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Diffusion process, isothermal

If the power requirement of the gaseous diffusion process were no greater than the power required to recompress the stage upflow from the pressure on the low-pressure side of the barrier to that on the high-pressure side, then the power requirement of the stage would be Z RTLq (1 /r) for the case where the compression is performed isotherm ally. The power requirement per unit of separative capacity would then be given simply by the ratio... [Pg.87]

In an attempt to provide further information relative to the validity of the diffusion mechanism, a typical set of results was selected from the isothermal release work, and the volume of volatile matter released was plotted against the square root of time. For a pure diffusion process such a plot should be almost linear initially (4) whereas for a true logarithmic time law, dVt/dt should tend to infinity for very small values of t. Figure 12 shows that by this criterion the rate controlling mechanism appears to be diffusion and not chemisorption. The fact that the curve does not pass through the origin is undoubtedly caused by the fact that it was not possible to heat the sample to... [Pg.610]

The catalyst intraparticle reaction-diffusion process of parallel, equilibrium-restrained reactions for the methanation system was studied. The non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key components have been established, and solved using an orthogonal collocation method. The simulation values of the effectiveness factors for methanation reaction Ch4 and shift reaction Co2 are fairly in agreement with the experimental values. Ch4 is large, while Co2 is very small. The shift reaction takes place as direct and reverse reaction inside the catalyst pellet because of the interaction of methanation and shift reaction. For parallel, equilibrium-restrained reactions, effectiveness factors are not able to predict the catalyst internal-surface utilization accurately. Therefore, the intraparticle distributions of the temperature, the concentrations of species and so on should be taken into account. [Pg.33]

R. W. H. Sargent The COj-No (or rather C02-air) values were obtained indirectly from studies on a fixed-bed separation process for removal of CO2 from air. These studies were made on a bed of pellets 4 ft long and 4 inches in diameter two pellet sizes were used, and a range of air flow rates was covered at pressures from 1 to 25 atm and from +15° to —40°C. All the results were successfully predicted by a model assuming both pellet-pore and intracrystalline diffusion under isothermal conditions the two relevant diffusivities were used as adjustable parameters to fit the experimental break-through curves by least squares for one set of conditions at each temperature, and these values then pre-... [Pg.162]

Sorption Kinetics. The adsorption and desorption data were analyzed in terms of a model based on the following main assumptions. Micropore diffusion within the sieve crystals is the rate-controlling process. Diffusion may be described by Fick s law for spherical particle geometry with a constant micropore diffusivity. The helium present in the system is inert and plays no direct role in the sorption or diffusion process. Sorption occurs under isothermal conditions. Sorption equilibrium is maintained at the crystal surface, which is subjected to a step change in gas composition. These assumptions lead to the following relation for the amount of ethane adsorbed or desorbed by a single particle as a function of time (Crank, 4). [Pg.174]

As we have seen previously, the separation mechanism in pervaporation is explained by an adsorption-diffusion process. In this way, the selective adsorption of the components in the zeolite will be responsible for the selectivity in the separation. Adsorption is an exothermic nonactivated process. In general, the isotherm of adsorption on zeohtes follows a single site Langmuir-type isotherm [74]. [Pg.290]

Hie subscript M refers to the method of moments. The method of moments is applicable to all chromatographic systems characterized by a linear partition isotherm (that is, for K = constant) irrespective of diffusion processes deforming the elution peak. [Pg.35]

We start with the case of d(z) injection profile into an isothermal column under laminar gas flow regime. The factors which cause broadening of the initial profile are longitudinal diffusion and radial diffusion across streamlines. These continuously change the concentration distribution and gradients. In the absence of any adsorption sojourn time of molecules on the wall (i.e. negligible adsorption-desorption energy), and only in this case, the two above diffusion processes yield ... [Pg.95]

This equation assumes that the contribution of the probe vapour to the gas flow rate across the column is negligible and can be considered as ideal, and that the contribution of the injection band and diffusion processes along the column play a minor role. One of the main advantages of the chromatographic method, especially when applying the Rudzinski-Jagiello s method, is the fact that this method provides directly the first derivative of the isotherm and therefore, in a very direct way the DFCA. [Pg.494]

For diffusion in isothermal multicomponent systems the generalized driving force was written as a linear function of the relative velocities (m/ — My). In the general case, we must allow for coupling between the processes of heat and mass transfer and write constitutive relations for and q in terms of the (m — My) and V(l/r). With this allowance, the complete expression for the conductive heat flux is... [Pg.268]

Water acts as a plasticizer for soy flour (Yildiz and Kokini, 2001). Therefore, increase in water content will plasticize the matrix causing an increase in available free volume for molecular transport. Moisture diffusion as a result will be effected from the water activity of the system. The relationship between moisture content and a can be established using the moisture sorption isotherm (MSI) of soy flour. The glass transition temperature is a very important concept in the diffusion process. At the vicinity of the glass-transition temperature the diffusion process increases at a higher rate. Figure 46.1 shows the plasticization effect of moisture on soy flour and Gordon-Taylor prediction of Tg vs. moisture content (Yildiz and Kokini, 2001). [Pg.598]

From a formal (macroscopic) viewpoint, the diffusion process can be described in many cases of practical interest by Fick s two laws (1-5). These laws are represented by the following equations for the isothermal diffusion of a substance in or through a V-dimensional, hyperspherioal polymer body of sufficiently large area [V=l for a slab or membrane (film), v=2 for a hollow cylinder, and V=3 for a spherical shell] (2) ... [Pg.22]

