Theoretical studies of the implementation of possible types of stationary states for a countercurrent liquid–liquid plug reactor are carried out. States such as a stable node and focus, and an unstable focus with a stable limit cycle (oscillations) are found. Using these data, the evolution of stationary states with continuous changes in the external control parameters is studied. When the relationship between the flow rates of the phases changes, a structure of stationary states, which can be realized both at the entrance and exit of the dispersion medium, is found.

A mathematical model of an exothermal chemical transformation in a concurrent plug reactor is formulated. A criterion for the independence of the interaction of bubbles (drops) when they move in a dispersion medium is determined. A numerical analysis of the dynamics of the reactor reaching a steady operating mode is carried out. It is shown that the reactor reaches a steady mode through the maximum heating of the dispersion medium. With the increase in the parameter characterizing the independence bubbles, the difference between the maximum heating of the dispersion medium and the maximum heating of the steady mode decreases and, at large values of it, practically disappears. For a two-stage concurrent reaction, it is found that in the reactor, depending on the control parameters, the steady state can be realized in two modes: high-temperature and low-temperature. In this case, the transition to the steady mode occurs through the high-temperature state.

Mathematical models of the dynamic behavior of a multivelocity heterogeneous reacting medium in a plug flow reactor are formulated. The correctness of the mathematical model is studied. A particular analytical solution of the system is obtained, which can be used as a test to check the accuracy of the numerical solution of the model system. The possibility of extending this modeling technique to more complex regimes of exothermic chemical interaction in multivelocity mixed media is shown. A numerical study of the oscillatory regime of the displacement reactor is carried out.

Сформулированы математические модели динамического поведения многоскоростной гетерогенной реагирующей среды в проточном реакторе вытеснения. Исследована корректность математической модели. Получено частное аналитическое решение системы, которое может использоваться в качестве теста для проверки точности численного решения модельной системы. Показана возможность расширения данной методики моделирования на более сложные режимы экзотермического химического взаимодействия в многоскоростных смесевых средах. Проведено численное исследование колебательного режима реактора вытеснения.

The mechanism and evolution of the oscillatory modes are studied for a single high-temperature stationary state of a flow-through reactor of ideal mixing with a heterogeneous reacting liquid–liquid system, with a change in the wide range of the parameter that determines the stability of the stationary state but does not affect its position. It is shown that of the two possible mechanisms for the creation of oscillations, soft and hard, in our case the latter is realized. In the region of a stable focus, oscillations of a finite amplitude immediately appear. The source of a stable limit cycle (mathematical image of oscillations) is a semistable limit cycle.

The types of the steady states for a continuous stirred-tank reactor are studied depending on the process parameters, in particular, a parameter not affecting the position of the steady states, by way of example of a liquid–liquid heterogeneous system, in which an exothermic reaction proceeds. It is shown that the change in the coarse steady states occurs through degenerate steady states.

Для гетерогенной системы жидкость-жидкость, в которой протекает экзотермическая реакция, исследованы топология и устойчивость стационарных состояний проточного реактора идеального смешения. Показано, что тепловой эффект реакции, величина энергетического барьера и интенсивность массопереноса сильно влияют на тип структуры возникающего стационарного состояния. При этом изменение топологической картины происходит через вырожденные стационарные состояния.

For a heterogeneous liquid - liquid system in which an exothermal reaction takes place, the topology and stability of the steady states of CSTR are investigated. It is shown that the thermal effect of the reaction, the magnitude of the energy barrier and the intensity of mass transfer strongly influence the type of steady state that arises. In this case, a change in the topological picture occurs through degenerate steady states.

A mathematical model of the dynamic behavior of a heterogeneous liquid-liquid reaction system in a plug flow reactor is formulated. Numerical investigation of the oscillatory instability of the reactor is carried out. The region of oscillatory regimes in a parametric space is examined for the Semenov parameter — the temperature at the entrance to the reactor. A hard birth of low-frequency high-amplitude oscillations is detected. The death of these oscillations and occurrence of high-frequency low-amplitude oscillations is analyzed. A model of this phenomenon based on the classical theory of stability of systems described by systems of ordinary differential equations is proposed.

The process of obtaining and micronization of polymeric materials using an original method of nonisothermal polymerization in the medium of supercritical fluid is investigated. Polystyrene microparticles and fibers are synthesized. The influence of the conditions of the microdispersion process on the morphology of the isolated product is evaluated.

A plug flow reactor operating on a heterogeneous liquid−liquid system in which an exothermic bimolecular reaction takes place is modeled. The effect of the main governing parameters (Peclet and Damkheler numbers and a dimensionless parameter P characterizing mass transfer between the liquid phases) on the thermal modes of the reactor is examined. Depending on the values of these parameters, one or three steady states can be realized in the reactor. It is established that, with increasing parameter P, the region of multiplicity of steady states expands and shift toward lower values of the Damkohler number. The phenomenon of hysteresis is observed in the region of multiplicity of steady states.

In this paper, the regularities of a thermal explosion of a heterogeneous system consisting of two immiscible liquids have been studied. Each phase is a solution of A and B reagents. Reagent B is extracted into a solution of reagent A, where the bimolecular exothermic reaction A + B → Products takes place. It has been shown that an exothermic reaction (combustion regime) continues to proceed in the system at high mass-exchange rates between phases after a thermal explosion. As a result, the maximal temperature may significantly exceed the temperature of the thermal explosion. The critical value of the Semenov parameter decreases with an increase in the mass-exchange rate between phases. In the limited range of values of the distribution coefficient of reagent B between phases, the increase of this coefficient is also accompanied by a decrease in the critical value of the Semenov parameter. The concentration of reagent B in the initial phase decreases monotonically due to its extraction into another phase. However, the equilibrium of the extraction of reagent B can shift, due to the temperature dependence of the distribution coefficient during the reaction. Thus, the time dependence of the concentration of reagent B on may be more complex and can pass through a minimum.

The thermal modes of a flow plug reactor with an exothermic chemical reaction are numerically simulated. A heterogeneous reaction system consisting of two immiscible liquids is studied: one of the liquids (dispersed phase) in the form of droplets is distributed in the other (dispersion phase). The characteristics of the thermal modes of the reactor at various values of two governing parameters, the Damköhler number and the rate of extraction of the dissolved substance from the dispersed phase into the dispersion phase is examined. Two modes of chemical reaction in the reactor are demonstrated to be possible: low-temperature and high-temperature. Critical criteria of thermal ignition are formulated. The dependence of the structure of the thermal wave on the governing parameters is investigated.

The physical concepts and the results of the thermal theory of combustion are used as a basis for the qualitative analysis and mathematical simulation of transformation of stationary temperature distributions along the length of an adiabatic reactor in the case of periodic perturbations of the velocity of the reagent in the reactor and its temperature at the entrance of the reactor. It is established that, with certain values of the amplitude and frequency of harmonic perturbations of the velocity of the reagent, it is possible to improve the thermal stability of the process (increase the pre-explosion heating).