An Analytical Study of Hydrodynamic Instability in the Flame. 1. Viscous Gas in the Flame Zone

The problem of the hydrodynamic stability of slow combustion is analytically solved with consideration given to the viscosity of the gas in the flame zone, the temperature dependence of the viscosity, and the dependences of the flame speed on the front curvature according to the Markstein model and on the pressure. The viscous forces in the flame zone alone cannot ensure the stability of the flame at any values of the Reynolds number. These forces act only as amplifiers of the stabilizing factor according to the Markstein model or in the case of a negative dependence of the flame velocity on the pressure. This property of internal friction forces is the more pronounced, the stronger the viscosity increases with the temperature. Thermal expansion is not only a destabilizing factor, leading to an increase in viscosity and other transport coefficients, but also produces a stabilizing effect.