Concentration dispersion

Diflfiisive processes nonnally operate in chemical systems so as to disperse concentration gradients. In a paper in 1952, the mathematician Alan Turing produced a remarkable prediction [37] that if selective diffiision were coupled with chemical feedback, the opposite situation may arise, with a spontaneous development of sustained spatial distributions of species concentrations from initially unifonn systems. Turmg s paper was set in the context of the development of fonn (morphogenesis) in embryos, and has been adopted in some studies of animal coat markings. With the subsequent theoretical work at Brussels [1], it became clear that oscillatory chemical systems should provide a fertile ground for the search for experimental examples of these Turing patterns. 

Lignosulphonate cationic salt Conductance (m.mhos) at 5% dispersant concentration Print paste viscosity (cps) at 25 °C... 

The first two columns of Table I are taken from Ref. 4, p° was calculated from Equation 2, A from Equation 4 and C from Equation 14, using Equation 12 for g(A/a). In each series, C turns out to be approximately constant, and for the 1% dispersions does not deviate by more than a few per cent from the average value. This is gratifying since y° varies over 3 decades and r by a factor of 15. Only for the 5% dispersion does there seem to be a slight, but systematic downward trend in the values for C. This decrease is probably related to the assumption that Ass is independent of the presence of the polymer. If such a dependency does exist, the effects would show up more strongly for lower values of -Ass, i.e., for higher dispersion concentrations. 

Figure 12. Comparison of the dispersant concentration and dependence of the stability ratio W the conductivity of carbon black dispersions in dodecane. Reproduced with permission from Ref. (16). Copyright 1983, Elsevier Science Publishers.

Formulations Granular oil-dispersible concentrate wettable powder... 

Spatial dispersion concentrated, host-market, specialized, vertical in-tegration... 

The first PCC has a particle size of 70% < 2 microns. The slurry was prepared at 75% solids, and the dispersant concentration was 0.80% (as polymer solids/dry CaC03). 

Many plastic materials are colonred nsing pre-dispersed concentrates of the colonr in the same polymer or a compatible resin these are known as masterbatches. Masterbatches overcome the problems of dispersing the conventional solid pigments into the polymer matrix. 

One of the principal factors to be considered is the concentration of pigment m the dispersion concentrate. Compatibility of the carrier (solvent additives, etc) used in the preparation of concentrated dispersion and that used in the finished color product also plays an important role. In some cases this can be difficult because the earners having the best performance, from the standpoint of processing, could be poor in the application systems. However, in the majority of the applications, particularly in coatings and colored plastics, the concentration of the pigment in the finished product is quite low. and the incompatibility problem is easily overcome. 

An engineering breakthrough is required for the final step—recovery of hydrates in dispersed concentration (usually around 3.5 vol% in 30% porosity) in the deep ocean (>500 m water depth), which may prove problematic. 

Fig. 16 Temperature dependence of average hydrodynamic radius (< Rh)) and average radius of gyration Pg of PNIPAM microgels grafted with linear PEO chains in the heating-and-cooling cycle, where the dispersion concentration is 1.0 x 10 5 g/mL [70]...

Chemical parameters What is meant by chemical parameters in oil formulation Which of the following is a chemical parameter adsorption, detergent, dispersant, concentration, ZDDP, or surface roughness ... 

The lower rejection ratio of 16 was accompanied by high selectivity in pyritic sulfur dispersion. This was due to the higher (10 mg/l) flocculant concentration which resulted in higher coal yield (93.1 wt) in the flocculated fraction. On the other extreme, when higher dispersant concentration (500 mg/l) was used with lower flocculant concentration (2 mg/l), much less coal was flocculated (77 wt) and more sulfur was apparently rejected (39 ). The intermediate conditions of 300 mg/l PAAX dispersant and 2 mg/l flocculant produced correspondingly intermediate results. 

The effect of heat on the polysaccharide-water interaction in several dispersions and suspensions was studied by comparative viscometry and rheometry (Tables I-IV). The polysaccharides were the purest manufacturers grade laboratory washed and dried before dispersion. The dispersion concentrations were below c to accommodate capillary viscometry, and the suspension concentrations were above c to accommodate rheometry. It is seen in Tables I and II that the cellulose derivatives made the most stable dispersions and the propylene glycol alginate made the least. Dispersions of the neutral polysaccharides were more stable than those of the ionic polysaccharides. From Tables III and IV, it can be argued that suspensions benefit... 

A rheometer measures higher dispersion concentrations than a viscometer and, unlike the latter, can also measure suspensions. 

All the above formulas are one-parameter equations, i.e. they relate the dispersion viscosity only to the volume fraction of particles contained in it. This limits the range of applicability of the equations to not very high dispersion concentrations. To take account of the influence of the structure of concentrated dispersions on their rheological behavior, Robinson [12] suggested that the viscosity of dispersions is not only propertional to the volume fraction of solid phase, but is also inversely proportional to the fraction of voids in it. (At about the same time Mooney [40], who proceeded from a hydrodynamic model, arrived, using theoretical methods, at the same conclusion). Robinson s equation contains the relative sedimentation volume value — S, which depends on the particle size distribution of the dispersion... 

The theoretical equations relating relative fluidity (l/qrci) to dispersion concentration also became widely known. Among them is Brinkman s equation [31], valid for dispersions of particles with a wide particle size distribution ... 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

Expression (61) is claimed to holdover the whole range of dispersion concentrations from diluted systems to the solidification point. 

Fungi clearly play significant direct and indirect roles in effecting and modulating transport of a wide range of elements in soil systems. The principal transport modes that they are implicated in can be summarized as dispersion, concentration, inter-organism and bulk transfer (Fig. 3.5). 

The incorporation of insouluble, powdered solids into liquid media is generic to the chemical coatings, printing ink and pigment dispersions and likewise to the preparation of dispersion concentrates of pesticides. 

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