Dispersed medium model

The floe rupture model may also be used to explain the maximum observed in versus temperature (figure 5). According to equation (4) Tg = f (< > H) Eg, where f(2H) is the collision frequency term. Although Eg increases with increase of temperature, f(< > H) is a decreasing function of temperature as a result of decrease of solvency of the dispersing medium which leads to the contraction of the adsorbed layer (13). The increase of Eg with increase of temperature initially outweighs any reduction of f (< > H), but at higher temperatures, the reduction in f (4> j ) as a result of chain contraction may exceed the increase in Eg and this results in reduction in the measured Tg. 

In the elastic floe model, the structural units (which persist at high shear rates) are assumed to be small floes of particles (called floccules) which are characterized by the extent to which the particle structure is able to trap some of the dispersion medium. The degree to which liquid is trapped in the floe is measured by the floe volume ratio, CFF, given by,... 

The work was planned on the basis of a model of a dispersed solid particle onto which one type of sequences of a BG copolymer is adsorbed selectively while the other type sequence is dissolved in the dispersion medium. A sketch of this model is shown in Figure 1. The model is the result of applying the same arguments which had been advanced (12) in discussing the mechanism of stabilization of polymeric oil-in-oil emulsions by BG copolymers to the problem of stabilization of dispersions of solid particles in organic media. Previously, essentially the same arguments had led to the demonstration of micelle formation of styrene-butadiene block copolymers in organic media under certain conditions (15). 

Historically, ideas of casein micelle structure and stability have evolved in tandem. In the earlier literature, discussions of micellar stability drew on the classical ideas of the stability of hydrophobic colloids. More recently, the hairy micelle model has focused attention more on the hydrophilic nature of the micelle and steric stabilization mechanisms. According to the hairy micelle model, the C-terminal macropeptides of some of the K-casein project from the surface of the micelle to form a hydrophilic and negatively charged diffuse outer layer, which causes the micelles to repel one another on close approach. Aggregation of micelles can only occur when the hairs are removed enzymatically, e.g., by chymosin (EC 3.4.23.4) in the renneting of milk, or when the micelle structure is so disrupted that the hairy layer is destroyed, e.g., by heating or acidification, or when the dispersion medium becomes a poor solvent for the hairs, e.g., by addition of ethanol. 

In most cases, the propagation equations discussed in this chapter do not require a specific form of material response. However, for the sake of concreteness, as well as for discussion of numerical methods, we want to describe a generic model of nonlinear material response. We consider a nonmagnetic, dispersive medium with relative permittivity e that is a function of the transverse coordinates x, y and of the angular frequency u>... 

In order to put the standard SC generation scenario to a test, we compare the water SC generation simulations with analogous simulations performed using an artificial medium which is the same as the original but with a modified linear dispersion. The later is constructed such that the artificial medium exhibits self-focusing and plasma dynamics that are almost identical to those of the real medium model. 

The structure of the disperse system (the gas phase content and its distribution) exerts considerable influence on thermal conductivity. A large number of models are proposed to clarify the effect of the structure of the disperse system on thermal conductivity. Among them one of Russell s models [87] corresponds most fully to the foam structure (the pores are isometric gas cubes, uniformly distributed in the disperse medium). According to this model the thermal conductivity is... 

Two models are available for interpreting attenuation spectra as a PSD in suspensions with chemically distinct, dispersed phases using the extended coupled phase theory.68 Both models assume that the attenuation spectrum of a mixture is composed of a superposition of component spectra. In the multiphase model, the PSD is represented as the sum of two log-normal distributions with the same standard deviation, that is, a bimodal distribution. The appearance of multiple solutions is avoided by setting a common standard deviation to the mean size of each distribution. This may be a poor assumption for the PSD (see section 11.3.2). The effective medium model assumes that only one target phase of a multidisperse system needs to be determined, while all other phases contribute to a homogeneous system, the so-called effective medium. Although not complicated by the possibility of multiple solutions, this model requires additional measurements to determine the density, viscosity, and acoustic attenuation of the effective medium. The attenuation spectrum of the effective medium is modeled via a polynomial fit, while the target phase is assumed to have a log-normal PSD.68 This model allows the PSD for mixtures of more than two phases to be determined. 

