque (dipole term) as well as from the induced electroosmotic (ICEO) flow field. The two effects usually act in opposite directions. Under ROT excitation, we obtain a cofield rotation at high frequencies (MHz) and a counter-field behavior at low frequencies (KHz). The low-frequency dispersion is generally governed by electric double-layer charging and the high frequency by a Maxwell–Wagner relaxation process. ICEO generally dominates the low-frequency cofield response; however, it can be shown that depending on the electrolyte asymmetry, yet another dielectrophoretic related switching (reversal) point might exist. Furthermore, for large frequencies and depending on the complex permittivity ratio between the particle and electrolyte, we find a second switching point. Explicit expressions for the above two frequency reversal values are obtained in terms of the problem physical parameters and are compared against experimental results. Finally, we provide an analytical solution for the ROT ICEO velocity field of a microsphere as a function of electrolyte asymmetry and Debye length and compare it with numerical simulations.     

Chromatography of Suspensions – An Experimental and Theoretical Investigation of Axial Dispersion Phenomena

Abstract

Herein is reported an experimental and theoretical investigation of axial dispersion phenomena in the chromatography of spherical suspensions in the submicron range. Peak separation and broadening were measured for a number of particle suspensions (polystyrene, polyvinylacetate, styrene-acrylic acid copolymer, butadiene-acrylonitrile copolymer latices and silica particles) using different column combinations containing porous inorganic packing materials (Fractosils, Bioglass, Corning Glass) and over a wide range of carrier fluid (water containing 1 g/l Aerosol O.T. and 1 g/l potassium nitrate) flowrates. Peak separation was virtually independent of carrier fluid flowrate while peak broadening increased significantly. Analytical solutions of the integral equation which describes axial dispersion in the chromatography of suspensions have been found for a general detector which includes light scattering, refractometer and viscosity-concentration detectors. These solutions were used to obtain dispersion corrections for various particle diameter averages (number, surface, weight and volume). Corrections to number and surface average particle diameters for axial dispersion are excessive with a light scattering detector. These large corrections are related to the fact that in the Rayleigh scattering regime, the extinction coefficient is proportional to diameter to the fourth power. The refractometer gives reasonable dispersion corrections for all particle diameter averages. The theoretical equations derived herein are equally applicable to hydrodynamic chromatography (HDC) and capillary particle chromatography (CPC).     

Rheological Modeling of Dispersion System of Nano/Microsized Polymer Particles Considering Swelling Behavior

Rheological behavior of dispersion system containing nano/microsized cross-linked polymer particle was studied considering particle hydration and swelling. Viscosity of the dispersion system depends on swelling kinetics of polymer particles. Under shear flow, dispersion of swollen polymer particles is shear thinning. According to experimental results, kinetics of particle swelling and hydration was described well by second-order kinetic equation. Relational expression between equilibrium particle size and influencing factors of swelling such as salt concentration and temperature was presented. Assume that swollen polymer particles are uniform and have a simple core-shell structure, interacting through a repulsive steric potential. The rheological modeling of such dispersion system at low shear rate was presented using the concept of effective volume fraction, which depends on swelling kinetics and interparticle potential. Cross model was introduced to describe shear-thinning behavior. The viscosity equation allows correlation of experimental data of relative viscosity versus shear rate or hydration time; accounting for effect of temperature and salt concentration on viscosity. Predictions of the model have a good agreement with experimental results.     

Critical coagulation concentration of a salt-free colloidal dispersion

Both exact and approximate analytical solutions of the Poisson-Boltzmann equation for two planar, parallel surfaces are derived for the case when a dispersion medium contains counterions only, and the results obtained are used to evaluate the critical coagulation concentration of a spherical dispersion. A correction factor, which is a function of the valence of counterions, the surface potential of a particle, and the potential on the midplane between two particles at the onset of coagulation, is derived to modify the classic Schulze-Hardy rule for the dependence of the critical coagulation concentration on the valence of counterions. The correction factor is found to increase with the increase in the valence of counterions and/or with the increase in the surface potential. However, it approaches a constant value of 0.8390 if the surface potential is sufficiently high.     

聚氨酯脲-丙烯酸酯水分散液的粒径及形态研究

研究了羧基含量、异氰酸酯指数（［ － ＮＣＯ］／［ － ＯＨ］） 、聚氨酯脲与聚丙烯酸酯组成比（ＰＵＵ／ＰＡ） 以及一系列制备工艺因素对聚氨酯脲—丙烯酸酯（ＰＵＡ） 水分散液粒子尺寸及形态的影响。结果表明：羧基含量和ＰＵＵ／ＰＡ 组成比增大或异氰酸酯指数减小都会导致分散液粒径减小;ＰＵＡ 中ＰＡ 含量越大,ＰＵＡ 水分散液粒子形态越不规整;工艺因素如搅拌强度、升温速率等对ＰＵＡ 水分散液粒子尺寸及形态的影响不符合传统乳液聚合的规律。     

A chromatographic analysis of hindered diffusion of saccharides in silica gels

Summary The chromatographic technique as a means for experimental studies of diffusion in porous solids has been demonstrated. In this paper we report the effective diffusion coefficients which we have chromatographically obtained for two dextran samples and three low molecular weight solutes. The chromatographic method of measuring diffusional resistances in porous solids has the advantages of rapidity and simplicity. This method also provides information on the axial dispersion and distribution of a solute between the moving phase and the solvent held stationary in the pore. The elution curves of a packed column in pulse response experiments were analyzed by the method of moments to give the parameters of interest. The results indicate that pore diffusion of the solutes was appreciably restricted in comparison with diffusion in bulk solution. The degree of hindrance depended on the size of the diffusing substances.