An interface constitutive modeling problem for compressible flows with mass transfer

It is well known that the characteristic equations in any hyperbolic system give a complete picture of the required boundary conditions or interface shock conditions. In this paper, the limiting form of a set of characteristic equations will be used to determine the nature of the phasic interface conditions that are required in a compressible, viscous, conducting fluid at a mass transfer interface. The analysis will show that the traditional interface modeling constitutive equations are insufficient in number and hence lead to multiple solutions and therefore to an ill-posed problem. The source of the insufficient number of interface conditions will be discussed.