Volume-averaging

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. 

I>D Average volume fraction of discontinuous phase Dimensionless Dimensionless... 

Figure 12 shows the dependence of the average aspect ratio and the TLCP volume fraction on the relative sample thickness for the four processing conditions in the core layer, transition layer and skin layer, respectively, by a morphological examination [13]. Generally, the aspect ratio increases from core to skin layer, whereas the situation is reversed for the volume fraction. An average volume fraction about 20% can be clearly seen. 

Odiot S., and Daudel, R., Compt. rend. 238, 1384, "Relation between the average volume occupied by an electron in the electron could of an atom and the average electric potential existing in that domain."... 

Fig. 6.6. Comparison of activation volume and average volume of the strands between crosslinks. The effective molecular mass Mc between crosslinks is varied from 0.1 to 10 kg/mol. The cubes represent the activation volume of 2 nm3.

Apparently, crosslinks between the molecular chains do not interfere with the yield process in the activation volume. Yielding involves the cooperative movement of about 10 to 20 chain segments, if the average volume of one segment measures about 0.15 nm3. Such a volume seems to be reasonable according to molecular parameters [73-75]. 

Generally, the closure problem reflects the idea of a spatially periodic porous media, whereby the entire structure can be described by small portions (averaging volumes) with well-defined geometry. Two limitations of the method are therefore related to how well the overall media can be represented by spatially periodic subunits and the degree of difficulty in solving the closure problem. Not all media can be described as spatially periodic [6,341 ]. In addition, the solution of the closure problem in a complex domain may not be any easier than solving the original set of partial differential equations for the entire system. 

Curry et al. Neurosurgery 2005 56(4) 681-692 Retrospective chart, operative report, and imaging review 38 patients treated with hemicraniectomy for large hemispheric infarcts (average volume 407 cm ) Survival and surgical selection of patients 32 patients survived at 1 year. Age but not time to surgery, volume of infarction or craniectomy size correlated with ability to walk and Barthel score... 

One of the recent advances in magnetic studies is that it enables not only the estimation of the average volume v of clusters from the LF and HF approximations of the Langevln function, but also enables to compute particle size distribution based on an assumed function. By judiciously combining the parameters of the Langevln and of the "log normal function, we obtained a particle (cluster) size distribution of Y Fe203 in ZSM-5. The essential features of such computation are shown in Fig. 6. 

Figure 2.36 Multichannel flow domain with typical averaging volume for obtaining volume-averaged enthalpy equations.

In case when K " > K" and Ny < Ny < Ny2, i.e. in case of average volume concentrations of radicals and recombination mechanism of their heterogeneous annihilation we arrive at the following expression characterizing the stationary electric conductivity of adsorbent... 

After quenching to ambient temperature the laterally averaged volume fraction versus depth profile was measured by TOF-ERDA, and Figure 4.29 shows a series of dPS profiles for increasing annealing times. After 10 min annealing at 180°C,... 

Zink et al. used a blend of polystyrene (hPS) and its deuterated counterpart (dPS), both of molecular weight 1.95 x 106 (abbreviated 1.95 M). The average volume fraction (4>dPS) of deuterated polystyrene was 30%. The polymers were dissolved in toluene and spin cast on thin silicon wafers (about 10 x 10 mm), the resulting film thickness being about 300 nm. The samples were annealed at 245°C for 8 days, and the measurement of the resulting depth profiles was conducted by NRA using a monoenergetic 700 keV 3He beam. The nuclear reaction employed can be written ... 

An alternative way to find out the expression for C is to assume that the same form of the structure factor, Eq. (58), will be valid also locally for the inhomogeneous system, if the average volume fraction <[)0 in Eq. (58) is replaced by its local values < )(r). Guided by this assumption, one can allow the coefficient at the gradient term to be dependent on the local volume fractions and write down C as... 

Equation (53) has to be solved numerically. The field < )(r) at time t is represented by the discrete set < ), -)t(t) on a lattice, and the time evolution is obtained by performing iterations over t. The initial conditions are generated by assigning the average volume fraction < )0 to each lattice point, and the interface is defined as < )(r) < )0. An example of the interface evolution for symmetric... 

Figure 40. Time evolution of the Euler characteristic density for different average volume fractions, 4)0 — 0.5, 0.4, 0.375, 0.36, 0.35, and 0.3, quenched from the homogeneous state binary mixture. The negative Euler characteristic corresponds to the bicontinuous morphology, while the... 

The most important VD value for dictating the dosing regimen is the steady-state volume of distribution (VDSS). This volume represents the extent of distribution when the rate of transit to and from the tissues is equal. It is more representative of a time-averaged volume of distribution and its value will reside somewhere in between VDC and VDp. The steady-state VD is calculated from the mean-residence time (MRT). 

Typically at NAPL recovery sites (i.e., refineries and bulk terminals), some quantity of groundwater is coproduced. A major concern arises from this process in that the coproduced water must be treated, disposed of, or both. An evaluation process then follows on how to handle the coproduced water. A number of factors that control the ultimate fate of the water include the average volume produced on a regular basis, the level of contamination, and site-specific physical constraints. 

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