Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.     

Complex shear modulus of concentrated suspensions of solid spherical particles

Starting from the complex shear modulus equation for a dilute suspension system, three new equations are developed for the complex shear modulus of concentrated suspensions of solid spheres. The continuous phase (matrix) and the dispersed particles are treated as viscoelastic materials in the derivation. Complex shear modulus data on suspensions of spherical glass beads in polymeric liquid were obtained experimentally and compared with the predictions of the proposed equations. The proposed equations describe the experimental data reasonably well.     

Fluid dynamics of dilute suspensions and fouling of tubular membrane modules

The role of dilute suspensions in fouling a ultrafilter tubular membrane module is studied in detail for a wide range of wall permeation flux conditions. The inlet flow profiles are assumed to be either uniform (plug flow) or parabolic (fully developed) shape. It is assumed that the particles are neutrally buoyant and the concentrations are so low that it does not influence the fluid flow. Furthermore, the particle-particle interactions and the forces of interaction between the particle and the membrane wall are assumed to be unimportant. The governing equations of motion for the fluid are solved by a finite difference scheme. To compute the particulate fouling, the equations of motion for the particles are solved by the fourth-order Runge-Kutta-Gill method. Results are presented for both hydrodynamics and membrane fouling by dilute suspensions for conditions such as the effect of assumed inlet velocity profiles, and a wide range of wall permeation flux conditions.     

The use of dielectric spectroscopy for the characterization of polymer-induced flocculation of polystyrene particles

The flocculation of colloidal suspensions is an important unit operation in many industries, as it greatly improves the performance of solid separation processes. The number of available techniques for evaluating flocculation processes on line is limited, and most of these are only functional in dilute suspensions. Thus, techniques usable for flocculation characterization in high-solids suspensions are desirable. This study investigates the use of dielectric spectroscopy to monitor the flocculation of polystyrene particles with a cationic polymer. The frequency-dependent permittivity is modeled and the model parameters are used to describe the particle aggregation. The results show a peak in the modeled time constants of the dielectric relaxation at the onset of flocculation. Further, the adsorption of polymeric flocculant onto the particle surface results in a reduction in particle charge, evident as a decrease in the magnitude of the dielectric dispersion. The use of dielectric spectroscopy is found to be valuable for assessing flocculation processes in high-solids suspensions, as changes in parameters such as floc size and charge can be detected.     

Sieve mechanism of microfiltration separation

A theoretical model of dead-end microfiltration (MF) of dilute suspensions is proposed. The model is based on a sieve mechanism of MF and takes into account the probability of membrane pore blocking during MF of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and the particle size distributions is deduced. According to the suggested model a similarity property is applicable, which allows one to predict the flux through the membrane as a function of time for any pressure, and dilute concentration, based on one experiment at a single pressure and concentration. The suggested model includes only one fitting parameter, β>1, which takes into account the range of the hydrodynamic influence of a single pore. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in good agreement with the measurements on different track-etched membranes. A simple approximate solution of the IDE is derived and that approximate solution, as well as the similarity principal of MF processes, is in good agreement with measurements using a commercial Teflon microfiltration membrane. The theory was further developed to take into account the presence of multiple pores (double, triple and so on pores) on a track-etched membrane surface.

A series of new dead-end filtration experiments are compared with the proposed initial and modified pore blocking models. The challenge suspension used was nearly monodispersed suspension of latex particles of 0.45 μm filtered on a track-etched membrane with similar sized pores 0.4 μm. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the cross-membrane pressures varied from 1000 to 20,000 Pa. Three stages of microfiltration have been observed. The initial stage is well described by the proposed pore blocking model. The model required only a single parameter that was found to fit all the data under different experimental operational conditions. The second stage corresponds to the transition from the blocking mechanism to the third stage, which is cake filtration. The latter stage occurred after approximately 10–12 particle layers were deposited (mass = 0.006 g) on the surface of the microfiltration membrane.     

Numerical and approximate studies on the theoretical dielectric relaxation of colloidal suspensions in the time domain

In this work we show numerical calculations on the dielectric behavior of colloidal suspensions in the time domain. The theory elaborated by DeLacey and White ((1981) J Chem Soc Faraday Trans 2 77:2007–2039) for dilute suspensions in the frequency domain, will be the basis for the present study. The different contributions, and their relative importance, to the transient current density generated in the suspensions after the application of a step electric field, are calculated from the dielectric response function associated to the DeLacey and White's model. In particular, we analyze the conduction and absorption current densities in the transient states upon changing the concentration of the supporting electrolyte in the suspension. With the aim of characterizing the response of the suspension for short times, an approximation to the distribution function of relaxation times that best fits the dielectric model, is calculated. Finally, an exhaustive analysis of the behavior of the dielectric response function is carried out, together with a comparison with other models in the time domain.     

