Homogeneous Approximation

Therefore, once again invokingthe pseudo-homogeneous approximation, the equations we mustsolveare ... 

Space Group and Pearson Symbol Pnma, oP20 Composition narrow range of homogeneity (approximately 39 0 at/°C)... 

This monomer concentration Ma in the formalism of the quasi-homogeneous approximation, unlike M a, refers to the whole volume of the two-phase system. The aforementioned quantities are connected by the simple relationship Ma = flM a where y01 stands for the volume fraction of the a-th phase in miniemulsion. An analogous relation, Ra = sdaR a, exists between the concentrations Ra of the a-th type active centers in the entire system and those R a in the surface layer of the a-th phase. This layer thickness da has the scale of average spatial size of the a-th type block, which hereafter is presumed to be small as compared to the average radius of miniemulsion drops. Apparently, in this case, the curvature of the interphase surface can be neg-... 

Extraction of sediment samples. Prior to extraction, sediment samples were freeze-dried and homogenized. Approximately 10 g of dried sediment were placed in a preextracted thimble, and a small piece of silanized glass wool was placed in the thimble on top of the sample to prevent sediment parts from leaving the thimble. The thimble was placed in a Soxhlet setup and extract for 16 h (overnight) with 200 ml hexane/acetone (3/1 v/v). The extracts were concentrated in the rotation evaporator until approximately 5 ml (/ = 0.05 bar T = 40°C) of extract remained. If the extraet still contained solid particles, the extract was filtered with diatomaceous earth or sodium sulfate. The extract was transferred to a diatomaceous earth- or sodium sulfate-filled funnel and flushed with 10 ml hexane. The eluted extract was evaporated again in the rotary evaporator until approximately 5 ml of extract remained. The extract was transferred to a cleaned glass tube and concentrated until near dryness. The dried extract was finally redissolved in 3 ml hexane. 

Several characteristic ratios of heterogeneity as functions of titanium particle size and sample porosity are shown in Figs. 75a and b, respectively. For the quasi-homogeneous approximation to be valid, the heterogeneity of the reactant medium should be small in comparison to the thermal length scale. As a result, the heterogeneity of the combustion front (shape and propagation) should also be small relative to the macroscopic behavior ... 

We persist with the homogeneity approximation for h3q>erbolic surfaces, to calculate the local/global relation. The local constraint for a binar surfactant/water mixture is given by eq. 43. 

One may also derive a closed expression for the correction Uc,fs using the homogeneity approximation (rj) w /> together with Etjs. (5.27b) and (5.30) to obtain... 

ZPR-3 Assembly 60 is a homogeneous approximation of current-type EBR-Il core loadings having a radial blanket rich in depleted uranium. -The atom densities of the quasi-hexagonal core are U -0.00SS9 - 0.00457 Na - 0.0103 0-0.00214 Fe-... 

In practice, the potential theory of single-component adsorption is used in the form of the homogeneous approximation (51). The value of is interpreted as an effective chemical potential jig of the adsorbate and as an effective adsorbate density. Thus, in addition to the dependence e(h), a correlation is required for ng(iig) [more generally T)]. In many cases, only the temperature dependence of itg is taken into account However, as shown in Ref. 101, at extremely high effective pressures developed close to a surface, neglecting the pressure compressibility may lead to errors around 10%. 

Let us first verify that the complete potential theory of adsorption, without introduction of the homogeneous approximation (51) and with the same EoS for the bulk phase and for the adsorbate, is able to correlate experimental data on single-component adsorption. Figure 18 presents an example of successflil correlation of adsorption isotherms of methane and nitrogen on activated carbon at elevated pressures. Experimental data are taken from Refs. 103 (methane at 298 K) and 104 (nitrogen at 210 K). Although the estimate obtained on the basis of the... 

Equation (73) simplified by the application of Eq. (52) may be used for fast derivation of expressions for spreading pressures of single-component adsorbates in homogeneous approximation. Introducing the potential as an integration variable, we obtain... 

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