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Based on mesoscale lattice Boltzmann (LB) numerical simulations, weinvestigate the effects of viscoelasticity on the break-up of liquid threads inmicrofluidic cross-junctions, where droplets are formed by focusing a liquidthread of a dispersed (d) phase into another co-flowing continuous (c)immiscible phase. Working at small Capillary numbers, we investigate theeffects of non-Newtonian phases in the transition from droplet formation at thecross-junction (DCJ) to droplet formation downstream of the cross-junction (DC)(Liu $\&$ Zhang, ${\it Phys. ~Fluids.}$ ${\bf 23}$, 082101 (2011)). We willanalyze cases with ${\it Droplet ~Viscoelasticity}$ (DV), where viscoelasticproperties are confined in the dispersed phase, as well as cases with ${\itMatrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined inthe continuous phase. Moderate flow-rate ratios $Q \approx {\cal O}(1)$ of thetwo phases are considered in the present study. Overall, we find that theeffects are more pronounced in the case with MV, where viscoelasticity is foundto influence the break-up point of the threads, which moves closer to thecross-junction and stabilizes. This is attributed to an increase of the polymerfeedback stress forming in the corner flows, where the side channels of thedevice meet the main channel. Quantitative predictions on the break-up point ofthe threads are provided as a function of the Deborah number, i.e. thedimensionless number measuring the importance of viscoelasticity with respectto Capillary forces.

A Lattice Boltzmann study of the effects of viscoelasticity on droplet formation in microfluidic cross-junctions