Determination of static microstructure of dilute and concentrated suspensions of anisotropic particles by ultra-small-angle X-ray scattering

Ultra-small-angle X-ray scattering was performed on suspensions of anisotropic polystyrene particles of varying degrees of anisotropy. The wave vector dependence of particle form factors is well described by a model developed by Debye for the scattering from fused spheres. As volume fraction is raised, all suspensions undergo a disorder/order phase transition. The scattering from disordered and ordered suspensions of anisotropic particles is the same as that of spheres up to volume fractions of 0.45, suggesting that, in the dilute crystalline phase, the anisotropic particles order into a rotator or plastic crystal phase, where the particle centers of mass are ordered, but the particle directors are randomly distributed. Further increase in particle volume fraction leads to differences in scattering between homonuclear dicolloids and spheres, implying that the homonuclear dicolloids form a body-centered tetragonal phase with both positional and directional order. This conclusion is supported by real-space imaging of dried films of the particles.     

The primary electroviscous effect in colloidal suspensions

Although a well-defined electrokinetic phenomenon, the primary electroviscous effect in dilute colloidal suspensions is still an unsolved problem. Most of the experimental tests of the different theories that we have studied have shown a lack of agreement. We have developed, during the last years, new theoretical approaches obtaining, finally, a much better agreement with the experimental results. The corrections are defined in two lines: first, it is accepted that ions present into the Stern layer, in which the fluid is stagnant, can tangentially move; second, it is accepted that the hydrodynamic interaction between colloidal particles exists although the suspensions are extremely diluted. The remarkable conclusion of our work is that the combination of both corrections should give correct theoretical results.     

Theory of dielectric relaxations due to the interfacial polarization for two-component suspensions of spheres

A theoretical formula of dielectric relaxation in a form of complex relative permittivity is derived for dilute suspensions of spherical particles of two kinds on the basis of the Maxwell-Wagner theory of interfacial polarization. Another theoretical formula is derived further for concentrated suspensions of spheres of two kinds on condition that the formula derived above holds for the infinitesimally increasing process in concentration of the dispersed spheres. Furthermore a theoretical formula is derived for concentrated suspensions of shelled spheres of two kinds as the extension of the formula for concentrated suspensions. By use of the theoretical formulas proposed, values of the permittivities and the conductivities of the two-component suspensions were calculated for some examples with different sets of phase parameters. Results of the numerical calculation demonstrates dielectric relaxation profiles full of variety and characteristic of the suspensions containing two kinds of spheres covered with or without shells.     

The effect of preparation procedure and composition of water-ethanol suspensions of amorphous silica on their aggregative stability and kinetics of coagulation

The method of flow ultramicroscopy is employed to study the effect of the composition and preparation procedure of dilute water-ethanol suspensions of two samples of amorphous silica (fractionated fused quartz and monodisperse amorphous silica) on the kinetics of their coagulation. It is revealed that all suspensions prepared by the addition of silica powders to water-ethanol mixtures with ethanol contents of 96 and 40 vol % are stable with respect to aggregation, as the suspensions prepared by the addition of aliquots of concentrated dispersions of the aforementioned silica samples in 96% ethanol aged for different time periods to water-ethanol mixtures containing 96 vol % ethanol. At a 40-vol % content of ethanol in the mixture, the coagulation whose character (including “superfast” coagulation) substantially depends on the time of aging of initial concentrated silica dispersions occurs. Furthermore, kinetic studies are performed for the coagulation of dilute silica suspensions prepared by the addition of silica powders to water-ethanol solutions containing 40 vol % of ethanol and traces (<1 ppm) of poly(ethoxysilane), poly(acrylic acid), and a supernatant prepared by the centrifugation of concentrated silica dispersion in 96% ethanol aged for more than 3 months. It is found that the addition of aliquots of the aforementioned ethanol solutions to silica suspensions in 40% ethanol, which are initially stable with respect to aggregation, causes their superfast coagulation.     

Rheology of contcentrated suspensions of slender rods

The rheology og suspensions of slender rods is discussed for various concentration regimes (i.e. dilute, semi-dilute, concentrated and liquid crystalline regimes) on the basis of the general kinetic theory of Brownian particles.     

