Two-phase modelling of a fluid mixing layer

We analyse and improve a recently-proposed two-phase flow model for the statistical 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 equations admit a self-similar solution for an arbitrary scaling of lengths. We show that the constitutive law for v * 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 solution based on a simple zero-parameter model for v * . Closure of the two-phase flow model requires boundary conditions for the surfaces that separate the two-phase and single-phase regions, i.e. the edges of the mixing layer. We propose boundary conditions for Rayleigh-Taylor mixing based on the inertial, drag, and buoyant forces on the furthest penetrating structures which define these edges