Scaling densities

Density Gauges These are used to measure the density or suspended solids content of the feed and underflow streams. Gamma radiation devices are the most commonly used for automatic control, but ultrasonic devices are effective in the lower range of slurry density. Marcy pulp density scales are an effective manually operated device. A solids mass flow indication is usually obtained by combining a density gauge output with the output from a flowmeter. 

Method Product size (mm) Granule density Scale of operation Additional comments Tyj)ical applications... 

Figure 5-17. Power consumption by impeller type/dimensions for turbulent flow conditions. Knowing impeller type, diameter, speed and batch density connect RPM with diameter. The Intersection with A, connected to the density scale, makes an intersection on B. A line from this point to the impeller scale intersects the horsepower scale at the correct value. By permission, Quillen, C. S., Chem. Engr., June 1954, p. 177 [15].

This is an indication of the collective nature of the effect. Although collisions between hard spheres are instantaneous the model itself is not binary. Very careful analysis of the free-path distribution has been undertaken in an excellent old work [74], It showed quite definite although small deviations from Poissonian statistics not only in solids, but also in a liquid hard-sphere system. The mean free-path X is used as a scaling length to make a dimensionless free-path distribution, Xp, as a function of a free-path length r/X. In the zero-density limit this is an ideal exponential function (Ap)o- In a one-dimensional system this is an exact result, i.e., Xp/(Xp)0 = 1 at any density. In two dimensions the dense-fluid scaled free-path distributions agree quite well with each other, but not so well with the zero-density scaled distribution, which is represented by a horizontal line (Fig. 1.21(a)). The maximum deviation is about... 

FIG. 16. Time-averaged densities of (a) charged and (b) neutral species for the discharge settings given in Table IV. Note the difference in density scales. (Compiled from G. J. Nienhuis. Ph.D. Thesis. Universiteit Utrecht, Utrecht, the Netherlands. 1998.)... 

Fig. 36 Three-dimensional map of the local bond orientational order. The bond order is expressed by the density-scale given in the legend to the right... 

Valleau, J. P. The Coulombic phase transition density-scaling Monte Carlo. J. Chem. Phys. 1991, 95, 584-589... 

Valleau, J. P. Temperature-and-density-scaling Monte-Carlo methodology and the canonical thermodynamics of Lennard-Jonesium. Mol. Sim. 2005, 31, 223-253... 

FIGURE 6 Morphological evaluation of MSCs. CFU-F of MSCHPL compared to MSf I BS differ in size, morphology, and density (scale bar identifies magnification in the upper panel colony photographs taken on day 12, 40x original magnification). 

One pA cm is very much in the useful electrochemical range and then a given site, within present assumptions, would only have to be active every 0.6 s. At the other end of the usual current density scale, 1 A cm, the number would be up to 6 x 10 s1. These are simple concepts. 

A further consequence of intermediate-range interactions adding up are very high almost isotropic repulsive barriers around compact clusters. This has consequences for the density scaling [32] and favors small islands with more narrow distributions of sizes and spacings than the ones obtained without interactions [29]. We finally note that atomic superlattices with smaller lattice constant may be stabilized by dipolar interactions of relatively short range. The most prominent examples for such interactions are alkali metals on metal surfaces. A phase transition from a dilute liquid into a well-ordered solid has been reported for Cs/Ag/Si(lll)-( /3 x %/3) [33]. 

For the high-density scaling limit of KFEc[n], Gorling and Levy [11], using their adiabatic perturbation theory, arrived at... 

In the PIC simulations no surface fast electrons are observed when a preplasma is added in front of the sharp-boundary plasma slab. This agrees with experimental measurements for the larger density scale case. 

The Brix scale is a density scale for sugar (sucrose) solutions. The degrees Brix are numerically equal to the percentage of sucrose in solution (wt/wt).The term Brix solids refers to the solids in solution as determined by a refractometer. 

---