Hybrid Lattice Boltzmann/Finite Difference simulations of viscoelastic multicomponent flows in confined geometries

TL;DR

This paper introduces a hybrid Lattice-Boltzmann and Finite Difference simulation method for viscoelastic multicomponent flows in confined geometries, enabling detailed analysis of complex fluid behaviors and interfaces.

Contribution

It develops a novel hybrid numerical approach combining LBM and FD to simulate viscoelastic multicomponent flows with non-ideal interfaces, validated against theoretical models.

Findings

Validated rheological behavior of dilute solutions in various flows

Simulated viscoelastic droplet behavior in shear flows

Quantified LBM capabilities for complex multicomponent flows

Abstract

We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical results are compared with the predictions of various theoretical models. The proposed numerical simulations explore problems where the capabilities of LBM were never quantified before.