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

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.

Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study

“…Overall, the numerical simulations performed to quantify the shear rheology reveal a very good agreement with the theoretical predictions both in the polymer shear viscosity and in the first normal stress difference. Similar analysis can be performed for extensional flows, showing that the increase of the extensional viscosity predicted by the theory [26,27,25] is indeed found in the numerical simulations [42]. The coupling between normal stresses and single droplet dynamics under simple shear has also been extensively verified in the numerical simulations.…”

“…Here, instead, we aim to illustrate the effects of viscoelasticity. As already stressed in section 2, our numerical approach offers the possibility to tune the viscosity ratio of the two Newtonian phases [42,43]. By fixing the polymer viscosity η P , we can use such flexibility to achieve unitary viscosity ratio, defined in terms of the total (fluid + polymer) shear viscosity λ = η d /(η c + η P ) = 1.0 for MV and λ = (η d + η P )/η c = 1.0 for DV.…”

“…The FENE-P constitutive equations are solved with a finite difference scheme which is coupled with the solvent LBM as described in [42,43]. The numerical approach has been extensively validated in our previous works [42,43], where we have provided evidence that the model is able to capture quantitatively rheological properties of dilute suspensions as well as deformation and orientation of single viscoelastic droplets in confined shear flows. The main essential features of the model are recalled in Appendix A.…”

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

“…It would have been possible to work under more favorable conditions by keeping the interfacial tension constant, and by playing with the viscosities of the°uids instead, as it is for example done in Ref. 54. Globally, we point out that the PPM o®ers a relatively limited choice of allowed interfacial tension values in lattice units.…”

“…54 It is important to understand under which hypotheses this relation is derived. The¯rst hypothesis made in the perturbation analysis is that the°o w is Newtonian, isothermal, incompressible and Stokesian, 53 requiring that Re ( 1.…”