Two-fluid kinetic theory for dilute polymer solutions

TL;DR

This paper develops a Boltzmann-type kinetic model for dilute polymer solutions based on two-fluid theory, leading to a numerical scheme that captures elastic effects like suppression of inertial instability.

Contribution

It introduces a novel kinetic description and numerical algorithm for dilute polymer solutions grounded in two-fluid theory and Boltzmann-type relaxation mechanisms.

Findings

The model reproduces macroscopic equations for polymer-solvent mixtures.

The numerical scheme is similar to lattice Boltzmann methods.

Application to Kolmogorov flow shows elastic effects suppress inertial instability.

Abstract

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasi-equilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equations for the polymer-solvent mixture. The proposed kinetic scheme leads to a numerical algorithm which is along the lines of the lattice Boltzmann method. Finally, the algorithm is applied to describe the evolution of a perturbed Kolmogorov flow profile, whereby we recover the major elastic effect exhibited by a polymer solution, specifically, the suppression of the original inertial instability.