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Transient concentration profiles

Ion-Exchange Rate and Transient Concentration Profiles The numerically implicit finite difference method was used to solve the set of nonlinear differential equations (8) for a wide range of model parameters such as diffusivities, Dg, D,, and Dy, dissociation constants. Kg, exchanger capacity, ag, and bulk concentration, Cg, of the solution. [Pg.158]

This result demonstrates that experimental observations of rates and even transient concentration profiles can be explained with either set of assumptions so that no conclusive information concerning the actual physical mechanism can be obtained in this way [44]. [Pg.170]

Figure 2 Transient concentration profile for severely coking conditions... Figure 2 Transient concentration profile for severely coking conditions...
Measurement of transient concentration profiles of deuterated polymers in polymer blends using forward recoil spectroscopy Measurement of transient concentration profiles of fluorescently labeled molecules in capillary tubes using epifluorescence microscopy Measurement of transient concentration profiles of fluorescently labeled molecules in biological tissues using epifluorescence microscopy Fluorescence recovery (or redistribution) after photobleaching (FPR)... [Pg.55]

Fig. 17 Transient concentration profiles in y-direction (i.e., along 8-ring channels) measured by interference microscopy for a adsorption and b desorption of methanol in a large crystal of ferrierite for pressure steps 5 -> 10 and 10 5 mbar. The form of the profiles shows that both surface resistance and internal diffusion (along the 8-ring chan-... Fig. 17 Transient concentration profiles in y-direction (i.e., along 8-ring channels) measured by interference microscopy for a adsorption and b desorption of methanol in a large crystal of ferrierite for pressure steps 5 -> 10 and 10 5 mbar. The form of the profiles shows that both surface resistance and internal diffusion (along the 8-ring chan-...
Assessing Surface Resistances from Transient Concentration Profiles. .. 198... [Pg.135]

Figure 36 compares the actual measurements of transient concentration profiles during molecular uptake by a silicalite-1 crystal as displayed in Fig. 34 with uptake simulations. The diagrams show the integrals of concentration in the x direction as a function of z (this is in longitudinal extension of the... [Pg.176]

Figure 41 illustrates the system under study and the coordinates of measurement, showing the SEM image of a typical Mn(HC02)2 crystal (a) [84,85], a scheme of the one-dimensional channel structure along the y direction (b), and the crystal under study with its extensions, the axes denomination, and the plane along which the concentration profiles have been recorded (c) (observation in z direction, plane extension iny direction, x = 41 xm). Figure 42a provides an impression of the transient concentration profiles measured dur-... [Pg.181]

Fig. 45 Comparison of the transient concentration profiles during methanol uptake by the MOF-type crystal as recorded by interference microscopy (symbols) with the corresponding profiles recalculated from the measured diffusivities with surface permeabilities (full line in Fig. 44) which lead to the best fit to the experimental points... Fig. 45 Comparison of the transient concentration profiles during methanol uptake by the MOF-type crystal as recorded by interference microscopy (symbols) with the corresponding profiles recalculated from the measured diffusivities with surface permeabilities (full line in Fig. 44) which lead to the best fit to the experimental points...
In all the transient concentration profiles considered so far (Figs. 36, 42, 45, 46, 48, and 50), in no case did the boundary concentration immediately assume the equilibrium value. The consequences of this finding on the relation between the transport resistances exerted by the intracrystalline bulk phase and by the crystal surface on the overall uptake and release behavior will be... [Pg.193]

Fig. 53 Transient profiles of 2-methylpropane as a guest molecule in a nanoporous material (crystal of type silicalite-1). a Overview of the intracrystalline concentration profile to s after the onset of adsorption, b Evolution of the guest profiles along the x axis at 0 to xm during uptake, c Host crystal with indication of the cross section to which the transient concentration profiles in d refer, e Evolution of the guest profiles along the x axis during release over different cross sections as indicated by c... Fig. 53 Transient profiles of 2-methylpropane as a guest molecule in a nanoporous material (crystal of type silicalite-1). a Overview of the intracrystalline concentration profile to s after the onset of adsorption, b Evolution of the guest profiles along the x axis at 0 to xm during uptake, c Host crystal with indication of the cross section to which the transient concentration profiles in d refer, e Evolution of the guest profiles along the x axis during release over different cross sections as indicated by c...
Solution of (4.3-82) with these initial and boundary conditions is the following equation for the transient concentration profile ... [Pg.219]

FIGURE 6.13. Transient concentration profiles as a function of time in film that results from a linear increase in fluidity from x/d = 0 to x/d = 1, where Dm(Box 1) = 0.225 and D (Box Jmax) = 0.45. [Reprinted with permission from I. Fritsch-Faules and L. R. Faulkner, J. Electroanal. Chem. 331,997 (1992).]... [Pg.110]

A major advantage of the recently developed interference microscopy technique [74, 75] is that in addition to allowing a direct measurement of sorption/desorption rates on the single crystal scale it provides, from the form of the transient concentration profiles, direct experimental evidence concerning the nature of the rate controlling resistances to mass ffansfer. Recent studies by this technique have shown that the influence of sffuctural defects and surface resistance to mass transfer are far more important than has been generally assumed [76-80]. For some systems it appears that sorption rates are controlled by surface resistance while in other cases the profiles suggest a combination of... [Pg.22]

Figure 14. Shape, dimensions and transient concentration profiles during uptake of methanol in a ferrierite crystal measured by interference microscopy, (c) shows the actual profiles along the length of the crystal at the mid point, and (e) shows the same profiles normahzed by subtracting the effect of the roof-hke structures. AQ profiles are at the same times (0, 30, 130 and 370 secs). From Kortunov etal [81]. Figure 14. Shape, dimensions and transient concentration profiles during uptake of methanol in a ferrierite crystal measured by interference microscopy, (c) shows the actual profiles along the length of the crystal at the mid point, and (e) shows the same profiles normahzed by subtracting the effect of the roof-hke structures. AQ profiles are at the same times (0, 30, 130 and 370 secs). From Kortunov etal [81].
First of all, it was verified that the dynamic simulations converged to the steady-state data obtained in the bench-scale unit in order to check the consistency of the model. The energy balance was not considered in the simulations because this unit operates in isothermal mode. Figure 8.26 shows the transient concentration profiles of sulfur and nitrogen in the liquid and solid phases at stabilized catalyst state. [Pg.307]

Figure 12.9. Transient concentration profiles for die tubular chemical reactor wifli parameters of Listing 12.10. Figure 12.9. Transient concentration profiles for die tubular chemical reactor wifli parameters of Listing 12.10.

See other pages where Transient concentration profiles is mentioned: [Pg.138]    [Pg.122]    [Pg.385]    [Pg.31]    [Pg.63]    [Pg.74]    [Pg.188]    [Pg.194]    [Pg.198]    [Pg.412]    [Pg.179]    [Pg.195]    [Pg.209]    [Pg.232]    [Pg.290]    [Pg.372]   


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