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

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.

34 Pages, 13 Figures. This Work applies the Numerical Methodology described in arXiv:1406.2686 to the Problem of Droplet Break-up in confined microchannels

References in corpus (2)

• Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
• Interaction Pressure Tensor for a class of Multicomponent Lattice Boltzmann models

Cited by in corpus (12)

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• Deformation and break-up of viscoelastic droplets Using Lattice Boltzmann Models
• A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations
• The role of BKM-type theorems in $3D$ Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis
• Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow
• Lattice Boltzmann simulations of droplet breakup in confined and time-dependent flows