One-component Suspensions Research Articles

On the rheology of thixotropic and rheopexic suspensions: accounting of the trimers formation

Semi-empirical equations are derived that describe the dependence of shear stress on shear rate during the flow of a one-component suspension. The suspension is considered as consisting of three fractions: single grains of the solid phase, their dimers and trimers, between which reversible dimerization and trimerization reactions occur. In this case, dimerization and trimerization are considered as reactions with invariable rate constants, and dissociation of dimers and trimers as reverse reactions with rate constants that increase linearly with shear rate. The derived equations are based on the Krieger-Doherty formula generalized to the case of a multicomponent suspension. The equations describe well pseudoplasticity, dilatancy, thixotropy and rheopexy, as well as suspensions with variable behaviour (when pseudoplastic behaviour is replaced by dilatant behaviour, and thixotropic behaviour is replaced by rheopexic one and vice versa).

Numerical Investigation of the Two-Component Suspension Filtration in a Porous Medium Taking into Account Changes in the Characteristics of the Porous Medium

The paper explores a mathematical model of the filtration of dual-component suspension within a porous medium characterized by two distinct zones. This model encompasses mass balance equations of suspended particles, kinetic equations of deposition formation for both reversible and irreversible deposition types for each suspension component, and incorporates Darcy’s law. In order to solve the problem, we formulate a numerical algorithm for computer-based experimentation on the basis of the finite difference method. Through the analysis of numerical findings, we establish key features of two component suspension filtration within a porous medium. Furthermore, we examine the effects of model parameters on the transport and deposition of suspended particles in a two-component suspension within porous media. The polydispersity of the suspension and the multi-stage nature of deposition kinetics can induce effects that differ from those typically observed in the transport of onecomponent suspensions with single-stage particle deposition kinetics.

On the Rheology of Thixotropic and Rheopexic Suspensions

Semi-empirical equations are derived that describe the dependence of shear stress on shear rate during the flow of a one-component suspension. The suspension is considered as consisting of two fractions: single grains of the solid phase and their dimers, between which a reversible dimerization reaction occurs. In this case, the dimerization of single grains is considered as a reaction with an invariable rate constant, and the dissociation of dimers is considered as an inverse reaction with a rate constant that increases linearly with the shear rate. The equations are based on the Krieger−Doherty formula, generalized to the case of a multicomponent suspension.

Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals.

Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions, including local-density approximations based on the ideal-gas, virial, and Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes, such as solvent drying, solvent freezing, and sedimentation.

Pulsatile crossflow improves microfiltration fractionation of cells and proteins

The application of pulsatile crossflow is known to mitigate fouling and enhance permeate flux during filtration of simple one-component suspensions. However, previous studies lack a systematic investigation of the effect on pulsation frequency and amplitude on permeate flux, but also on solute transmission during fractionation processes, which hinders industrial application. We used a model feed containing yeast cells as deposit forming material and bovine serum albumin as permeating solute to investigate the influence of pulsatile crossflow with a rather low frequency of 0.1–0.5 Hz on permeate flux and protein transmission in comparison to conventional steady crossflow microfiltration. We found that pulsatile crossflow microfiltration has the highest effect, when it is applied at high transmembrane pressure, high pulsation amplitude, and a frequency above 0.2 Hz. Then, besides enhancing the permeate flux up to 25% (from approximately 200 to 250 L m−2 h−1), pulsatile crossflow is able to double the protein transmission (from approximately 30 to 60%), which has a strong beneficial effect on fractionation efficiency. Further to that, this work contributes to enhance the implementation of pulsatile crossflow filtration by suggesting an easy to implement and scalable pulsatile filtration plant as well as suitable process conditions.

Effect of prenucleation clusters arising from liquid-liquid phase transition on nucleation in a one-component charged colloidal suspension

It is generally thought that liquid-liquid phase transition (LLPT) in a one-component suspension never or only very rarely happens. If this were true, it would contradict the two nonclassical nucleation models building on either liquid droplets or prenucleation clusters (PNCs). One way out of this paradox is to suppose that LLPT occurs in pathway to nucleation. This study specifies the physical parameters of charged colloids which can bring out LLPT according to the consistent prediction of the DLVO (Derjaguin-Landau-Verwey-Overbeek) potential and the Sogami potential about long-range attraction, and reveals that surface charge is not the only factor to affect attraction, size also plays an essential role. For the first time, we follow exactly the evolution from LLPT to nucleation in which PNCs participate, and characterize pre-ordered liquid-like property of the PNCs and their particle-like and template effect by optical microscopy and light scattering. Furthermore, it is found that when the configuration of the PNCs is changed by a little salt, the pathway to nucleation is altered significantly. Our results demystify LLPT in a one-component suspension and dissolve the paradox, thus extending the range of applicability of the nonclassical nucleation models.

A Deep Bed Filtration Model of Two-Component Suspension in Dual-Zone Porous Medium

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy’s law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone.

