Compatibility of the generalized BMP model and the two-fluid Langevin formulations

Abstract

The main objective of this work is to demonstrate the agreement between the two-fluid linear Langevin formulation and that described by the extended irreversible thermodynamics (EIT). The two-fluid model, originally proposed by de Gennes, has been widely analyzed by many authors in various flow situations, especially to compare predictions with experimental data of the structure factor in many complex flows. The canonical Langevin equations together with the fluctuation-dissipation theorem ensure consistent thermodynamic behavior for constitutive equations. Therefore, agreement between the EIT formulation and the two-fluid Langevin equations demonstrates the thermodynamic consistency of the EIT formulation. Extension of this analysis to include normal stresses is also considered.