Deformation and breakup 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 τ P , the maximum extensibility L of the polymers, and the degree of confinement, i.e. the ratio of the droplet diameter to wall separation. In unconfined shear flow, the effects of droplet viscoelasticity on the critical Capillary number Ca cr for breakup 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.

Generation of Oil Droplets in a Non-Newtonian Liquid Using a Microfluidic T-Junction

“…Numerical simulations [20] indicate that (for fixed flow conditions) the effects of viscoelasticity are more pronounced in the case of Newtonian droplets in a viscoelastic carrier liquid than in the complementary case of viscoelastic droplets in a Newtonian medium. This difference is quantitatively attributed to the fact that the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by a viscoelastic behavior of the continuous phase, obtained for example by adding polymers [20].…”

“…This difference is quantitatively attributed to the fact that the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by a viscoelastic behavior of the continuous phase, obtained for example by adding polymers [20]. We thus decided to investigate the viscoelastic effects of the continuous phase on the formation of (Newtonian) droplets.…”

Viscoelastic multicomponent fluids in confined flow-focusing devices

“…The parameter L 2 is actually related to the extensional viscosity of the polymers [26,30]. In the spirit of the work that we recently developed for characterizing droplet deformation and break-up in confined shear flow [25], it would be of extreme interest to study the impact of a change in the finite extensibility parameter L 2 for the geometries studied in this paper [13,16]. Finally, we wish to underscore the role played by numerical simulations: in real experiments all the various processes (hydrodynamic forces, viscoelastic effects, confinement effects) occur at the same time and it is next to impossible to separately quantify their relative importance.…”

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

“…LBM is instrumental to solve the diffuse-interface hydrodynamic equations of a binary mixture of two components [36,37,38,39,40,41]: the resulting physical domain can be partitioned into different subdomains, each occupied by a "pure" fluid, with the interface between the two fluids described as a thin layer where the fluid properties change smoothly. 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 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.…”