Flow of a viscous dispersing gas-air mixture due to a sudden release of gas into the mine atmosphere

Mining of coal deposits leads to forming outburst-prone areas, which are prone to sudden emissions of coal, rock and gas into mine workings. These sudden outbursts can result in severe accidents that are often fatal. As a rule, outbursts occur at high speeds, sometimes exceeding the speed of sound. From the point of view of gas dynamics, a gas outburst is a disturbance that creates a shock wave in the quasi-stationary mine atmosphere, the intensity of which depends on the velocity of the outburst gas. The shock wave is capable of injuring miners, destroying the mine support and ruin mechanisms and technological equipment located in the vicinity of the outburst. In this regard, the problems of the gas-air mixture flow caused by a sudden outburst seem to be highly relevant, both from the scientific and practical point of view. This article considers the problem of the gas–air mixture flows with viscous and dispersive properties, described by the Korteweg–de Vries–Burgers partial differential equation, which closed-form solution is presented in the paper. Computational procedures were used as the basis to build the graphs that characterize the flow conditions of the gas-air mixtures at various parameters of their viscosity and dispersion. The graphs were analyzed and a number of patterns were revealed in the flow of the gas-air mixtures.