In the vicinity of the interface the values of p,0 change for different ions from values corresponding to the bulk of one phase to those corresponding to the bulk of another phase. This results in ion distributions in which the cp(x) function becomes a lot more complicated than the one described by the Helmholtz model. One usually identifies the potential of the surface of the solid phase with respect to the dispersion medium, cp0, which is not an experimentally assessable quantity. If in a solid there are no excessively accumulated charges of one sign present near the surface, the potential cp0 represents the potential difference between phases in contact. Similar to the... 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

Foam is a disperse system in which the dispersed phase is a gas (most commonly air) and the dispersion medium is a liquid (for aqueous foams, it is water). Foam structure and foam properties have been a subject of a number of comprehensive reviews [6, 17, 18]. From the viewpoint of practical applications, aqueous foams can be, provisionally, divided into two big classes dynamic (bubble) foams which are stable only when gas is constantly being dispersed in the liquid 2) medium and high-expansion foams capable of maintaining the volume during several hours or even days. In general, the basic surface science rules are established in foam models foam films, monodisperse foams in which the dispersed phase is in the form of spheres (bubble foams) or polyhedral (high-expansion foams). Meanwhile, real foams are considerably different from these models. First of all, the main foam structure parameters (dispersity, expansion, foam film thickness, pressure in the Plateau-Gibbs boarders) depend... 

Mackor (1951) was perhaps the first to endeavour to calculate the free energy of repulsion between sterically stabilized particles. This work was instigated after van der Waarden (1950 1951) had shown experimentally that aromatic molecules with long-chain aliphatic substituents could have a profound effect on the stability of carbon black particles dispersed in a paraffin (see Section 2.4.2). For this reason, Mackor adopted a model in which he assumed that the aromatic nuclei were adsorbed onto the carbon black particles in a flat configuration, thus anchoring the alkyl chains to the surface. These chains were assumed to project into the dispersion medium and were modelled as rigid rods, of length L, flexibly attached to the particle surfaces by ball joints. 

The constant segment density model is, of course, only an approximation at best. It would be expected that in general the segment density would be a function of the distance from the surface of the particle. The precise form adopted by the segment density distribution function should depend upon the steric layer properties. These properties will be determined by such factors as the chemical nature of the surface and the polymer, the quality of the solvency of the dispersion medium, the surface coverage, and the mechanism of attachment of the polymer chains to the surface. Some of these expectations have been confirmed by the recent experimental determinations of the segment density distribution functions for several different systems. 

The first attempts to investigate the consequences of the addition of free polymer to model colloidal systems were undertaken by Sieglaff (1959). He studied microgel particles composed of polystyrene cross-linked by 0-3% divinylbenzene dispersed in toluene. Free polystyrene of weight average molecular weight 5 x 10 or 2 x 10 was dissolved into the dispersion medium. 

The understanding of factors that lead to enhanced band intensities and dispersive band shapes is of central interest in studies with nanostructured electrodes. Effective medium theory has often been employed to identify mechanisms for enhanced infrared absorption [28, 128, 172, 174, 175]. Osawa and coworkers applied Maxwell-Garnett and Bruggeman effective medium models in early SEIRAS work [28, 128]. Recently, Ross and Aroca overviewed effective medium theory and discussed the advantages and disadvantages of different models for predicting characteristics of SEIRAS spectra [174]. When infrared measurements on nanostructured electrodes are performed by ATR sampling, as is typically the case in SEIRAS experiments, band intensity enhancements occur, but the band shapes are usually not obviously distorted. In contrast, external... 

The peak maximum temperatures of the blown bitumens are not so uniform and therefore the calculation of means is not worth while. Some of the blown bitumens, their dispersion medium and their petroleum resins demonstrate peak maxima both in the distillation and in the pyrolysis range because of the content of low boiling flux oils. The activation energies computed for the distillation range are equal to the enthalpies of vaporization, as shown by experiments on model substances. 

It may be seen from Fig. 4-163 and 4-164 that the pyrolysis behavior of the vacuum residue is governed fundamentally by its oil component (dispersion medium). The steadiness of the functions E = f(F) and log A = f(P) permits extrapolation towards higher pressures. These plots show that neither n-hexacontane nor n-hexylpyrene are suitable as model substances for simulation of the pressure dependence of the pyrolysis behavior of heavy components of petroleum. 

Among various isotherms, Langmuir and Freundlich are foimd to be the two most popular models. It is important to point out that the above isotherms are often applied to the adsorptions case by case. One model may be suitable for particular adsorbent-adsorbate-dispersion medium system whereas deviates for other systems. However, by plotting the suitable terms to obtain linear lines, the regression constants can be obtained such that the higher regression constant for particular model indicates its more suitability toward the concerned system. 

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