The convective model of cross-flow microfiltration is not inconsistent

The approximate analytical equations of the convective model and of the model of Romero and Davis are compared. Introducing the approximations used by Romero and Davis in the convective model gives the same functional dependence of the average filtration flux, 〈ν〉, on particle radius and solute volume fraction and a different dependence on the shear rate, γ_s. The convective model gives an explicit dependence of 〈ν〉 on transmembrane pressure and non-Newtonian ‘apparent’ viscosity of the cake. It is shown that the pseudoplastic rheological behaviour of concentrated colloidal solutions (cakes) rationalizes the experimentally established dependence 〈nu;〉 ∼ γ^m_s with 0.4 < m < 1.5.     

The scaling behavior of a highly aggregated colloidal suspension microstructure and its change in shear flow

The nature of the network structure and the evolution of structural change in shear flow were investigated for metal particle dispersions in terms of fractal aggregation of colloidal particles. Polymer-stabilized metal particle inks were prepared via a polyvinyl chloride coating dispersed in solvent. The fractal dimension of 1.74 was calculated with the scaling model based on the power law relationship between the elastic modulus and volume fraction. This scaling behavior can be explained by considering the deformable network structure of soft materials. While the elastic property of the floc was dominant, the limit of linearity was found at the inter-floc link, which is relatively weak and brittle. The steady shear results reveal two mechanisms that contribute to the breakdown of the microstructure in metal particle inks at increasing shear rate. Scaling of steady shear viscosity shows that these mechanisms are related to both inter-floc interactions and the elasticity of the floc itself. Further, these results suggest that individual flocs deform with weak inter-floc interactions and rupture into smaller flocs or aggregates at high shear stress, which is associated with the increased shear rate.     

Hydrodynamic forces and critical stresses in low-density aggregates under shear flow

The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.     

Measurement of rheology of distiller's grain slurries using a helical impeller viscometer

Current research is focused on developing a process to convert the cellulose and hemicellulose in distiller's grains into fermentable sugars, increasing both ethanol yield and the amount of protein in the remaining solid product. The rheologic properties of distiller's grain slurries were determined for concentrations of 21, 23, and 25%. Distiller's grain slurries are non-Newtonian, heterogeneous fluids subject to particle settling. Traditional methods of viscosity measurement, such as cone-and-plate and concentric cylinder viscometers, are not adequate for these fluids. A helical impeller viscometer was employed to measure impeller torque over a range of rotational speeds. Newtonian and non-Newtonian calibration fluids were utilized to obtain constants that relate shear stresses and shear rates to the experimental data. The Newtonian impeller constant, c, was 151; the non-Newtonian shear rate constant, k, was 10.30. Regression analysis of experimental data was utilized for comparison to power law, Herschel-Bulkley, and Casson viscosity models with regression coefficients exceeding 0.99 in all cases.     

Transient free radicals in viscous solvents

The majority of free radicals are highly reactive species which participate in bimolecular reactions with each other. Validation of the theory of molecular diffusion and reactivity in the liquid state requires knowledge of rate constants of radical–radical reactions (recombination, disproportionation) and their viscosity dependencies. An accurate comparison of theory and experiment has become available due to experimentally measured diffusion coefficients of reactive radicals by transient grating technique. Initial distribution of radicals in solution can be not random but pair-wise as in photo- or thermoinitiation of free radical polymerization reactions. Probability of a radical escape of a partner (cage escape) characterizes the initiator efficiency. Despite decades of measurement of cage effect values, cage effect dynamics with free radicals have only been investigated quite recently. The present tutorial review considers the effect of viscosity of Newtonian liquid on two types of recombination—in the solvent bulk and in a cage. Further, since radicals are paramagnetic species, external magnetic field affects probability of their reactions in pairs. These effects are also observed in viscous liquids, and reasons for such observations are explained. The recently discovered low magnetic field effect is also observed on radical pairs in viscous liquids.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

Scale invariance of viscosity and cluster structure of epoxy formulations

The concentration dependences of the relative viscosity of epoxydiane resins (M _n = 400–650) in solutions of monoglycidyl esters, Cardura and Laproxide, and of the dynamic viscosity of filled epoxy formulations in a shear flow were studied. The optimal concentrations of the formulation components and structural parameters of the fractal aggregates of oligomers and clusters of pigment (filler) particles were calculated in the approximation of the cluster lattice model.     

Nonequilibrium structure of primary particles in colloidal bidispersion

The nonequilibrium aggregation structure of primary particles in colloidal bidispersions is investigated at high volume fractions by Brownian dynamics simulations. It is found that introducing limited different sized particles in the monodispersion can obviously affect the short-range structures of primary particles. In a bidispersion, fractal dimension of aggregates, only consisting of primary particles, increases with increasing the size difference in the long-range scale. The structure factor S(q) of aggregates, obtained from the particle correlation function g(r), suggests that fractal structure disappears when the primary particles become not “primary” in volume fraction.     

