Kinetics diffusion

EJ Lightfoot. Kinetic diffusion in polymer gels. Physica A 169 191-206, 1990. 

Figures 3 and 4 show the variation of the attachment coefficient with count median diameter for the diffusion, kinetic, hybrid and kinetic-diffusion theory for geometric standard deviations of 2 and 3 respectively.

The kinetic-diffusion approximation predicts an attachment coefficient similar to the hybrid theory for all CMDs and for both Og m 2 and 3 (Figs. 3 and 4). The advantage of this theory is that the average attachment coefficient can be calculated from an analytical solution numerical techniques are not required. 

The variation of attachment coefficient with Og for CMD =0.2 ym and 0.3 ym is shown in Figures 6 and 7. Again it is apparent that the kinetic theory or diffusion theory are correct only at certain CMD and og. Neither is applicable under all circumstances. It is also evident that the kinetic-diffusion theory is a good approximation to the hybrid theory under all circumstances. 

Unattached fractions of RaA (at t = °°) for two mine aerosols and for a typical room aerosol are shown in Table III. It is usually assumed that the attachment of radon progeny to aerosols of CMD < 0.1 ym follows the kinetic theory. In Table III it is apparent that the hybrid and kinetic theories predict similar unattached fractions for monodisperse aerosols. However, for more polydisperse aerosols, the kinetic theory predicts lower unattached fractions than the diffusion theory and thus the diffusion theory is the more appropriate theory to use. It is also evident that the kinetic-diffusion approximation predicts unattached fractions similar to those predicted by the hybrid theory in all cases. 

Although the hybrid theory is the most correct theory to use in the prediction of unattached fractions, the error in using the kinetic-diffusion theory in place of the hybrid is small. The kinetic-diffusion theory has the advantage that the solution is in analytical form and thus is more convenient to use than the hybrid theory, which must be solved numerically. 

Figure 14 shows a schematic representation of a mixed potential diagram for the electroless deposition reaction. Oxidation of the reductant, in this case hypophos-phite, is considered to be under 100% kinetic control. A mixed kinetic-diffusion curve is shown for the reduction of the metal ion, in our case Co2+, in the region close to the mixed potential, Em. Thus, since Co deposition occurs under a condition of mixed kinetic and diffusion control, features small relative to the diffusion layer thickness for Co2+ will experience a higher concentration of the metal ion, and hence... 

The total output photovoltage must exceed the thermodynamic potential difference for water splitting (1.229 V at 25°C), the energy level mismatches for the anodic and cathodic processes, and the polarization loss or overvoltages due to kinetic, diffusion, and IR potential losses in the bulk of electrolyte. 

Cell Voltage - For an identical stack the overall cell voltage will be lower as temperature decreases due to the decreased kinetics, diffusion, and ionic conductivity versus the improved electrical conductivity which typically does not dominate the cell polarizations. This is partially but not fully offset by the increased theoretical open circuit voltage of the electrochemical reaction at the lower temperature. 

This kinetic-diffusion problem in the steady state can be described by the coupled second-order differential equations ... 

X 10 M s . This illustrates the degree to which electrostatic interactions can change a reaction from a diffusion-limited process to one that involves other types of protein-ligand interactions. See Chemical Kinetics Diffusion-Limited Reaction... 

ENCOUNTER-CONTROLLED RATE DIFFUSION-LIMITED REACTION CHEMICAL KINETICS DIFFUSION OF LIGAND TO RECEPTOR DIFFUSION OF MOLECULES INTO A PORE... 

On the basis of the Hatta number, the transformations carried out in biphasic systems can be described as slow (Ha < 0.3), intermediate (with a kinetic-diffusion regime 0.3 < Ha < 3.0), and fast (Ha > 3). These are diffusion limited and take place near the interface (within the diffusion layer). Slow transformations are under kinetic control and occur mostly in a bulk phase, so that the amount of substrate transformed in the boundary layer in negligible. When diffusion and reaction rate are of similar magnitude, the reaction takes place mostly in the diffusion layer, although extracted substrate is also present in the continuous phase, where it is transformed at a rate depending on its concentration [38, 50, 54]. 

Modern Methods in Kinetics Diffusion-limited Reactions... 

Adsorption Kinetics Diffusion and Kinetic Controlled Models... 

Agrawal, R., Kinetics Diffusion in Hydrodemetallation of Nickel and Vanadium Porphyrins. Sc.D. thesis, MIT, 1980. 

The high isomer selectivity observed for ZSM-5 can be further enhanced by imposing kinetic diffusion-al effects upon the thermodynamic selectivity, thereby magnifying the preference for p-xylene sorption (1 ). ... 

Kinetics, Diffusion Continuous stirred tank reactor (CSTR) Plug-flow reactor (PFR) ... 

Based on Eq. (4.4), the enhancement factor E is defined as the enhancement on the maximum flux J"max of a drug across skin by increasing the (kinetic) diffusivity and/or the (thermodynamic) solubility in the stratum corneum.79 Thus... 

Modern Methods in Kinetics Diffusion-limited Reactions Electrode Kinetics Principles and Methodology Electrode Kinetics Reactions Reactions at the Liquid-Solid Interface... 

N. L. Thompson, A. W. Drake, L. Chen, and W. V. Broek, Equilibrium, kinetics, diffusion and selfassociation of proteins at membrane surfaces Measurement by total internal reflection fluorescence microscopy, Photochem. Photobiol. 65, 39-46 (1997). 

FIGURE 1.21 An example of a complex-plane impedance plot (Nyquist plane) for an electrochemical system under mixed kinetic/diffusion control, with the mass transfer and kinetics (charge transfer) control regions, for a finite thickness 8N of the diffusion layer. Assumption was made that Kf Kh at the bias potential of the measurement, and D0I = Dmd = D, leading to RB = RCT (krb8N/ >). 

Different forms of the impedance plots can be obtained for an electrochemical system described by a mixed kinetic/diffusion control process, depending on the parameters of diffusion and charge transfer. An example of a Nyquist plot is presented in Figure 1.21. 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

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