Coupling between polymer adsorption and colloidal particle aggregation

Studies of the adsorption of high molecular weight polymers on colloidal latex and silica particles and their subsequent flocculation were carried out. Neutral polyethylene oxide samples with both a narrow and a broad molecular weight distribution were used together with low charged cationic copolymers. The influence of the particle concentration and polymer dose on the flocculation were systematically investigated under quiescent conditions.Equilibrium bridging only occurred with polyelectrolyte, even in very dilute suspensions, at high particle coverage. In contrast to this, non-equilibrium bridging occurred with both neutral polymer and polyelectrolytes but only for more concentrated suspensions and small amounts of adsorbed polymer. Polymer adsorption in dilute suspensions, which did not show particle aggregation was measured an electrophoretic technique. In more concentrated suspensions, where flocculation takes place, we found that aggregation prevents further polymer adsorption and induces both an excluded volume and a surface effect. The consequences on the shape of the isotherms differ according to the aggregation mechanism.A significant decrease of the amount, , of adsorbed polymer is observed with non-equilibrium bridging. When both mechanisms simultaneously contribute to the aggregation, the value of depends on their relative importance. In the intermediate range of copolymer dose their respective contributions are critically sensitive to the details of the mixing step and stirring, leading to non reproducible experimental results.     

Interparticle interactions in concentrated suspensions and their bulk (rheological) properties

The interparticle interactions in concentrated suspensions are described. Four main types of interactions can be distinguished: (i) "Hard-sphere" interactions whereby repulsive and attractive forces are screened. (ii) "Soft" or electrostatic interactions determined by double layer repulsion. (iii) Steric repulsion produced by interaction between adsorbed or grafted surfactant and polymer layers. (iv)and van der Waals attraction mainly due to London dispersion forces. Combination of these interaction energies results in three main energy-distance curves: (i) A DLVO type energy-distance curves produced by combination of double layer repulsion and van der Waals attraction. For a stable suspension the energy-distance curve shows a "barrier" (energy maximum) whose height must exceed 25kT (where k is the Boltzmann constant and T is the absolute temperature). (ii) An energy-distance curve characterized by a shallow attractive minimum at twice the adsorbed layer thickness 2δ and when the interparticle-distance h becomes smaller than 2δ the energy shows a sharp increase with further decrease of h and this is the origin of steric stabilization. (iii) an energy-distance curve characterized by a shallow attractive minimum, an energy maximum of the DLVO type and a sharp increase in energy with further decrease of h due to steric repulsion. This is referred to as electrosteric repulsion. The flocculation of electrostatically and sterically stabilized suspensions is briefly described. A section is devoted to charge neutralization by polyelectrolytes and bridging flocculation by polymers. A distinction could be made between "dilute", "concentrated" and "solid suspensions" in terms of the balance between the Brownian motion and interparticle interaction. The states of suspension on standing are described in terms of interaction forces and the effect of gravity. The bulk properties (rheology) of concentrated suspensions are described starting with the case of very dilute suspensions (the Einstein limit with volume fraction Φ≤0.01), moderately concentrated suspensions (0.2>Φ≥0.1) taking into account the hydrodynamic interaction and concentrated suspensions (Φ>0.2) where semi-empirical theories are available. The rheological behavior of the above four main types of interactions is described starting with "hard-sphere" systems where the relative viscosity-volume fraction relationship could be described. The rheology of electrostatically stabilized suspensions was described with particular reference to the effect of electrolyte that controls the double layer extension. The rheology of sterically stabilized systems is described using model polystyrene suspensions with grafter poly(ethylene oxide) layers. Finally the rheology of flocculated suspensions was described and a distinction could be made between weakly and strongly flocculated systems.     

On the Viscosity of Dilute Emulsions

The slow motion of a liquid droplet in a shear flow in the presence of surfactants is studied. The effects of the interfacial viscosity, Gibbs elasticity, surface diffusion and bulk diffusion of surfactants in both phases are taken into account. The analytical solution of the problem for small Reynolds and Peclet numbers gives a simple criterion for estimation of the tangential mobility of the droplet interface. By applying the standard procedure for averaging of the stress tensor flux at an arbitrary surface of the dilute emulsion, an analytical formula for the viscosity of emulsions in the presence of surfactants is derived. The result is a natural generalization of the well-known formula of Einstein for the viscosity of monodisperse dilute suspensions and of the expressions derived by Taylor and Oldroyd for the viscosity of monodisperse dilute emulsions taking into account the Marangoni effect. Copyright 2001 Academic Press.     