高磺化度聚苯胺体系中的分形结构研究

通过透射电镜的观察研究发现磺化聚苯胺的胶体聚集体和胶粒内部结构都具有分形体的特征 ,从而将分形的概念及其数学模型引入共轭导电聚合物体系之中 .磺化聚苯胺胶体的聚集体为很不均匀的分支状开放结构 ,其形成过程可用扩散控制集团聚集模型 (DLCA)进行模拟 ,计算机模拟生成的图形及其分形维数都与实验观测结果相当吻合 .胶粒由于是在分散介质所形成的平均化场中生成 ,屏蔽效应减弱 ,是比由它组成的聚集体要致密的球形结构 ,该结构的生成可用随机雨点模型模拟且结果相近 .     

Electrokinetic diffusioosmotic flow of Ostwald-de Waele fluids near a charged flat plate in the thin double layer limit

Electrokinetic diffusioosmotic flow of Ostwald-de Waele, or power-law, fluids near a large charged flat plate is theoretically investigated for very thin double layers. Solutions to the flow velocity both up-close and far from the flat plate as well as the effective viscosity are presented for general values of the flow behavior index. Results show that given a wall zeta potential, ζ, diffusivity difference parameter, β, and constant imposed solute concentration gradient, both the near and far field diffusioosmotic flow velocities obtained for the respective dilatant and pseudoplastic liquids considerably deviate from those obtained for Newtonian liquids as found in previous literature. This likely suggests that the electrokinetic diffusioosmosis and its complementary effect of diffusiophoresis depend sensitively not only on the ζ-β parametric pair, but also on the possible non-Newtonian characteristics of the electrolytic liquid phase of the system. The theory presented herein can also be readily modified to model or describe electrodiffusioosmosis in power-law fluids, which is likely found in flow situations where the fluid non-Newtonian response, imposed solute concentration gradient, and an additional externally applied electric current density (or electric field) are of equal importance.     

Structural transformations in magnetic suspensions

Structural transformations in dispersions of micron-sized iron particles suspended in a magnetite ferrofluid (the colloidal suspension of ferromagnetic nanoparticles in nonmagnetic liquid) are theoretically considered. An attempt is made to explain the tendency of iron particles to form doublets and longer chain aggregates with finite distance between particles in external magnetic field observed in recent experiments; in colloidal ferrofluid, micron-sized iron particles approach one another to finite distance that is equal approximately to the particle diameter. At moderate magnetic fields, minimal distance between approached particles is nearly independent of the strength of magnetic field. In ordinary magnetorheological dispersions, which are suspensions of magnetizing micron-sized particles in nonmagnetic liquid, the approach of particles practically does not occur up to their physical contact.     

Transport coefficients and orientational distributions of rodlike particles with magnetic moment normal to the particle axis under circumstances of a simple shear flow

We have investigated the influences of the magnetic field strength, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This dispersion is composed of ferromagnetic spheroidal particles with a magnetic moment normal to the particle axis. In the present analysis, these spheroidal particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the rodlike particle is significantly restricted in the field direction, so that the particle points to a direction normal to the flow direction (and also to the magnetic field direction). However, the present particle does not exhibit a strong directional characteristic, which is one of the typical properties for the previous particle with a magnetic moment parallel to the particle axis. That is, the particle can rotate around the axis of the magnetic moment, although the magnetic moment nearly points to the field direction. The viscosity significantly increases with the field strength, as in the previous particle model. The particle of a larger aspect ratio leads to the larger increase in the viscosity, since such elongated particles induce larger resistance in a flow field. The diffusion coefficient under circumstances of an applied magnetic field is in reasonable agreement between theoretical and experimental results.     

ON THE MICRORHEOLOGICAL MODELING OF AGGREGATING COLLOIDS

ABSTRACT

Microrheological modeling of the aggregating colloidal dispersions in frames of the mean-field approach Is used to relate their Theological behavior to the parameters of the aggregates. Three parameters are shown to form a minimum set of values which one should know to elaborate the simplest self-consistent microrheological model of aggregating colloids. They are: the yield strength of the compact structure o, fractal dimension D and the exponent m, which characterizes the dependence of the aggregates radius R vs shear rate S (R ∝ S^?m). Analytic consideration and computer simulations are carried out to determine the exponent m for the aggregates of different type. The behavior of the aggregate depends on the character of the particles Interaction. In general the interaction force can be considered a superposition of central component (equivalent to ordinary spring) and some non-central component. If the non-central Interaction Is relevant, the aggregate internal structure is rigid (I.e. it elastically responds to small deformation), while in the case of purely central Interaction it Is soft (i.e. it Is irreversibly deformed even under the action of lnfinlteslmally small force). The system with purely central particles interaction seems to be a reasonable model for the coagulation in secondary energy minimum, while the system with non-central component represents (at lest qualitatively) the coagulation in primary minimum. The theoretical calculations of the shear viscosity of aggregating     

剪应力下弱作用势胶体颗粒聚团的特点

探讨了不同剪应力下，具有Ｌｅｎｎａｒｄ－Ｊｏｎｅｓ势的胶体颗粒聚团的结构特性，包括簇团的大小分布，径向分布函数，分形维数和原子配位数。研究表明，在弱作用力下，胶体簇团的分布随剪应力的增加而趋向小簇团一边；径向分布函数曲线随剪应力的增加而降低，胡在近程距离内降低得最多；分形维数随剪应力的增加表现为先增加后减小的趋势，其值随模拟条件的不同而在１．９－２．４之间变动。剪应力“场”对分形维数的大小没有太大     

