Suspension concentration, empirical

Empirical multiple linear regression models were developed to describe the foam capacity and stability data of Figures 2 and 4 as a function of pH and suspension concentration (Tables III and IV). These statistical analyses and foaming procedures were modeled after data published earlier (23, 24, 29, 30, 31). The multiple values of 0.9601 and 0.9563 for foam capacity and stability, respectively, were very high, indicating that approximately 96% of the variability contributing to both of these functional properties of foam was accounted for by the seven variables used in the equation. 

Table III. Empirical multiple linear regression model describing foaming capacity as a function of pH and suspension concentration.

The two steps in the removal of a particle from the Hquid phase by the filter medium are the transport of the suspended particle to the surface of the medium and interaction with the surface to form a bond strong enough to withstand the hydraulic stresses imposed on it by the passage of water over the surface. The transport step is influenced by such physical factors as concentration of the suspension, medium particle size, medium particle-size distribution, temperature, flow rate, and flow time. These parameters have been considered in various empirical relationships that help predict filter performance based on physical factors only (8,9). Attention has also been placed on the interaction between the particles and the filter surface. The mechanisms postulated are based on adsorption (qv) or specific chemical interactions (10). 

The construction of calibration curves is recommended in nephelometric and turbidimetric determinations, since the relationship between the optical properties of the suspension and the concentration of the disperse phase is, at best, semi-empirical. If the cloudiness or turbidity is to be reproducible, the utmost care must be taken in its preparation. The precipitate must be very fine, so as not to settle rapidly. The intensity of the scattered light depends upon the number and the size of the particles in suspension, and provided that the average size of particles is fairly reproducible, analytical applications are possible. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

A number of empirical equations have been obtained for the rate of sedimentation of suspensions, as a result of tests carried out in vertical tubes. For a given solid and liquid, the main factors which affect the process are the height of the suspension, the diameter of the containing vessel, and the volumetric concentration. An attempt at co-ordinating the results obtained under a variety of conditions has been made by Wallis 8 . ... 

An empirical rule summarizing the general tendency of the critical coagulation concentration (CCC) of a suspension, an emulsion, or other dispersion, to vary inversely with about the sixth power of the counter-ion charge number of added electrolyte. Also termed the sixth-power law . 

Cell models constitute a second major class of empirical developments. Among these, only two will be mentioned here as constituting the most successful and widely used. The first, due to Happel (1957,1958), is useful for estimating the effective viscosity and settling velocity of suspensions. Here, the suspension is envisioned as being composed of fictitious identical cells, each containing a single spherical particle of radius a surrounded by a concentric spherical envelope of fluid. The radius b of the cell is chosen to reproduce the suspension s volume fraction

[Pg.21]

Equation 2 represents a type of additive equation — sometimes described as a special-cubic equation — that has been widely used to correlate properties of mixtures. In Equation 2, Y represents the value of the response variable XI, X2, and X3 the concentrations of the variable components and k is a constant term. In this study, fitting the experimental data by regression analysis to a modification of Equation 2 provides an empirical equation that satisfactorily correlates suspensibility with concentrations of clay, dispersant, and surfactant. The reason for modifying Equation 2, by reducing the number terms in the polynomial, is discussed in the next section. 

In general, these formulas hold well for < 0.10, while empirical models using higher-order polynomials in can be used to fit almost any viscosity data. An equation that is often used for emulsions and concentrated suspensions of rigid spheres is that by Krieger and Dougherty ... 

In addition to blending with SPMI copolymers, PMI can be incorporated into ABS using mass, emulsion [46-50] or suspension [42] free radical polymerization techniques. The high heat ABS resin can be completely produced by mass polymerization, or mass polymerized PMI-SAN can be blended with (emulsion polymerized) SAN-grafted rubber concentrates and/or conventional mass ABS. Sumitomo Naugatuck determined an empirical relation for the compatibility of SAN/SAN-PMI blends based on the polar monomers in each component [51]. Figure 15.4 shows that the miscibility window with SANs becomes wider with increasing PMI level in the terpolymer [52]. 

Empirical methods such as neural networking can be used in place of optical methods to estimate the size distribution of concentrated suspensions. The method determines particle size distribution and... 

Most food particles are not spherical in shape so that the empirical equation (Equation 2.25) that described well (Kitano et al., 1981 Metzner, 1985) the relative viscosity versus concentration behavior of suspensions of spheres and fibers... 

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