Mathematical model of finite amplitude wave propagation in chemically active aerocolloids

In a chemically reactive medium, amplitude of the wave can increase during its propagation through the media. It is shown that the rate of the wave intensification depends on the heat being released from the chemical reaction between the aerocolloid phases and value of losses due to the interphase exchange processes. Depending on the rate of the heat emission from chemical reaction, the evolution of the perturbed wave profile can lead to the formation of a wave similar to the shock wave if the losses are not prevailing over this emission. The mathematical model of finite amplitude wave propagation in aerocolloids with chemical reaction is studied in this paper. The equations describing the evolution of arbitrary wave disturbances of finite amplitude velocity (density, or temperature) perturbations have been developed, with correction for heat transfer and momentum exchange between the phases under significantly unsteady conditions and also with possibility to initiate the chemical reaction. A single equation describing the evolution of the finite amplitude wave in chemically reactive media is obtained. The resulting equation incorporates the amplitude of the perturbation and also the energy of chemical reaction source as well as interphase exchange terms. Similar equations could be obtained for any aerocolloid properties. These formulae are valid for description of the evolution of waves at any ratio between the time of the internal process and the characteristic period of perturbation. Because of the interaction between the particles and surrounding gas, the finite amplitude wave is dissipative if there is no chemical reaction activated. It will be also shown that the rate of dissipation is limiting the activation of the chemical reaction in the media. In the case of a chemically reactive medium, the amplitude of the wave could be increasing during its propagation through the media. It is shown that the rate of the wave intensification depends on the heat being released from the chemical reaction between the aerocolloid's phases and also on the interphase exchange processes. Depending on the rate of the heat emission from chemical reaction, the evolution of the perturbed wave's profile can lead to the formation of a wave similar to the shock wave. Depending on the rate of dissipation of the wave amplitude, different scenarios of the wave evolution are possible. These scenarios are considered in the paper.