Volumetric fraction

Critical Volume The critical volume of a compounci is the volume occupieci by a set mass of a compounci at its critical temperature anci pressure. While useful in itself, the critical volume is extensively useci in equations for estimating volumetric fractions. 

FIG. 22-44 E mpirical relationship between 2), the volumetric fraction of hq-iiid in common polydisperse foam, and K, the electrical conductivity of the foam divided hy the electrical conductivity of the liquid. [Chang and Lemhch, J. Colloid Interface Sci., 73, 224 (1980).]... 

Fig. 8.7 shows a second example (Cycle A2) of carbon dioxide removal by chemical absorption from a CCGT plant, but one in which the semi-closed concept is introduced— exhaust gas leaving the HRSG is partially recirculated. This reduces the flow rate of the gas to be treated in the removal plant, so that less steam is required in the stripper and the extra equipment to be installed is smaller and cheaper. This is also due to the better removal efficiency achievable—for equal reactants flow rate—when the volumetric fraction of CO2 in the exhaust gas is raised from the 4-6% value typical of open cycle gas turbines to about 12% achievable with semi-clo.sed operation. 

Because the gas always flows at a velocity greater than that of the liquid, the in situ volumetric fraction of liquid at any point in a pipeline will be greater than the input volume fraction of liquid furthermore it will progressively change along the length of the pipe as a result of expansion of the gas. 

SG gas hold-up (volumetric fraction of gas in reaction mixture) dimensionless 0.02-0.4... 

Levy, S., 1966, Forced Convection Subcooled Boiling—Prediction of Vapor Volumetric Fraction, Rep. 

The viscosity of the suspension (/i ) is also modified by the presence of the solids. For uniform spheres at a volumetric fraction of 2% or less,... 

A fluidised bed of total volume 0.1 m3 containing the same particles is maintained at an approximately uniform temperature of 425 K by external heating, and a dilute aqueous solution at 375 K is fed to the bed at the rate of 0.1 kg/s so that the water is completely evaporated at atmospheric pressure. If the heat transfer coefficient is the same as that previously determined, what volumetric fraction of the bed is effectively carrying out the evaporation The latent heat of vaporisation of water is 2.6 MJ/kg. 

The technique of self-nucleation [75] can be very useful to study the nucleation and crystallization of block copolymer components, as already mentioned in previous sections. In block copolymers, factors like the volumetric fraction and the degree of segregation affect the type of confinement and therefore modify the self-nucleation behavior. In the case of semicrystalline block copolymers, several works have reported the self-nucleation of either one or both crystallizable components in PS-fc-PCL, PS-b-PB-b-PCL, PS-b-PE-b-PCL, PB-fr-PIB-fr-PEO, PE-fr-PEP-fr-PEO, PS-fc-PEO, PS-h-PEO-h-PCL, PB-b-PEO, PB/PB-fc-PEO and PPDX-fc-PCL [29,92,98,99,101-103,134] and three different kinds of behavior have been observed. Specific examples of these three cases are given in the following and in Table 5 ... 

In open water bodies the volumetric fraction occupied by particles is so tiny that the porosity <)) is equal to 1. Also, since Vx Vw, the mass of solids per total volume (Ms / Ft) is about equal to rsw = MJ Vw. Thus, we can approximate Eqs. 23-2 and 23-3 by ... 

Several models have been proposed to estimate the thermal conductivity of hydrate/gas/water or hydrate/gas/water/sediment systems. The most common are the classical mixing law models, which assume that the effective properties of multicomponent systems can be determined as the average value of the properties of the components and their saturation (volumetric fraction) of the bulk sample composition. The parallel (arithmetic), series (harmonic), or random (geometric) mixing law models (Beck and Mesiner, 1960) that can be used to calculate the composite thermal conductivity (kg) of a sample are given in Equations 2.1 through 2.3. 

It can precipitate as potassium hydrogen tartrate (KHT) or as calcium tartrate (CaT), the latter being practically insoluble in aqueous solutions. Their equilibrium solubility varies with temperature, pH, and alcohol content, while the presence of a few wine components, such as polysaccharides and mannoproteins, may hinder spontaneous nucleation even if the solution is supersaturated. From Figure 14 that shows the equilibrium tartaric acid-dissociated fractions versus pH and ethanol volumetric fraction (Berta, 1993 Usseglio-Tomasset and Bosia, 1978), it can be seen that in the typical pH range (3 4) of wines KHT is predominant. As temperature is reduced from 20 to 0°C, KHT solubility in water or in a 12% (v/v) hydro-alcoholic solution reduces from 5.11 to 2.45 kg/m3 or from 2.75 to 1.1 kg/m3, respectively (Berta, 1993). Each of these data also varies with pH and reaches a minimum at the pH value associated with the maximum concentration of the hydrogen tartrate anions. For the above-mentioned solutions, the solubility minimum shifts from pH 3.57 to pH 3.73 as the ethanol content increases from 0 to 12% (v/v) (Berta, 1993). 

FIG. 14 Effect of pH on the equilibrium tartaric acid dissociated fractions ( , O, [HT-]/ [T] , , [T2-]/[T] A, A, [H2T]/[T]) at two different ethanol volumetric fractions (0% v/v, closed symbols 18% v/v, open symbols), as estimated according to Berta (1993) and Usseglio-Tomasset and Bosia (1978) H2T, free tartaric acid concentration HT-, hydrogen tartrate concentration T2-, tartrate concentration T, overall tartaric acid concentration. 

It should be noted that both the process fluid and the tracer are fed at the inlet of the drawing tube and that the volume of the drawing tubes occupies about one fifth, so there must be En = 0 for r < / 5. If the volumetric fraction of the plug flow region is... 

In comparison, the micromixing time in a general stirred tank reactor (STR) ranges from 500 to 1000 ms. If it is noted that the impingement zone in the SCISR occupies only a small volumetric fraction (less than 20% of the total), the value of 192 ms for the micromixing time in the SCISR indicates clearly that impinging streams do promote micromixing very efficiently. 

The micromixing occurs mainly in the impingement zone [31J. If the volumetric fraction of the impingement zone is denoted by/, we arrive at... 

Figure 11.9 Volumetric fraction of fluctuation intensity lower than PSD at different impinging...

V = volume to be stirred es = volumetric fraction of solid pM = density of the suspension us = particle sedimentation rate... 

In Eq. (12.69) Oy and eL represent the volumetric flow rate and the volumetric fraction of the liquid bulk. 

When the monomer phase is still present, the activity coefficient of the monomer dissolved in the gel phase is unity. Therefore, the volumetric fraction of polymer in the gel phase is calculated by solving, for the unknown cp2, the following equation ... 

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