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Advances in Colloid and Interface Science (v.113, #2-3)
Further insights into the universality of colloidal aggregation by Peter Sandkühler; Marco Lattuada; Hua Wu; Jan Sefcik; Massimo Morbidelli (pp. 65-83).
Dynamic light scattering (DLS) performed at various scattering wave vectors provides detailed information about the aggregation kinetics and the cluster mass distribution (CMD) in colloidal dispersions. Detailed modeling of the aggregation kinetics with population balance equations requires a quantitative connection between the CMD and measurable quantities such as the angle dependent hydrodynamic radii obtained by DLS. For this purpose we evaluate and compare various models for the structure factor of fractal aggregates. Additionally, we introduce a simple scattering model that accounts for the contribution of internal cluster dynamics of fractal clusters to the first cumulant of the dynamic structure factor. We show that this contribution allows to quantitatively describe previously measured experimental data [Lin M, Lindsay H, Weitz D, Ball R, Klein R, Meakin P. Universality in colloid aggregation. Nature 1989;339:360.] on the scattering wave vector dependence of the hydrodynamic radius in diffusion limited cluster–cluster aggregation (DLCA), which was shown to exhibit some kind of universality behavior (master curve). Using the same scattering model, we analyze a similar set of experimental data but in reaction limited cluster–cluster aggregation (RLCA). We find that in this case the crossover from RLCA to DLCA and gravitational settling both have a significant influence on the CMD and consequently on the scattering wave vector dependent DLS data. Only when accounting for both these effects they temporarily compensate each other and a satisfactory representation of the aggregation master curve is possible for the RLCA data at longer times. Indeed, we find that either crossover from RLCA to DLCA or gravitational settling, when present individually, causes the loss of a master curve for aggregation.
Keywords: Multiangle dynamic light scattering; Aggregation; Population balance equations; Master curves
Modelling dewatering behaviour through an understanding of solids formation processes by A.C. Dustan; B. Cohen; J.G. Petrie (pp. 85-97).
An understanding of the mechanisms which control solids formation can provide information on the characteristics of the solids which are formed. The nature of the solids formed in turn impacts on dewatering behaviour.The ‘upstream’ solids formation determines a set of suspension characteristics: solids concentration, particle size distribution, solution ionic strength and electrostatic surface potential. These characteristics together define the suspension's rheological properties. However, the complicated interdependence of these has precluded the prediction of suspension rheology from such a fundamental description of suspension characteristics. Recent shear yield stress models, applied in this study to compressive yield, significantly reduce the empiricism required for the description of compressive rheology. Suspension compressibility and permeability uniquely define the dewatering behaviour, described in terms of settling, filtration and mechanical expression. These modes of dewatering may be described in terms of the same fundamental suspension mechanics model. In this way, it is possible to link dynamically the processes of solids formation and dewatering of the resultant suspension. This, ultimately, opens the door to improved operability of these processes.In part I of this paper [1] [Dustan AC, Cohen B, Petrie JG. ‘Modelling dewatering behaviour through an understanding of solids formation processes. Part I—solids formation considerations’,doi:10.1016/j.cis.2005.01.004] we introduced an integrated system model for solids formation and dewatering. This model was demonstrated for the upstream processes using experimental data. In this current paper models of colloidal interactions and dewatering are presented and compared to experimental results from batch filtration tests. A novel approach to predicting suspension compressibility and permeability using a single test configuration is presented and tested.
Keywords: Solids formation; Colloids; Filtration; Rheology; Dewatering
Modelling dewatering behaviour through an understanding of solids formation processes. Part I—Solids formation considerations by A.C. Dustan; B. Cohen; J.G. Petrie (pp. 99-110).
An understanding of the mechanisms which control solids formation can provide information on the characteristics of the solids which are formed. These characteristics will in turn impact on dewatering behaviour. In this paper a model for solids formation is proposed.The first part of the model considers the hydrodynamics in the precipitation vessel, from which a reactant mixing model is developed. Spatially variant solution conditions are quantified (dynamically) using an equilibrium speciation model. These calculations are performed in conjunction with an adsorption model, accounting for equilibria involving adsorbed species. The kinetics of solids formation, including nucleation, growth and aggregation, are described empirically using spatially variant supersaturation profiles. These, together with moment transformations of the solids population balance, describe the evolution of particle sizes throughout the precipitation process.Precipitation of nickel hydroxide is explored experimentally, and models developed are fitted to the results. Comments are offered on the impact of simplifications required for computational reasons, and assumptions required due to lack of information, on the accuracy of the model. In part II of this paper, the use of model outputs in predicting filtration behaviour is explored.
Keywords: Precipitation; Crystallisation; Mixing; Filtration; Suspension; Population balance
Microstructure and rheology of stimuli-responsive microgel systems—effect of cross-linked density by Beng H. Tan; Kam C. Tam; Yee C. Lam; Chee B. Tan (pp. 111-120).
The effect of cross-linked density on the rheological behavior of model pH-responsive microgel systems consisting of methacrylic acid-ethyl acrylate (MAA-EA) cross-linked with di-allyl phthalate (DAP) was examined. Neutralization of acid groups increases the osmotic pressure exerted by counter-ions trapped in the polymeric network against the ions in bulk solution, which is responsible for the swelling and increase in viscosity. The viscosity exhibits a maximum at ∼1 wt.% DAP and it decreases to a steady value at 4 wt.% DAP, which is independent of pH and particle concentrations. Static light scattering results confirmed this optimum density as the critical point where sufficient cross-link points are present to produce permanent junctions that permit optimal swelling of the microgel particles. In addition, the variation of relative swelling with cross-linked densities of our model microgel systems agrees with the theoretical scaling law, Q�( yαNx)3/2 for cross-linked densities beyond this optimum point ( Q is the swelling ratio, y is the acidic MAA content, Nx is the average number of monomer units between two cross-linked points, and α is the degree of neutralization). By combining the results from light scattering and rheological measurements, we are able to correlate the microstructural evolution of the colloidal systems with their bulk rheological behavior.
Keywords: pH-responsive microgel; Optimum cross-linked density; Static light scattering; Theoretical scaling law; Swelling ratio
Surface free energy and wettability of silyl layers on silicon determined from contact angle hysteresis by Emil J. Chibowski (pp. 121-131).
Using the literature data [A.Y. Fadeev and T.J. McCarthy, Langmuir 15 (1999) 3759; A.Y. Fadeev and T.J. McCarthy, Langmuir 16 (2000) 7268] of the advancing and receding contact angles for water, diiodomethane and hexadecane measured on various hydrophobic silyl layers (mostly monolayers) produced on silicon wafers the apparent surface free energies γstot were calculated by applying new model of the contact angle hysteresis interpretation. It was found that, for the same silyl layer, the calculated γstot values to some degree depended on the probe liquid used. Therefore, thus calculated the surface free energies should be considered as apparent ones. Moreover, also the values of the dispersion component γsd of these layers depend on the probe liquid used, but to a less degree. This must be due to the strength of the force field originating from the probe liquid and the spacing between the interacting molecules. The relationships between γstot and γsd are discussed on the basis of the equations derived. It may be postulated that applying proposed model of the contact angle hysteresis and calculating the apparent total surface free energies and the dispersion contributions better insight into wetting properties of the silyled silicon surface can be achieved.
Keywords: Silyl layers; Surface free energy
Analysis of the relationship between liquid droplet size and contact angle by S. Vafaei; M.Z. Podowski (pp. 133-146).
The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace–Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.
Keywords: Droplet shape; Contact angle; Gas/liquid interfacial forces