Contents Online
Communications in Mathematical Sciences
Volume 18 (2020)
Number 5
Thermodynamically consistent hydrodynamic models of multi-component compressible fluid flows
Pages: 1441 – 1468
DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n5.a11
Authors
Abstract
We present a systematic derivation of thermodynamically consistent hydrodynamic models for multi-component, compressible viscous fluid mixtures under isothermal conditions using the generalized Onsager principle and the one-fluid multi-component formulation. By maintaining momentum conservation while enforcing mass conservation at different levels, we obtain two compressible models. When the fluid components in the mixture are incompressible, we show that one compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several different approaches to arriving at the quasi-incompressible model are discussed. Finally, we conduct a linear stability analysis on all the binary fluid models derived in the paper to show the differences of the models in near equilibrium dynamics.
Keywords
compressible fluid, quasi-incompressible fluid, multi-component fluid mixtures, phase field model, linear stability
2010 Mathematics Subject Classification
35Q30, 35Q35, 35Q79
Received 25 January 2019
Accepted 14 March 2020
Published 23 September 2020