Stability of sputter-deposited gold nanoparticles in imidazolium ionic liquids

The stability of gold nanoparticles synthesised by sputter deposition has been studied in situ in 1-butyl-3-methylimidazolium ionic liquids with bis(trifluoromethylsulfonyl)imide, tetrafluoroborate, hexafluorophosphate and dicyanamide anions with UV-VIS absorption spectroscopy and transmission electron microscopy. Besides the growth of the gold nanoparticles, two other processes were observed after sputtering, namely aggregation and sedimentation of these nanoparticles. To model the absorption spectra of the sputtered gold nanoparticles, generalized multiparticle Mie calculations were performed. These theoretical calculations confirm the increase in absorbance at longer wavelength for larger aggregates and are in agreement with the experimental observations. It was found that the kinetics of aggregation and sedimentation scale with the viscosity of the ionic liquid. Small amounts of water were found to have a large detrimental influence on the stability of the colloidal suspensions of the gold nanoparticles in ionic liquids. From the large discrepancy between the theoretical and the experimentally observed stability of the NPs, it was concluded that structural forces stabilize the gold nanoparticles. This was also borne out by AFM measurements.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

Assessment of phenomenological models for viscosity of liquids based on nonequilibrium atomistic simulations of copper

The shear viscosity of liquid copper is studied using nonequilibrium molecular-dynamics simulations under planar shear flow conditions. We examined variation of viscosity as function of shear rate at a range of pressures (ca. 0 - 40 GPa). We analyzed these results using eight different phenomenological models and find that the observed non-Newtonian behavior is best described by the Powell-Eyring (PE) model: eta(gamma) = (eta(0)-eta(infinity))sinh(-1)(taugamma)(taugamma) + eta(infinity), where gamma is the shear rate. Here eta(0) (the zero-shear-rate viscosity) extracted from the PE fit is in excellent agreement with available experimental data. The relaxation time tau from the PE fit describes the shear response to an applied stress. This provides the framework for interpreting the shear flow phenomena in complex systems, such as liquid metal and amorphous metal alloys.     

Interfacial rheology of stable and weakly aggregated two-dimensional suspensions

The interfacial rheological properties of stable and weakly aggregated two-dimensional suspensions are studied experimentally using a magnetic rod interfacial rheometer. Particle monolayers with well controlled structures were prepared. Charged polystyrene particles create two-dimensional colloidal crystals at the water-decane interface over a wide range of concentrations. Under similar conditions a predominantly liquid structure is obtained at the water-air interface for the same particles. The addition of appropriate combinations of the anionic surfactant sodiumdodecylsulfate (SDS) and sodium chloride (NaCl) to the aqueous subphase leads to a destabilization of these monolayers with the formation of fractal aggregates at low concentrations and a heterogeneous gel forming as the surface coverage is increased. After the structures have been built up a reproducible structure can be obtained, of which the interfacial rheological properties can be investigated using a magnetic rod stress rheometer. In all cases, numerical calculations were used to assess the importance of instrumental artifacts and the effect of the coupling between surface and subphase flows. The rheology of aggregated suspensions was compared to the reference case of a colloidal crystal. The two-dimensional aggregated suspensions display rheological features which are similar to their three-dimensional counterparts. These include an elastic response with small linearity limits, a power law dependence on surface coverage and a dependence on the strength of attraction. The results shed some light on the possible role of interfacial rheology on the stability of particle laden high interface systems. Additionally, the 2D suspensions could present fundamental insights in the rheological properties of dense colloidal suspensions.     

Modified graessley theory for non-newtonian viscosities of polydimethylsiloxanes and their solutions

A deviation from Graessley's theory of entanglement viscosity appears at very high shear rates when the flow of polydimethylsiloxanes of various molecular weights and their solutions with various concentrations is measured by the capillary method. In order to explain this deviation, a modified Graessley theory is proposed according to the previously reported suggestion that frictional viscosity appears not to be negligible at high shear rates. A reducing procedure taking a frictional viscosity parameter into account was performed. All of the reduced data are combined to give a master curve in spite of a wide range of molecular weight, concentration, and shear rate (from the lower Newtonian to very highest non-Newtonian flow region). The findings from the reducing procedure completely explain the mechanism of non-Newtonian flow for the bulk polymers with various molecular weights, including those below the critical molecular weight for entanglement, and for polymer solutions at any concentration. The viscosity of the linear polymer system consists of the shear-dependent entanglement term η_ent proposed by Graessley and the shear-independent frictional term η_fric. The non-Newtonian behavior depends on the ratio of η_ent/η_fric at the shear rate of measurement. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric and the critical shear rate for onset of the non-Newtonian flow may be used as a measure of the non-Newtonian behavior of the system and a measure of capability for its rising, respectively. The Graessley theory is to be included in the present modified theory and is applicable to the case of η_entη_fric ? 1.