Average size

The mean square end-to-end distance of the Gaussian chain follows from equation (2) as 

Another quantity which measures the size of the chain is the mean square radius of gyration, R, defined by  

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Frozen fish fingers and similar products are made from a mixture of different fish that arrive at the processing plant as frozen blocks of the average size 62.7 x 254 x 482 mm (thick x width x length). The frozen blocks are minced and the still frozen minced fish blocks are mixed and pressed into the desired shape, covered with batter and bread crumbs, baked on the outside (still with a frozen core), packed and stored in a deep freezer. 

Figure C2.17.9. Size-dependent changes in PXRD linewidtlis. PXRD can be used to evaluate tire average size of a sample. In tliese cases, different samples of nanocrystalline titania were analysed for tlieir grain size using tire Debye-Scherr fonnula. As tire domain size increases, tire widtlis of tire diffraction peaks decrease.

Another important class of titanates that can be produced by hydrothermal synthesis processes are those in the lead zirconate—lead titanate (PZT) family. These piezoelectric materials are widely used in manufacture of ultrasonic transducers, sensors, and minia ture actuators. The electrical properties of these materials are derived from the formation of a homogeneous soHd solution of the oxide end members. The process consists of preparing a coprecipitated titanium—zirconium hydroxide gel. The gel reacts with lead oxide in water to form crystalline PZT particles having an average size of about 1 ]lni (Eig. 3b). A process has been developed at BatteUe (Columbus, Ohio) to the pilot-scale level (5-kg/h). 

Most distribution functions contain an average size and a variance parameter typicaUy based on the cumulative droplet number or volume distributions. For example, the Rosin-Rammler function uses the cumulative Hquid volume as a means of expressing the distribution. It can be expressed as... 

Many of the borate chemicals are sold in a variety of particle size distributions, and average size analyses for the various cuts are available from the manufacturer. 

Com symp soflds are also dry products, have a smaller average size, and are comparatively sweeter (12). Both maltodextrins and com symp soflds are used to prevent caking enhance dispersibiUty and solubiUty provide body or bulk impart deskable texture bind, carry, and protect flavors control extmsion expansion provide viscosity form films and coatings provide an oxygen barrier inhibit crystallization control sweetness improve sheen improve organoleptic characteristics slow meltdown and improve freeze—thaw stabiUty. 

Finely ground cements often called ultrafine cements, having particles less than 10 p.m and an average size of 4 pm are used to grout soils with fine pore spaces, such as fine sand with a permeabiUty of lO " cm/s. These cements can be made with a wide combination of Pordand cement, slag, or siUca fume (72). 

Finally, some general rules for the amount of surfactant appear to be vaHd (13). For anionic surfactants the average size of droplets is reduced for an increase of surfactant concentration up to the critical micellization concentration, whereas for nonionic surfactants a reduction occurs also for concentrations in excess of this value. The latter case may reflect the solubiHty of the nonionic surfactant in both phases, causing a reduction of interfacial tension at higher concentrations, or may reflect the stabilizing action of the micelles per se. 

Average Particle Size A powder has many average sizes hence it is essential that they be well specified. The median is the 50 percent size half the distribution is coarser and half finer. The mode is a high-density region if there is more than one peak in the frequency cui ve, the distribution is said to be multimodal. The mean is the center of gravity of the distribution. The center of gravity of a mass (volume) distribution is defined by. Xyw = X XdV/X dV where dV = X dN dV is the volume of dN particles of size X This is defined as the volume-moment mean diameter and differs from the mean for a number or surface distribution. 

Material Product average size, im Feed Fluid consumption, g fluid/g sohd ... 

Calculate the settling velocity of coal particles in water at 20 C. The average size of the particles is 225 /tm. 

Figure 8.26 shows that with inereasing number of eonstituent primary partieles, the speeifie surfaee area of agglomerates deereases. This oeeurs sinee the average size (age) of the primary partieles inereases with average number of primary partieles within the agglomerate. 

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