Diffusional relaxation

Let us emphasize that as a result of scaling t with the characteristic hydrostatic time to 260 sec long as compared with that of diffusional relaxation time L2/D 10 sec, D emerges in the system (6.3.9)-(6.3.15) as a large parameter. 

Figure 2.8 Diffusional relaxation following momentary creation of a vacancy at an inert barrier. Semi-infinite conditions prevail. Density map and concentration-distance profiles are shown, (a) Initial condition (b) vacancy creation (c) vacancy extends farther into bulk of medium (d) relaxation begins (e) relaxation continues (f) relaxation continues (g) initial condition restored.

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

The presence of the film decreases the amplitude of the response to the flow perturbation. If the film develops over time, then the film thickness can be calculated, knowing SD from the characteristics of the flow. Furthermore, the relaxation time for the composite system is the sum of the two diffusional relaxation times ... 

Fig. 4K is discussed later. Suffice it to note here that the relaxation time for the activation-controlled process is inversely proportional to the exchange current density while x, the diffusional relaxation time, is independent of i. Thus, a large value of x /x indicates that the electrode reaction is slow, and vice versa. 

It is convenient to define also a diffusional relaxation time X which... 

The rate of diffusion depends primarily on the product Since the diffusion coefficient in simple lutions does not usually vary by more than an order of magnitude, e reach the rather obvious conclusion that the diffusional relaxation time depends primarily on the concentrations of the reactant and the product. If the product... 

Kinetic phenomena can also be used to delimit the timescales of magmatic processes and, unlike radiometric ages, do not require absolute constraints on the timing of eruption. Two important kinetic controls on crystal properties are crystal growth and diffusional relaxation of compositional heterogeneities in minerals. Rates of crystal settling are not described here but have also been used to delimit crystal storage times (e.g., Anderson et al., 2000 Resmini and Marsh, 1995). 

When diffusional relaxation of a suspension brought out of equilibrium by shearing is slow with respect to the time-scale of the process (De number), the suspension is said to be thixotropic. This behaviour is illustrated in Fig. 6.21. Thixotropy is usually imwanted in ceramic membrane support coatings, but does occur for some suspension formulations. The layer thickness obtained in film-coating with the same suspension but with a different shear history can then differ. 

The gating period ( 1 ns) is much shorter than the diffusional relaxation time of the enzyme-substrate system [t = R /D (402)/100 = 16 ns, where... 

Figure 9 illustrates the relaxation of EPL after turning off the electrical field at 40 and 80 V/cm. The field free diffusional relaxation at 80 V/cm is also shown in the presence of dextran. The time dependence of the EPL after termination of the prepulse indicates that the diffusional recovery is independent of the polarizing field intensity or of the viscosity of the solution. 

Figure 9. Diffusional relaxation of prepolarization. The time course of repopulation of the depleted poles by PSI. The depletion accomplished by prepulses of the amplitudes 40(0), 60 (%), and 80 (n) V/cm in the absence of dextran and 80 (m) V/cm in the presence of 4% dextran. (Reproduced with permission from reference 20. Copyright 1989 Biophysical Society.)...

The initial concentration distribution obtained from reference 11 for the different values of a can be obtained from eq 7 for different values of E. The equation for the diffusional relaxation is given by... 

Figure 10. Diffusional relaxation calculated by eq 10 taking EPLt proportional to re = 01 (at the depleted poles of the vesicles) for the following values of D and a D = 3 X 10 9, a = 0.375, dashed line D = 5 X 10 9, a — 0.8, dotted line D = 5 X 10 9, a — 0.375, solid line D = 6 X 10 9, a — 0.375, dash-dot line. The rectangles encompass the experimental points from Figure 9 after multiplying the ordinate by 1.25 to account for the incomplete recovery by setting EPLt=ao = EPL0 (without prepulse). (Reproduced with permission from reference 20. Copyright 1989 Biophysical Society.)...

Figure 13, continued (f Composition profiles of the monazite in (b) along the line A-B. fg) Composition profiles of the monazite m (c) along the line A -B. Note the sympathetic zoning of Pb with Th and U and Si + Ca with Th and U. Also note the sharp gradients in all elements indicating very little diffusional relaxation. ... 

The experimental data following the evaporation to dryness (Days 68, 69) showed a continuation of excess power that gradually decreased, as would be expected for a process controlled by a diffusional relaxation time for deuterium inside the palladium. The cooling of this cell was also slower than expected, and there was at least one period (Day 69) during which the cell contents reheated with no apphed electrochemical or heater power [31, 33]. Illustrations of these effects are shown in Ref. [31] (Figures A22, A23, and A24). 

On the other hand, a step decrease in feed hydrogen resulted in a relatively very rapid and monotonic decline to the final steady-state ethylene concentration. It should be noted that the sum of all hydraulic and mixing lags for this system is of the order of 75 s and the diffusional relaxation time (R /Dg) is much smaller than one second. Hence, the extremely slow response observed in the step-up experiment and its asymmetry compared to the step-down result suggest that non-linear dynamics of the gas phase-catalyst surface interaction play a major role in unsteady reactor behavior. 

Lucassen-Reynders EH, Cagna A, Lucassen J (2001) Gibbs elasticity, surface dilational modulus and diffusional relaxation in nonionic surfactant monolayers. Colloid Surf A 186(l-2) 63-72... 

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