Kinetic of diffusion

The kinetics of diffusion-controlled phase transformations has long been a focus of research and it is vital information for industrial practice as well as being a fascinating theme in fundamental physical metallurgy. An early overview of the subject is by Aaronson et ai (1978). 

When studying the kinetics of diffusion of hydrogen through palladium, Farkas (28) noticed the difference in catalytic activity of both sides of the palladium disks or tubes for the parahydrogen conversion the energy of activation was greater on the inlet side than on the outlet side, where due to extensive desorption of the hydrogen its concentration could be lower. 

I.M. Lifshitz and V.V. Slyozov Kinetics of Diffuse Decomposition of Supersaturated Solid Solutions. Soviet Physics JETP35, 331 (1959). 

The epithelium, the most superficial cellular layer of the cornea of the eye, is chemically less resistant than the keratinized epidermis of the skin. However, during ocular accidents, we know that it takes a few seconds for the first lesions to appear. This delay is bound to multiple factors, winking reflex, protective and diluting effect of the lachrymal liquid, effect of sweeping of the palpebral movements. After a short period, a kinetic of diffusion will set up in a variable way according to the nature of the corrosive. 

A.A. Ovchinnikov, S.F. Timashev and A.A. Belyi, Kinetics of Diffusion-Controlled Chemical Processes (Nuova Science, New York, 1988). 

The black sphere approximation permits us to obtain the most simple and physically transparent results for the kinetics of diffusion-controlled reactions. We should remind that this approximation involves a strong negative correlation of dissimilar particles at r ro, where Y(r, t) = 0, described by the Smoluchowski boundary condition... 

Fig. 5.12. The kinetics of diffusion-controlled recombination riA(f) for d = 2. Initial lattice densities pa(0) = Na/N = pb(0) = 0.4 on a lattice with N = 1000 x 1000. Solid curve - computer simulations, broken line - the superposition approximation, dotted line - linear approximation. Time is in units r (waiting time in a site).

KINETICS OF DIFFUSION-CONTROLLED REACTIONS OF MOBILE NON-INTER-ACTING PARTICLES... 

NMR imaging is becoming increasingly acknowledged as an important tool for the study of the structure of polymeric materials [47-54], including the kinetics of diffusion of small molecules. In many cases details of the kinetics of diffusion are only discernible from a knowledge of the concentration profile of the solvent in the swelling polymer. 

Although the previous equation signifies the importance of the diffusion characteristics of the reactant species, it cannot be used to describe adequately the rate of the reaction. The reason is that the concept of global concentrations for the riA and ng molecules is meaningless, since a unit volume cannot be conceived due to the local fluctuations of concentrations. Hence, the local concentrations of the reactants determine the rate of the reaction for diffusion-limited reactions. Accordingly, local density functions with different diffusion coefficients for the reactant species are used to describe the diffusion component of reaction-diffusion equations describing the kinetics of diffusion-limited reactions. 

DeGennes, P., Kinetics of diffusion-controlled processes in dense polymer systems I. Nonentangled regimes, Journal of Chemical Physics, Vol. 76, No. 6, 1982, pp. 3316-3321. 

Waite, T. R. Theoretical Treatment of the Kinetics of Diffusion-Limited Reactions. Phys. Rev. 107, 463 (1957) Diffusion-Limited Annealing of Radiation Damage in Radium. Phys. Rev. 107, 471 (1957). 

---