Density functional modelling in multiphase compositional hydrodynamics

This work is essentially a review of a density functional approach in multiphase hydrodynamics developed by the authors during the last 15 years [Dinariev, J Appl Math Mech 1995;59(5):745–752; Dinariev, J Appl Math Mech 1998;62(3):397–405; Demyanov and Dinariev, Fluid Dynam 2004;39(6):933–944; Demianov et al., “Basics of the Density Functional Theory in Hydrodynamics,” Fizmatlit, Moscow; 2009 (in Russian); Dinariev and Evseev, Fluid Dynam 2010;45(1):85–95]. The basic assumption is a representation of the entropy or the Helmholtz energy of the mixture as a functional that is dependent upon chemical component densities. The hydrodynamic system of equations (local conservation laws for chemical components, momentum, and energy) is used to describe multiphase processes, and the constitutive relations (expressions for stresses, diffusion, and heat fluxes) are derived from entropy growth requirement. The authors present the results of numerical simulations describing static and dynamic multiphase systems.