Two-phase modelling of a fluid mixing layer

We analyse and improve a recently-proposed two-phase how model for the stat istical evolution of two-fluid mixing. A hyperbolic equation for the volume fraction, whose characteristic speed is the average interface velocity v*, plays a central role. We propose a new model for v* in terms of the volume fraction and fluid velocities, which can be interpreted as a constitutive law for two-fluid mixing. In the incompressible limit, the two-phase equati ons admit a self-similar solution for an arbitrary scaling of lengths. We s how that the constitutive law for u* can be expressed directly in terms of the volume fraction, and thus it is an experimentally measurable quantity. For incompressible Rayleigh-Taylor mixing, we examine the self-similar solu tion based on a simple zero-parameter model for v*. It is shown that the pr esent approach gives improved agreement with experimental data for the grow th rate of a Rayleigh-Taylor mixing layer. Closure of the two-phase flow model requires boundary conditions for the su rfaces that separate the two-phase and single-phase regions, i.e. the edges of the mixing layer. We propose boundary conditions for Rayleigh-Taylor mi xing based on the inertial drag, and buoyant forces on the furthest penetra ting structures which define these edges. Our analysis indicates that the c ompatibility of the boundary conditions with the two-phase flow model is an important consideration. The closure assumptions introduced here and their consequences in relation to experimental data are compared to the work of others.