Surface properties and stability of shock waves in gases

Abstract

The boundary conditions on a curved shock wave are obtained from the laws of conservation of mass, energy, and momentum, ahead of the shock front, in the shock layer, and behind the shock front. They differ from the well-known conditions, allowing for the viscosity of the gas and heat conduction, in having extra terms, proportional to the shock-front curvature, the main extra term being the surface pressure with the surface tension. It must be said that, if the surface tension on the equilibrium inter-phase surfaces is linked with the anisotropy of the mean virial of the inter-molecular interaction force, then it is determined in the shock wave by the anisotropy of the viscous stresses in the shock layer and reaches a value 1 N/m at M 0 = 10 and 10 N/m at M 0 = 30. By taking account of surface tension when analysing the stability of a plane shock wave with respect to weak disturbance of the surface of discontinuity, we arrive at absolute instability of the mode of spontaneous sound radiation, which has previously been regarded as neutrally stable.