On a hybrid continuum-kinetic model for complex fluids

TL;DR

This paper introduces a new hybrid continuum-kinetic model for complex fluids, combining macroscopic conservation laws with microscopic kinetic behavior, and demonstrates its stability and ability to capture phenomena beyond standard fluids.

Contribution

It presents a novel multiscale modeling framework that integrates continuum and kinetic descriptions for complex fluids, including stability analysis and numerical validation.

Findings

Conditional stability in low-speed regimes

Instability in high-speed regimes for higher modes

Model captures phenomena not seen in Newtonian fluids

Abstract

In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and momentum for an isentropic macroscopic model with a kinetic representation of the microscopic behaviour. After introducing a small scale of interest, we compute the complex stress tensor by means of Irving-Kirkwood formula. The latter requires an expansion of kinetic distribution around an equilibrium state and a successive homogenization over the fast in time and small in space scale dynamics. For a new hybrid continuum-kinetic model the results of linear stability analysis indicates a conditional stability in the relevant low-speed regimes and instability for high speed regimes for higher modes. Extensive numerical experiments confirm that the proposed multiscale model can reflect new phenomena of complex fluids not being present in standard Newtonian fluids. Consequently, the proposed general technique can be successfully used to derive new interesting systems combining the macro and micro structure of a given physical problem.