Electrophoretic deposition of hydroxyapatite fiber reinforced hydroxyapatite matrix nanocomposite coatings

Two-component suspensions of hydroxyapatite nanoparticles with spherical (S-HA) and fiber (F-HA) morphologies were prepared in isopropanol using triethanolamine (TEA) as the dispersant. In-situ kinetics of deposition and current density were recorded during EPD at 60V from suspensions with different wt% of F-HA and TEA. f factor decreased against TEA concentration in all suspensions except the one-component suspension of F-HA particles. The detachment of particles from single component F-HA deposits did not occur during EPD due to the mechanical interlocking of F-HA particles in their microstructure. F-HA particles reinforced the coatings and prevented from their cracking during drying by bridging mechanism. S-HA particles infiltrated and filled the pores formed by stacking of the F-HA particles in deposit. S-HA particles were also grafted to F-HA particles in TEA-containing suspensions via hydrogen bonding between TEA molecules adsorbed on the particles. The coating deposited from the suspension with 75wt% of F-HA particles had the best corrosion resistance in SBF solution at 37.5°C.

Effective electrostatic interactions in suspensions of polyelectrolyte brush-coated colloids

Effective electrostatic interactions between colloidal particles, coated with polyelectrolyte brushes and suspended in an electrolyte solvent, are described via linear-response theory. The inner cores of the macroions are modeled as hard spheres, the outer brushes as spherical shells of continuously distributed charge, the microions (counterions and salt ions) as point charges, and the solvent as a dielectric continuum. The multicomponent mixture of macroions and microions is formally mapped onto an equivalent one-component suspension by integrating out from the partition function the microion degrees of freedom. Applying second-order perturbation theory and a random-phase approximation, analytical expressions are derived for the effective pair interaction and a one-body volume energy, which is a natural by-product of the one-component reduction. The combination of an inner core and an outer shell, respectively impenetrable and penetrable to microions, allows the interactions between macroions to be tuned by varying the core diameter and brush thickness. In the limiting cases of vanishing core diameter and vanishing shell thickness, the interactions reduce to those derived previously for star polyelectrolytes and charged colloids, respectively.

Motions in binary mixtures of hard colloidal spheres: melting of the glass.

Dynamic light-scattering experiments are performed on binary mixtures of hard-sphere-like colloidal suspensions with a size ratio of 0.6. The optical properties of the particles are such that the relative contrast of the two species is very sensitive to temperature, a feature that is exploited to obtain the three partial coherent intermediate scattering functions. The glass transition is identified by the onset of structural arrest, or arrest of the alpha process, on the time scale of the experiment. This is observed in a one-component suspension at a packing fraction of 0.575. The intermediate scattering functions measured on the mixtures quantify how, on introduction of the smaller spheres, the alpha process is released, i.e., how the glass melts. Increasing the fraction of smaller particles causes the alpha process to speed up but, at a given wave vector, also incurs a change to its amplitude in proportion to the change in the (partial) structure factor.

Phase behaviour and structure of colloidal suspensions

We describe three sets of experiments on suspensions of 'hard-sphere' colloids. Suspensions of equal-sized particles exhibit the hard-sphere freezing and glass transitions. Mixtures of spheres of two different sizes can form the ordered binary crystals AB2 and AB13. The addition of non-adsorbing polymer to a one-component suspension leads, through the depletion mechanism, to a range of phase behaviour, which includes colloidal gas, liquid, crystal and gel.

On the theory of light absorption in non-homogeneous objects

The semicontinuous cubic particle model for the sieve-effect in one-component suspensions is considered. Exact and approximate expressions for the most probable and average distributions of elementary homogeneous areas with respect to the number of particles are obtained. The conditions of validity of each expression are shown and the errors of approximation are estimated. The correlation between the absorbances of a suspension and the corresponding solution as a function of the parameters of suspension (absorptivity of the substance and number and size of particles) is obtained.

Study of the filtrational separation of suspensions in porous media through sorption dynamics theory 2. Relation of the shilov equation constants to the physicochemical conditions of filtration

1. Analysis of the separation of low-concentration one-component suspensions has led to a general, dimensionless relation between the complex of constants in the Shilov equation, the bed geometry, and the filtration regime. 2. The exact form of this relation has been established from data on the separation of natural and artificial suspensions on beds of pulverized cermet, quartz sand, and calcined rock.

Study of the filtrational separation of suspensions in porous media through sorption dynamics theory. 1. Parallel concentration front transfer in homogeneous suspensions

1. A self-similar regime can be established in the stationary front resulting from the sedimentation of a low-concentration one-component suspension in a uniform isotropic bed with formation of two sediment phase types: an elutable phase (with linear isotherm) and an unelutable phase (with a retangular isotherm). 2. The self-similar regime involves a co-phased displacement of the concentration and deposition fronts in the bed, with a linear increase in the pressure drop on the filter.