Deformation and break-up of viscoelastic droplets in confined shear flow

TL;DR

This study investigates how viscoelastic droplets deform and break up under confined shear flow using advanced numerical models, revealing that confinement and polymer properties significantly influence droplet stability and breakup conditions.

Contribution

It introduces a combined Lattice-Boltzmann and finite difference numerical approach to analyze viscoelastic droplet behavior in confined shear flows, highlighting the effects of polymer properties and confinement.

Findings

In unconfined flow, viscoelasticity has moderate effects on breakup.

In confined flow, the critical Capillary number varies with polymer extensibility.

Polymer relaxation time and confinement degree significantly affect droplet stability.

Abstract

The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, 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). We quantify the droplet response by changing the polymer relaxation time $\tau_P$, the maximum extensibility $L$ of the polymers, and the degree of confinement, i.e. the ratio of the droplet diameter to gap spacing. In unconfined shear flow, the effects of droplet viscoelasticity on the critical Capillary number $\mbox{Ca}_{\mbox{\tiny{cr}}}$ for break-up are moderate in all cases studied. However, in confined conditions a different behaviour is observed: the critical Capillary number of a viscoelastic droplet increases or decreases, depending on the maximum elongation of the polymers, the latter affecting the extensional viscosity of the polymeric solution. Force balance is monitored in the numerical simulations to validate the physical picture.