Instantaneous diffusion

The increase of thus induces a macroscopic creep under constant stress. Assuming an instantaneous diffusion of the solute within the pore space, the mechanical affinity is Am —psij/el. The strain concentration effect at the crack tip then implies that the dissolution process concentrates at this place and is negligible elsewhere. The rate of crack radius increase a is derived from (22) and gives the evolution f(t) of the damage parameter ... 

A spin-A spin interaction. The fluctuation of the precession frequency is also induced by the microwave pulses used for the excitation and the refocussing the microwave pulses induce the transition betwen a and p spin states, so that the magnetic interaction of a particular A spin with other A spins is changed instantaneously during the second microwave pulse of the ESE measurements. The relaxation process due to the thus-created fluctuation is called instantaneous diffusion. The relaxation rate due to the instantaneous diffusion depends on the distance between the A spins and the number of the A spins. Because the concentration of the A spin depends on the intensity of the microwave pulse, the rate of the instantaneous diffusion also depends on the intensity of the microwave pulse this process can be eliminated in the ESE experiments by lowering the power of the microwave pulses. When the instantaneous diffusion is the dominant process in the phase relaxation, this provides us with a means of studying the local spatial distribution of radical species [13],... 

In solving the equations for AN and A/, we can take diffusion of the enantiomers into account by averaging the concentrations over the sample length after every iteration step, so that the incident unpolarized light always feels a completely homogenous solution. In this way we mimic the extreme case of infinitely fast diffusion. We take the first-order result without diffusion and then assume instantaneous diffusion such that the -dependence of AN/N is averaged out ... 

If the Faraday constant is included in the numerical value the instantaneous diffusion current is... 

Echo detection of selectively-burned holes in photosynthetic systems led to estimates of distances between 25 and 50 A. If the contributions to spectral diffusion from motion, nuclear spin flip-flops, and instantaneous diffusion are smaller than the contribution from dipolar interaction between unpaired electrons, the spectral diffusion can be used to determine the interspin distance. (97-100). 

Instantaneous diffusion oo-approach) model assumes that the catalyst is virtually distributed at the gas/washcoat interface so that there is infinitely fast mass transport within the washcoat. This model eliminates the washcoat parameters, such as its thickness and porosity, and the diameters of the inner pores. Therefore, oo-approach does not account for internal mass transport limitations that are due to a porous layer. It means that mass fractions of gas-phase species on the surface are obtained by the balance of production or depletion rate with diffusive and convective processes (Deutschmann, 2008 Kee et al., 2001 Wamatz, 1992). Thus, the net production rate of each chemical species due to surface reactions can be balanced with the diffusive flux of that species at the gas-surface boundary, assuming that no deposition or ablation of chemical species occurs on/from the catalyst surface ... 

Einally, pulsed EPR experiments in solids allow determination of spin-lattice relaxation and phase memory times (Ti, Tm), whose dependence on temperature and nature of the environment can be analyzed to give information on the collective relaxation phenomena due to nuclear spin diffusion, electron-electron dipolar interaction, and instantaneous diffusion [9]. Note that the electron-electron dipolar interaction is also exploited in the DEER (PELDOR) technique for measuring the distance between paramagnetic centers. Instantaneous diffusion can give information on the microconcentration of radicals produced by high-energy irradiation in solids [e.g., 10]. 

For close systems with instantaneous diffusion, steady states are either stable or unstable depending on whether the solid phase consists in a single grain or in N grains (N>1). For open systems and uniform liquid phases, steady states are unstable saddle-points. For close systems with diffusion, results are similar to the first case ones. For open systems with diffusion, steady states are unstable and uniform. 

Instantaneous diffusive molar flux of species s in mixture (kmol/m s)... 

Generalized velocity vector in property space Bubble velocity vector in sample i measured by PDA (m) Instantaneous diffusion velocity for species c, relative to the local motion of the mixture stream (m/s)... 

Fig. 2 Electron spin T2 times for Si crystals with three different donor densities after extrapolating to the limit of zero duration refocusing pulse to remove instantaneous diffusion. The coherence time of the lowest concentration sample was further extended by applying an external magnetic field gradient to suppress donor flip-flops. Reprinted with permission from Macmillan Publishers Ltd A. M. Tyryshkin et a/.. Nature Materials, 2012, 11, 143, copyright 2012.

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