Global Solutions of a Viscous Gas-Liquid Model with Unequal Fluid Velocities in a Closed Conduit

Abstract

We consider a compressible gas-liquid drift-flux model with a general slip law commonly used to describe realistic two-phase flow scenarios. The slip law will introduce a difference in the magnitude of the two fluid velocities, and they possibly will also have different sign. This allows the model to describe the effect of buoyant forces, for example, in a vertical conduit, where heavy liquid will move downward due to gravity whereas light gas will be displaced upwardly. Combining the two mass equations and the mixture momentum equation with the slip law, the model can be expressed in terms of the gas-fluid velocity and a generalized pressure function that depends on the common pressure and three new terms that depend on the liquid mass and the gas velocity. This generalized pressure function introduces new nonlinear effects and coupling mechanisms between the two mass equations and the mixture momentum equation which require careful refinements of techniques previously used for the analysis of the classical Navier--Stokes model. In this work we discuss global existence and uniqueness of strong solutions considered in a closed one-dimensional conduit subject to appropriate smallness assumptions and regularity assumptions on the initial data. The analysis provides insight into the special role played by the slip parameters. This work presents a first global existence result for the drift-flux model with a general slip law.