Two-diffusivity model

Ishida and Wen [34] used such a two-diffusivity model for a spherical pellet with the internal structure corresponding to Fg = 1, and obtained an analytical solution. For first-order reactions, analytical solutions are possible, by following a similar procedure for slabs and cylinders made up of flat grains (Fg = 1) [26]. 

Before going on to the next section, we should mention a third way to correlate the results other than the two diffusion models. This third way is to assume that the dissolution shown in Fig. 1.2-2 is a first-order, reversible chemical reaction. Such a reaction might be described by... 

Fig. 9. Uptake curves for N2 in two samples of carbon molecular sieve showing conformity with diffusion model (eq. 24) for sample 1 (A), and with surface resistance model (eq. 26) for example 2 (0)j LDF = linear driving force. Data from ref. 18.

The diffusion of individual plume elements, according to Gifford (1959) can be deiernnned from the general Gaussian diffusion model. The model is usually in two basic forms, a puff release - appropriate for an accident, and a continuous release for "routine" release or an accident of long duration. 

Miyauchi and Vermeulen (M7, M8) have presented a mathematical analysis of the effect upon equipment performance of axial mixing in two-phase continuous flow operations, such as absorption and extraction. Their solutions are based, in one case, upon a simplified diffusion model that assumes a mean axial dispersion coefficient and a mean flow velocity for... 

The results of experimental capacitance studies at two plane model pc-Bi electrodes were in agreement with these conclusions.2 266 Thus it has been shown that the potential of the diffuse-layer capacitance minimum for a pc electrode does not correspond to the zero charge potential of the whole surface, i.e., Zfipj Oat E n-... 

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

Fig. 2.4. The asymptotic behaviour of the IR spectrum beyond the edge of the absorption branch for CO2 dissolved in different gases (o) xenon (O) argon ( ) nitrogen ( ) neon (V) helium. The points are experimental data, the curves were calculated in [105] according to the quantum J-diffusion model and two vertical broken lines determine the region in which Eq. (2.58) is valid.

Hollander, 1972) using basically the Noyes diffusion model (Noyes, 1954, 1955, 1956, 1961), treats the radicals as if they go on a random walk . It must be remembered, however, that the two radicals must maintain the correlation of their electron spins (Jee f ) or tl distinction between T and S manifolds for a given radical pair would be lost. 

The inadequacy of the two-box model of the ocean led to the box-diffusion model (Oeschger et al, 1975). Instead of simulating the role of the deep sea with a well-mixed reservoir in exchange with the surface layer by first-order exchange processes, the transfer into the deep sea is maintained by vertical eddy diffusion. In... 

For the case of a two-phase system with two parallel noninteracting paths that both contribute to the diffusion of the solute and where the diffusion coefficients of the solute of interest are different in the two phases, the solution of the two isolated one-dimensional steady-state diffusion models gives... 

B. Acock and Y. A. Pachep.sky, Convective-diffusive model of two-dimensional root growth and proliferation. Plant Soil I80 23 (1996). 

A simple two-state model for the observed water proton self-diffusion may be put forward in the form... 

FIG. 4 Apparent mole fraction (x) water in continuous phase of brine, decane, and AOT microemulsion system derived from the water self-diffusion data of Fig. 3 using the two-state model of Eq. (1). 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. was found to be... 

The description of the ion transfer process is closely related to the structure of the electrical double layer at the ITIES [50]. The most widely used approach is the combination of the BV equation and the modified Verwey-Niessen (MVN) model. In the MVN model, the electrical double layer at the ITIES is composed of two diffuse layers and one ion-free or inner layer (Fig. 8). The positions delimiting the inner layer are denoted by X2 and X2, and represent the positions of closest approach of the transferring ion to the ITIES from the organic and aqueous side, respectively. The total Galvani potential drop across the interfacial region, AgCp = cj) — [Pg.545]

Fig. 13 This figure illustrates the mesa response for the diffusion model. Two plateau functions corresponding to different Mr are shown.

S Neervannan, LS Dias, MZ Southard, VJ Stella. A convective-diffusion model for dissolution of two non-interacting drug mixtures from co-compressed slabs under laminar hydrodynamic conditions. Pharm Res 11 1228-1295, 1994. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Fig. 27 Schematic illustration of the sliding diffusion model of a secondary nudeation (two-dimensional nudeation) on the surface of a single crystal...

Discovery of the hydrated electron and pulse-radiolytic measurement of specific rates (giving generally different values for different reactions) necessitated consideration of multiradical diffusion models, for which the pioneering efforts were made by Kuppermann (1967) and by Schwarz (1969). In Kuppermann s model, there are seven reactive species. The four primary radicals are eh, H, H30+, and OH. Two secondary species, OH- and H202, are products of primary reactions while these themselves undergo various secondary reactions. The seventh species, the O atom was included for material balance as suggested by Allen (1964). However, since its initial yield is taken to be only 4% of the ionization yield, its involvement is not evident in the calculation. 

Mahlman and Sworski (1967) found that curves for scavenging of H2 by NOj- have nearly the same shape for neutral and 0.1 M acid solutions, over the concentration range 1 mM to 0.4 M of the solute, despite the fact that nitrate reacts much faster with eh than with H. Schwarz points out, however, that when two solutes (H+ and N03-) compete for the same intermediate (eh), the extrapolation to zero scavenger concentration is not a valid procedure. The calculation of the diffusion model agrees with experiment over the entire N03- concentration range. Further, the model predicts a lower H2 yield at very low scavenger concentrations. 

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