Diffusion regime of reaction

We divide both sides of (3.1.13) by ks and let the parameter ks tend to infinity. As a result, we arrive at the limit boundary condition (3.1.10), corresponding to the diffusion regime of reaction. This passage to the limit adequately illustrates the notion of an infinitely rapid reaction, which was used previously. 

Obviously, from the mathematical viewpoint, problem (3.1.33), (3.1.34) describing the body-medium heat exchange is identical to problem (3.1.8)—(3.1.10) describing the flow-particle mass exchange in the case of a diffusion regime of reaction on the particle surface. 

Further, following [419], we consider in detail another mechanism of the surface tension variability produced in the process of motion. We consider a drop moving at a constant velocity, on whose surface an exothermic or endothermal reaction is involved. It is assumed that a surfactants takes part in the reaction being dissolved in the surrounding liquid. Let the liquid temperature and the concentration of surfactants be constant remote from the drop, while on the interface, the concentration of the surfactants (the reactant) is zero (the diffusion regime of reaction). In this symmetric situation, the temperature variability, and, consequently, the thermocapillary stresses can be produced only in the process of motion of liquids. 

Remark. The problem of mass transfer to a drop for the diffusion regime of reaction on its surface under the conditions of thermocapillary motion is stated in the same way as in its absence (see Section 4.4) taking into account the corresponding changes in the fluid velocity field. In [144], a more complicated problem is considered for the chemocapillary effect with the heat production, which was described in [147-149,419], It was assumed that a chemical reaction of finite rate occurs on the drop surface. 

A -h B 0 reaction (provided equal reactant concentrations). Peculiarity of the diffusion-controlled regime of reaction is the existence of the marginal space dimensionality do-... 

At long times of annealing, according to the generally accepted theory, three stable flat phase layers must grow with the parabolic law Xi = Quite often real experiment reveals, however, a different behavior - either one stable phase or a metastable crystal or an amorphous layer is formed. Thus, phases compete with each other like different regimes of reaction-diffusion. 

Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control.

An important parameter characterizing the laminar regime is the intersegment spacing over which the species must diffuse to be able to react. For kinetic control, as opposed to diffusion control of the reaction, this spacing must not exceed a certain scale of segregation given by [53J ... 

The concept of reaction diffusion (also called residual termination) has been incorporated into a number of treatments.7 7 Reaction diffusion will occur in all conversion regimes. However at low and intermediate conversions the process is not of great significance as a diffusion mechanism. At high conversion long chains are essentially immobile and reaction diffusion becomes the dominant diffusion mechanism (when i and j are both "large" >100). The termination rate constant is determined by the value of kp and the monomer concentration. In these circumstances, the rate constant for termination k - should be independent of the chain lengths i and j and should obey an expression of the form 75... 

The possibility that adsorption reactions play an important role in the reduction of telluryl ions has been discussed in several works (Chap. 3 CdTe). By using various electrochemical techniques in stationary and non-stationary diffusion regimes, such as voltammetry, chronopotentiometry, and pulsed current electrolysis, Montiel-Santillan et al. [52] have shown that the electrochemical reduction of HTeOj in acid sulfate medium (pH 2) on solid tellurium electrodes, generated in situ at 25 °C, must be considered as a four-electron process preceded by a slow adsorption step of the telluryl ions the reduction mechanism was observed to depend on the applied potential, so that at high overpotentials the adsorption step was not significant for the overall process. 

Consider first the diffusion-limited regime. The simplest experiment to perform is a chronoamperometric measurement, i.e. to monitor the current after a potential step to a value where an electroactive species will undergo electron transfer. This effectively allows us to monitor the rate of reaction, v, as a function of time, through the relationship ... 

When diffusion of oxygen in the polymer occurs rapidly (Ak 1), we observe the kinetic regime of polymer oxidation (see Equation [13.16]). When penetration of oxygen into polymer is slow, the reaction rate v KXp02. 

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