Output details

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Significance of output:

Evolution of binary mixtures is defined by Cahn-Hilliard-Navier-Stokes equations. These are quasi-compressible equations: full continuity equation is required to describe evolution of two incompressible liquids, which makes numerical solution unfeasible. The Boussinesq approximations of these equations were earlier proposed, but were never strictly derived. Using multiple-scale method we separated fast quasi-acoustic and slow diffusive and convective processes and derived the low-Mach-number (Boussinesq) approximation of the full equations. The obtained equations represent a general model for the analysis of slow thermo- and hydro-dynamic evolution of multiphase systems with diffusing interfacial boundaries, i.e., for processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.