Diffusing-wave spectroscopy and interferometry

Diffusing-wave spectroscopy and interferometry, the extensions of dynamic light scattering to materials which exhibit a very high degree of multiple scattering, have been used to measure the early-time, short length scale motion of Brownian particles. The transition from “ballistic” to “diffusive” motion is observed. In very dilute samples, this transition is described very well by theories which explicitly account for the time-dependent hydrodynamic interaction between a Brownian particle and the surrounding fluid. For particle volume fractions exceeding a few per cent, the data deviate from the theory for dilute suspensions, but exhibit a remarkable scaling with the suspension viscosity.     

Accurate electrophoretic analyses of concentrated suspensions (electrophoresis of concentrates)

In conventional moving-boundary electrophoresis, boundary anomalies and erroneous analyses were shown to result in work with concentrated suspensions. An apparatus and a technique are described which, using auxiliary probes and an electrolyte tailored to the test suspension, allowed accurate data to be obtained even with highly concentrated suspensions. Thus, the usefulness of moving-boundary electrophoresis has been expanded, as now concentrated as well as dilute suspensions can be investigated.     

Screening of hydrodynamic interactions in Brownian rod suspensions

We present the details and results of a simulation study addressing the dynamics and rheology of rod suspensions over a wide regime of concentrations ranging from dilute to concentrated systems. Our study compares the results of two complementary simulation methods. The first method adapts a recently proposed explicit solvent simulation strategy and incorporates both hydrodynamical effects and steric interactions between the rod units. We compare the results of such a method with those obtained from a Brownian dynamics simulation approach which retains the steric interactions but neglects the effects of hydrodynamic interactions. Overall, our results in the context of the translational and rotational diffusivities are in agreement with the hydrodynamical predictions in the dilute regime and the corresponding results of the tube model and its extensions thereof in the semidilute regimes. The latter results suggest that effects of hydrodynamic interactions on the translational and rotational diffusivities are secondary relative to the steric interactions and at best lead only to a small correction to the results of the classical tube model. Our results in the context of linear viscoelasticity also broadly confirms the predictions of the tube model for the storage and loss moduli and allows us to extract for the first time the independent hydrodynamic and Brownian contributions to the zero shear viscosity. While the relative magnitudes of these contributions are consistent with the theoretical predictions, the quantitative magnitudes are quite different from the theoretical predictions. Overall, these results confirm the validity of the hydrodynamic "screening" hypothesis and ratify the neglect of hydrodynamical stresses in quantifying the linear rheology of Brownian rod suspensions.     

High-performance liquid chromatographic determination of polysorbate 80 in pharmaceutical suspensions

A quick HPLC method is reported for the analysis of polysorbate 80 in pharmaceutical suspensions. A typical pharmaceutical suspension was mixed with dilute potassium hydroxide, and heated at 40 degrees C for 6 h. This procedure resulted in quantitative hydrolysis of polysorbate 80 to release oleic acid. A quick HPLC procedure was used to analyze the hydrolyzed samples without further sample treatment. Polysorbate 80 USP, treated in the same way as the pharmaceutical suspensions, was used as standard. Full validation tests were carried out and the validation studies demonstrated that this method is suitable for accurate and reproducible analysis of polysorbate 80 in pharmaceutical suspensions.     

刚性聚合物稀溶液流变性质的计算 Ⅰ.定常流动

本文采用多棒刚杆分子模型,用Galerkin法计算了聚合物稀溶液在定常剪切流、平面拉伸流、单轴拉伸流、单轴拉伸与剪切流相组合的复杂流动的流变学性质。计算结果表明,多棒刚杆分子模型有希望成为描述聚合物稀溶液流变性质的较为完善的分子模型。本文的研究不仅可使人们用分子模型来代替连续介质本构方程进行粘弹性流体复杂流动的数值模拟,而且也为探讨描述聚合物浓溶液的分子模型提供了一种新的途径。     

Particle interactions and rheological effects in kaolinite suspensions

Particle interactions in kaolinite suspensions are modelled by representing the edge face of a kaolinite platelet as cylinder and flat plate, respectively. Computations of total energy of interaction show that at pH 6,7 and 8 and in the presence of 10^?4 ?10^?I M NaCl both face-edge and edge-edge modes of interaction are likely. Rheological parameters for flocculated suspensions (extrapolated shear stress and plastic viscosity) for dilute sodium kaolinite suspensions (volumetric concentration 0.02) are interpreted in terms of the proposed interaction models.