Deformation and break-up of viscoelastic droplets Using Lattice Boltzmann Models

TL;DR

This paper uses advanced numerical models combining Lattice-Boltzmann and Finite Difference methods to study how viscoelastic droplets break up in shear flow, revealing the influence of matrix and droplet viscoelasticity on breakup dynamics.

Contribution

It introduces a novel simulation approach integrating Lattice-Boltzmann and FENE-P models to analyze viscoelastic droplet breakup in confined shear flows, extending previous work to matrix viscoelasticity.

Findings

Droplet deformation and orientation are quantitatively analyzed.

Critical Capillary number for breakup is predicted.

Viscoelasticity influences necking and breakup behavior.

Abstract

We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and 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). We study both strongly and weakly confined cases to highlight the role of matrix and droplet viscoelasticity in changing the droplet dynamics after the startup of a shear flow. Simulations provide easy access to quantities such as droplet deformation and orientation and will be used to quantitatively predict the critical Capillary number at which the droplet breaks, the latter being strongly correlated to the formation of multiple neckings at break-up. This study complements our previous investigation on the role of droplet viscoelasticity (A. Gupta \& M. Sbragaglia, {\it Phys. Rev. E} {\bf 90}, 023305 (2014)), and is here further extended to the case of matrix viscoelasticity.