Dispersion size distribution

The CCA-model considers the filler network as a result of kinetically cluster-cluster-aggregation, where the size of the fractal network heterogeneity is given by a space-filling condition for the filler clusters [60,63,64,92]. We will summarize the basic assumptions of this approach and extend it by adding additional considerations as well as experimental results. Thereby, we will apply the CCA-model to rubber composites filled with carbon black as well as polymeric filler particles (microgels) of spherical shape and almost mono-disperse size distribution that allow for a better understanding of the mechanisms of rubber reinforcement. 

The present work deals with sintering of Ni/AbOa catalysts under reducing and steamreforming reaction conditions. The effects of preparation method (impregnation and coprecipitation), lanthanum oxide promoter, oxide phases developed after calcination, sintering temperature and atmosphere were studied in terms of the time evolution of metal dispersion, size distribution properties and kinetic parameters obtained from a GPLE model. 

Finally, recent investigations on mild UV-laser surface treatment of PEDOT layers [208,209] have shown that the surface chemical state of the polymer can become modified without any appreciable effect on the CP bulk properties. It was found [208] that UV-laser treatment results in activation of the surface with respect to metal nucleation and an increase in the number of dqjosited crystals by preserving a mono-disperse size distribution (Figure 7.7 c and d). 

The mean diameter dp is resolved in all runs with dpjl x = 6 grid cells. In case of the poly-disperse size distribution, dp varies with 30 %, having a constant probability. 

Fig. 6 Snapshots of the fluid velocity field (see colour scale) and particle cluster distribution with the poly-disperse size distribution at Rep = 1.0 and St = lA (Case R-P) at various instants of time fi m top to bottom tlhoi = 0.0 (a), 0.2 (b), 0.4 (c), 0.6 (d), 0.8 (e) and 1.0 (f). Spheres of the same colour have formed an agglomerate. Cut through the centre of the three-dimensional domain...

Fig. 7 Temporal development of a the total number of particles Np considering primary particles as well as agglomerates and b the total number of primary particles included in agglomerates with the particle Stokes number St as a parameter taking into account both mono- and poly-disperse size distributions (Table 1 Cases R and D)...

Fig. XVII-31. (a) Nitrogen adsorption isotherms expressed as /-plots for various samples of a-FeOOH dispersed on carbon fibers, (h) Micropore size distributions as obtained by the MP method. [Reprinted with permission from K. Kaneko, Langmuir, 3, 357 (1987) (Ref. 231.) Copyright 1987, American Chemical Society.]...

Clarke,. 1. and Freakley, P.K., 1995. Modes of dispersive mixing and filler agglomerate size distributions in rubber compounds, Plast. Rubber Compos. Process. Appl. 24, 261-266. 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

Fig. 7. The effect of preparation on the pore size distribution (a), titanium dispersion (b), and the activity for epoxidation of cyclohexene (c) of titania—siUca containing 10 wt % titania and calcined in air at 673 K. Sample A, low-temperature aerogel Sample B, high-temperature aerogel Sample C, aerogel.

Drop dispersions are hardly ever uniform, and size distribution must be allowed for in calculating a. This can be done by means of the Sauter mean drop diameter, based on the average volume-to-area ratio for N drops. 

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Fig. 3. Sedigraph particle size distribution for superground submicrometer alumina, (a) Partially dispersed (b) fully dispersed.

A wide variety of particle size measurement methods have evolved to meet the almost endless variabiUty of iadustrial needs. For iastance, distinct technologies are requited if in situ analysis is requited, as opposed to sampling and performing the measurement at a later time and/or in a different location. In certain cases, it is necessary to perform the measurement in real time, such as in an on-line appHcation when size information is used for process control (qv), and in other cases, analysis following the completion of the finished product is satisfactory. Some methods rapidly count and measure particles individually other methods measure numerous particles simultaneously. Some methods have been developed or adapted to measure the size distribution of dry or airborne particles, or particles dispersed inhquids. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

Suspension Polymerization. At very low levels of stabilizer, eg, 0.1 wt %, the polymer does not form a creamy dispersion that stays indefinitely suspended in the aqueous phase but forms small beads that setde and may be easily separated by filtration (qv) (69). This suspension or pearl polymerization process has been used to prepare polymers for adhesive and coating appHcations and for conversion to poly(vinyl alcohol). Products in bead form are available from several commercial suppHers of PVAc resins. Suspension polymerizations are carried out with monomer-soluble initiators predominantly, with low levels of stabilizers. Suspension copolymerization processes for the production of vinyl acetate—ethylene bead products have been described and the properties of the copolymers determined (70). Continuous tubular polymerization of vinyl acetate in suspension (71,72) yields stable dispersions of beads with narrow particle size distributions at high yields. 

Testing. Various test methods are provided by ASTM (16). These iaclude pigment tests of importance such as chemical analysis, presence of oversize particles, oil absorption, particle size distribution, degree of dispersion, presence of soluble components, etc. Numerous tests are also given by ASTM for the properties of filled and unfilled polymers. These iaclude, for example, such properties as impact resistance, stiffness, viscosity, tear resistance, hardness, color, and electrical resistivity. 

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