Usually, to simulate the operation of an insulating respirator, the problem of sorption dynamics is solved. The result obtained under the given initial and boundary conditions uniquely describes the evolution of impurity breakthrough through the filter. However, the coordinate of the elementary act of sorption is reliably unpredictable. Therefore, a probability-theoretic approach to modeling the workflow of an insulating respirator on chemically bound oxygen is possible. This publication is devoted to its further development.
An additional powerful resource is connected to the modeling of sorption dynamics in the form of the main theorems of the probability theory. The random coordinate of the elementary act of adsorption of the CO2 molecule, its dispersion, and the time of operation of the respirator are considered as a system of continuous, correlationally related random variables. Symmetry with respect to the permutation of the arguments of the conditional probability density of the coordinate of the elementary act of sorption is established for a given time value. It is shown that regardless of the critical breakthrough of the sorbitol, the period of the protective action of the filter is proportional to its length. With the help of the obtained correlation dependences, Chebyshev inequality and the condition of extremity of entropy, the normal asymptotic behavior of the evolution of the distribution law of the random coordinate of the elementary act of sorption and the related breakthrough of the sorbate through the filter is established. The limits of applicability of such asymptotics are substantiated.
The dependence of the dimensionless length of the filter, which is sufficient for the formation of the normal asymptotics of the sorption dynamics, on the level of critical impurity breakthrough was constructed. The minimum value of the critical breakthrough is indicated, which allows to use relations that reflect the normal asymptotics of the process to determine the period of the filter protective action.
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