Particles network

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

The aerosol data used in this paper were collected as part of the sampling program of the Western Fine Particle Network ( ). 

Concentrated particle suspensions may also show a yield point which must be exceeded before flow will occur. This may result from interaction between irregularly shaped particles, or the presence of water bridges at the interface between particles which effectively bind them together. Physical and chemical attractive forces between suspended particles can also promote flocculation and development of particle network structures, which can be broken down by an applied shear stress [2]. 

The durability of the particle network structure imder the action of a stress may also be time-dependent. In addition, even at stresses below the apparent yield stress, flow may also take place, although the viscosity is several orders of magnitude higher than the viscosity of the disperse medium. This so-called creeping flow is depicted in Fig. 11 where r (. is the creep viscosity. In practice this phenomenon is insignificant in the treatment of filled polymer melts, but may be relevant, for example, in consideration of cold flow of filled elastomers. 

Hermans, J. 1965. Investigation of the elastic properties of the particle network in gelled solutions of hydrocolloids. I. Carboxymethyl cellulose. J. Polym. Sci. A 3 1859-1868. 

At low ij), the cmve is linear. At high values of < >, there is a critical value, where no fiirther shrinks e takes place, corresponding to liquid just filling the pores at the leatherhard point. This critical volume fraction, <, occurs when the mechanical properties of the particle network is sufficiently rigid to resist the compressive capillary pressure. The liquid expansion of a ceramic green body, a, is defined by... 

The temperature at the surface of the sphere is determined by the evaporation rate obtained from simultaneous mass and heat transfer. Under some drying conditions, the heat transfer is the slow step, limiting evaporation, and in others the mass transfer is the slow step. The surface of the green body will continue to stay wet if the green body shrinks, expelling the solution, or sm-face tension driven flow continues to supply liquid. Shrinkage stops when the rigidity threshold of the particle network is reached. 

The following analysis of stresses assumes that the green body is purely elastic. Certainly this is not the complete picture because wet, sticlq powders or gels are not elastic but plastic, showing deformation of the particle network by the frictional movement of particles against each other. We have discussed these mecheinical properties in Sections... 

Two types of stress are important in drying. The first is the total stress, which corresponds to the force per unit area acting on both the liquid emd the particle network. When the pores are filled with liquid, the stress is spread evenly over the whole green body, because the essentially incompressible liquid distributes the stress evenly in all directions. The second t3q>e of stress is the network stress, which is the force per unit area acting only on the particle network. When we consider the warping and cracking of the particle network, the stress on the particle network is important not the total stress. 

Considerable effort has been spent to explain the effect of reinforcement of elastomers by active fillers. Apparently, several factors contribute to the property improvements for filled elastomers such as, e.g., elastomer-filler and filler-filler interactions, aggregation of filler particles, network structure composed of different types of junctions, an increase of the intrinsic chain deformation in the elastomer matrix compared with that of macroscopic strain and some others factors [39-44]. The author does not pretend to provide a comprehensive explanation of the effect of reinforcement. One way of looking at the reinforcement phenomenon is given below. An attempt is made to find qualitative relations between some mechanical properties of filled PDMS on the one hand and properties of the host matrix, i.e., chain dynamics in the adsorption layer and network structure in the elastomer phase outside the adsorption layer, on the other hand. The influence of filler-filler interactions is also of importance for the improvement of mechanical properties of silicon rubbers (especially at low deformation), but is not included in the present paper. 

The results imply that the diffusion coefficient represents the thermally activated transport of electrons through the particle network. Indeed, these and subsequent studies have been interpreted with models that involve trapping of conduction band electrons or electron hopping between trap sites [158, 159]. An unexpected feature of the diffusion constants reported by Cao et al. is that they are dependent on the incident irradiance. The photocurrent rise times display a power law dependence on light intensity with a slope of -0.7. The data could be simulated if the diffusion constant was assumed to be second order in the electron concentration, D oc n. The molecular origin of this behavior is not well understood and continues to be an active area of study [157, 159]. 

The migration of electrons within the Ti02 conduction band to the current collector involves charge carrier percolation over the mesoscopic particle network. This important process which leads to nearly quantitative eollection of injeeted electrons is at present attracting a great deal of attention [82, 96-99]. The mesoporous eleetrode is very different from a eompact semieonducting layer because... 

Disperse phase volume fraction. The viscosity of food emulsions tends to increase with increased disperse phase volume fraction (Figure 10). The viscosity increases relatively slowly, with 4> at low droplet concentrations, but increases steeply when the droplets become closely packed together. At higher droplet concentrations, the particle network formed has predominantly elastic characteristics. 

For Newtonian flnids, the viscosity does not change with the applied stress, curve (a) in Fignre 11.12. There is also the case where the viscosity decreases with increasing shear rate, and those flnids are called shear thinning (Figure 11.12, curve (b)). Sometimes the particle network can create an internal stress, as seen in curves (d) and (e). Finally, there is the case of shear thickening, where the viscosity of the fluid increases with increasing shear rate (c). ... 

To evaluate the impact of intraparticle convection it is necessary to impose a pressure gradient across the network. Such pressure gradients arise naturally in fixed-bed operation, though the pressure difference across a particle is usually only about I cm H O. By solving the Hagen-Poisenille equation across every pore in the network, the overall flow through the particle (network) is known. 

This section presents an overview of the great variety of soft particles encountered both in fundamental science and in applications. We propose a classification based on composition and architecture, distinguishing colloidal-like particles, network particles, polymer-colloid systems, and surfactant particles, as illustrated in Fig. 1 and discussed below. 

Franks, G.V. et al., Ion-specific strength of attractive particle networks, Langmuir, 15,4411, 1999. 

Yanez, J.A. etal.. Shear modulus and yield stress measurements of attractive alumina particle networks in aqueous slurries, 7. Am. Ceram. Soc., 19, 2917, 1996. 

Consequently, a particle network in which junctions can occasionally be broken will build up a pressure on the liquid, called endogenous syneresis pressure, psyn. If the liquid can indeed flow out, the Darcy equation can be used to obtain the rate of the process. We write it in the form... 

Our hypothesis that GMP is a particle network was confirmed by re-disper-sion and re-aggregation experiments. Clear differences between particles could be observed. These differences are possibly related to difference in HMWGS composition and help explain differences in G plateau values for GMP. 

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