Thickening factor

A plot (called the Hojfman-Weeks plot [36]) of T versus Tc is linear for a constant thickening factor, and the extrapolated intersection of T with Tc is taken to be the equilibrium melting temperature T . While this procedure has been improved [37], the whole concept is also contested [38]. 

In turbulent reacting cases the Dynamically Thickened Flame model [311 321 355 361] is used, where a thickening factor F is introduced to thicken the flame front and the efficiency function developed by Colin et al. [269] is used to account for subgrid scale wrinkling. 

The unstructured mesh is composed of 400,000 nodes and 2,300,000 tetrahedra, which is typical and reasonable for LES of such configuration. The explicit time step is At 0.22 /is. The mesh is refined close to the inlets and in the combustion zone (Fig. 10.3), leading to a flame thickening factor of the order of 10. A one-step chemical scheme fitted to JPlO/air flames is used for chemistry (JPIO is a substitute for kerosene and has the same thermochemical properties). It has been checked that in the simulation the flame mostly burns mixtures with an equivalence ratio in the range between 0.5 and 1, where the chemical scheme is valid. 

The properties of adsorbed layers of liquid may be evaluated not only in terms of the ratio i bf/r bik > but also in terms of a dimensionless boundary thickening factor [96] ... 

The product / det det h s the dimensions of dynamic viscosity. The ratio of this product to the bulk dynamic viscosity characterizes the change in mechanical properties of the liquid in the process of separating the bodies. For steel disks, the thickening factor" (with det 10 F = 3900 dyn/cm ) has... 

The time to establish equilibrium of interaction forces between plane-parallel disks is directly proportional both to the ratio r bfMbik od to the boundary thickening factor (i.e., the viscosity affects the kinetic adhesion). The viscosity, however, has little affect on the absolute value of the equilibrium adhesive force, i.e., on static adhesion. This can be seen by analyzing Eq. (VI.2). On the one hand, in fact, with/ = const,... 

According to Hoffman nucleation theory (see Sect. 1.6.1), if chains in a polymer crystal stayed as they were laid down, the crystal would melt almost immediately above its crystallization temperature (solid black line at 45 in Fig. 2.1) however, following subsequent processes the lamellar thickness increases by a thickening factor p (2 in the case of polyethylene) giving a slope with its reciprocal y (here 1/2) in a Hoffman-Weeks plot. The theory of this is quite complicated, and the simple linear plot has been called into question (Marand et al. 1998). Nevertheless, it suffices as a very practical guide to the use of DSC in relating thermal history of a polymer specimen to lamellar morphology. 

Dividing the scrolling rate by the solids feed rate gives an empirical "thickening factor , 5 , where ... 

Thus a good way of correlating digested sludge thickening results from a decanter is to plot solids recovery, and cake solids, separately, against the empirical thickening factor (N/ Qf. r... 

The data in Table A.6 are for a thickening application. For thickening, it is sometimes useful to calculate psi, the thickening factor. 

A feed stream to be clarified or thickened can exist at any state represented within this diagram. As it becomes concentrated owing to sedimentation, it may pass through all the regimes, and the settling rate in any one may be the size-determining factor for the required equipment. 

Scale-up Factors Factors used in thickening will vary, but, typically, a 1.2 to 1.3 multiplier applied to the unit area calculated from laboratory data is sufficient if proper testing procedures have been followed and the samples are representative. 

Thickener control philosophies are usually based on the idea that the Iindertlow density obtained is the most important performance criterion. The o ertlow clarity is also a consideration, but this is generally not as critical. Additional factors which must be considered are optimization of tlocciilant usage and protection of the raking mechanism. 

The factors which may make CCD a preferred choice over other separation systems include the following rapidly settling solids, assisted by flocculation relatively high ratio of solids concentration between underflow and feed moderately high wash ratios allowable (2 to 4 times the volume of hquor in the thickened underflows) large quantity of sohds to be processed and the presence of fine-size sohds that are difficult to concentrate by other means. A technical feasibihty and economic study is desirable in order to make the optimum choice. 

Torque Rating The choice of torque rating has been discussed earlier. Torque is a function of such factors as quantity and quality of underflow (therefore, of such parameters as particle characteristics and flocculant dosage that affect underflow character), unit area, and rake speed but, in the final analysis, torque must be specified on the basis of experience modified by these factors. Unless one is experienced in a given apphcation, it is wise to consult a thickener or clarifier manufacturer. 

An anaerobic digester is a no-recycle complete mix reactor. Thus, its performance is independent of organic loading but is controlled by hydraulic retention time (HRT). Based on kinetic theoiy and values of the pseudo constants for methane bac teria, a minimum HRT of 3 to 4 days is required. To provide a safety factor and compensate for load variation as indicated earlier, HRT is kept in the range 10 to 30 days. Thickening of feed sludge is used to reduce the tank volume required... 

Non-Newtonian fluids vary significantly in their properties that control flow and pressure loss during flow from the properties of Newtonian fluids. The key factors influencing non-Newtonian fluids are their shear thinning or thickening characteristics and time dependency of viscosity on the stress in the fluid. 

Determine the cementing operation time and thus the minimum thickening time. Assume a cement mixing rate of 25 sacks/min. Also assume an annular displacement rate no greater than 90 ft/min while the spacer is moving through the open-hole section and a flowrate of 300 gal/min thereafter. A safety factor of 1.0 hr is to be used. 

If K = 1 K, a = 0.25 nm, and z = 3, X = 30nm at 300 K, so that for a film 1 nm thick, the field increases the rate of growth by a factor of about 10 The term in the growth law due to the field, namely exp (K/X), is large only when X is small. Because of this a thin oxide film can form even at low temperatures where the ordinary rate of entry of ions into the oxide, is negligible. As the film thickens, the factor exp /X) decreases rapidly, and the rate of growth soon falls to such a low value that, for practical purposes, oxidation has ended. 

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