It seems to be the exception rather than the rule that the rate of sorption in zeolites is controlled by a simple diffusion process in the solid, characterized by a constant diffusion coefficient. This result is not surprising in view of the complexity of the structures of zeolites and related to the fact that the isotherms can in most cases not be explained by an ideal model. Sorption rates depend in many cases considerably on the type of cation in the solid and the pretreatment (degree of dehydration). [Pg.311]

The isothermal-diffusion process for fabricating carbon-carbon has been reviewed previously and is not repeated here [37]. Only recently [116-118] has the forced flow-thermal gradient proeess been applied to making carbon-earbon. The latter work is... [Pg.350]

To conclude this section, it is intriguing to observe how developments in instrumental analysis have led to an increase of sensitivity and a dramatic decrease of analysis time required by procedures based on isothermal distillation. The method of Conway, developed more than 35 years ago [4.11], still in use in clinical and pharmaceutical laboratories, requires many hours to perform an assay of a volatile species. The samples are kept in small, enclosed chambers containing the donor and the acceptor liquid, respectively, and after the diffusion process has reached equilibrium, the acceptor liquid is titrated. Gas-sensing probes, which operate on the principles of ion-selective electrodes, separated from the... [Pg.199]

Fig. 8 FR spectra of methane (a), ethane (b), propane (c), n-butane (d), n-pentane (e) and n-hexane (f) in sUicalite-l (cf. [65]). (n.o) indicate the experimental in-phase and out-of-phase KSqm characteristic functions, respectively. A single diffusion process model was used to fit the data in (1), while the non-isothermal diffusion model was used to fit the data in (2) except (f, 2) which was fitted using the two independent diffusion processes model. Solid lines denote the theoretical overall characteristic functions, and dash and dash-dot lines denote the theoretical diffusion processes occurring in the straight channels (dash) and the sinusoidal channels (dash-dot). Note 1 Torr= 133.33 Pa... Fig. 8 FR spectra of methane (a), ethane (b), propane (c), n-butane (d), n-pentane (e) and n-hexane (f) in sUicalite-l (cf. [65]). (n.o) indicate the experimental in-phase and out-of-phase KSqm characteristic functions, respectively. A single diffusion process model was used to fit the data in (1), while the non-isothermal diffusion model was used to fit the data in (2) except (f, 2) which was fitted using the two independent diffusion processes model. Solid lines denote the theoretical overall characteristic functions, and dash and dash-dot lines denote the theoretical diffusion processes occurring in the straight channels (dash) and the sinusoidal channels (dash-dot). Note 1 Torr= 133.33 Pa...
The FR spectra of Ci -Ce n-alkanes in silicalite-1 shown in Fig. 8a-f,2 cannot be fitted by the single diffusion process model and a bimodal behaviour had to be assiuned for these spectra. This bimodal behaviour can be elucidated by three models, i.e., non-isothermal diffusion model (cf Sect. 3.2.3) [28,38,55], two independent diffusion processes model (cf. Sect. 3.2.2) [8,38,55,59], and diffusion-rearrangement model [38,55,59,68], which assiunes that for zeolites such as MFI (cf. [65]) the sorbate molecules diffuse only along the transport channels, i.e., the straight channels, but can be stored in the sinusoidal channels, with a finite-rate mass exchange between the two channels. Which process actually operates can be determined by analysing the physical parameters derived from the fits of the theoretical models. [Pg.258]

Diffusion processes can be subdivided into various classes, e.g., translational, rotational, thermal, etc. Translational diffusion consists of the isothermal equilibration of matter between two phases of differing concentra-... [Pg.252]

The models and material property data for predicting fission metal release from fuel particles and fuel elements are described in Ref. 4. The transport of fission metals through the kernel, coatings, fuel rod matrix, and fuel element graphite is modeled as a transient diffusion process in the TRAFIC code (Section 4.2.5,2.2.1.2). The sorption isotherms which are used in the calculation of the rate of evaporation of volatile metals from graphite surfaces account for an increase in graphite sorptivity with increasing neutron fluence. [Pg.297]

Diffusion of small molecules, usually solvents, into glassy polymers exhibits anomalous or non-Fickian behavior 34). As the solvent penetrates, the diffusion coefficient increases because the glass transition temperature is lowered. The solvent acts as a plasticizer, increasing the free volume and the mobility of the solvent. Thus we have an autocatalytic diffusion process. This can be relevant in Isothermal Frontal Polymerization, which we discuss below. [Pg.11]

During the diffusion of solute molecules through the network of pores, some of the solute molecules are adsorbed onto the interior surface of the particle. This process of adsorption is normally very fast relative to the diffusion process, and so we can model it as local equilibrium between the solute in the pore fluid and the solute bound to the interior surface of the particle. This partitioning is often referred to as the adsorption isotherm, which implies constant temperature conditions. When the solute concentration in the pore is low enough, the relationship becomes linear (Henry s law) hence, mathematically, we can write... [Pg.522]


See other pages where Diffusion process, isothermal is mentioned: [Pg.306]    [Pg.469]    [Pg.478]    [Pg.251]    [Pg.108]    [Pg.385]    [Pg.609]    [Pg.610]    [Pg.271]    [Pg.33]    [Pg.306]    [Pg.268]    [Pg.321]    [Pg.159]    [Pg.2826]    [Pg.350]    [Pg.351]    [Pg.530]    [Pg.242]    [Pg.243]    [Pg.254]    [Pg.258]    [Pg.40]    [Pg.909]   


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