PSI - Issue 40

S.A. Filin et al. / Procedia Structural Integrity 40 (2022) 153–161

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S. A. Filin at al. / Structural Integrity Procedia 00 (2022) 000 – 000

0 / ( С K     . )

C

(5)

For the reaction rate under stationary conditions, we obtain at α = 1:

0 j K C  

(6)

,

where

* K К

К     .

(7) If in equation (7) K  β , then K* ≈ β , and the concentration of the active soluble component on the surface will be much less than its concentration in the bulk:

0 0 C C / K C    .

(8)

In this case, the rate of the total process ( jD 1 pr. ) is entirely determined by the rate of diffusion and is equal to the limiting diffusion flow:

. 0 1 pr jD C   .

(9) Equation (9) is valid when irreversible reactions occur in the diffusion region without taking into account the transport of products (in the reaction zone, their concentrations are constant). In the case of a reversible reaction, a concentration corresponding to thermodynamic equilibrium is established near the surface. In the absence of such an equilibrium for simple dissolution reactions, which are reduced only to the formation of solvates on the surface and their removal into the solution, the limiting diffusion flux is determined by an expression similar to the Nernst equation (stationary state): where C ss is the concentration of a saturated solution. Thus, in the diffusion region, the linear diffusion coefficient β, which depends not only on the physical properties of the solution, but also on the hydrodynamic conditions of the interaction of the contamination particle with the environment that surrounds it, is the rate constant of the true kinetic reaction. Unfortunately, even in those cases, when interphase surface is approximately considered as equally accessible, it is impossible to give a quantitative estimate of the dissolution rate according to equations (3, 4). This is explained by two circumstances: 1) there is no reliable data to judge the intensity of the diffusion process in the "ideal mixing" mode (the so-called reactor with a stirring device); 2) the total surface area of polydisperse particles of arbitrary shape can be estimated very approximately, especially when the degree of dissolution is above 10-20% (Maksimov et al. (1994)). The transitional regime between the cases of "perfect mixing" and "perfect displacement", due to the multifactorial nature of the process, is not yet amenable to correct calculation. For calculations of washing and cleaning processes and machines, used to clean optical elements, it is necessary to know the functional dependence of the cleaning speed (the amount of contaminations removed from the surface per unit of time) on time. This dependence, as shown in this study, is extremely complex and analytical methods for its determination have not yet been found. Dissolution of contaminants in industrial conditions is usually carried out in a reactor with intensive stirring ("perfect mixing" mode, creating a state of developed turbulence). In this case, the time of complete dissolution is determined by the formula: . pr ss jD C C    , 0 1 ( ) (10)