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

TL;DR

This study uses lattice Boltzmann simulations to explore how viscoelasticity in either the dispersed or continuous phase affects droplet formation in microfluidic cross-junctions, revealing that matrix viscoelasticity stabilizes and shifts the breakup point closer to the junction.

Contribution

It provides the first detailed analysis of viscoelastic effects on droplet breakup in microfluidic cross-junctions using mesoscale lattice Boltzmann simulations.

Findings

Viscoelasticity in the continuous phase stabilizes droplet breakup.

The breakup point shifts closer to the junction with increased matrix viscoelasticity.

Quantitative relationship between Deborah number and breakup location is established.

Abstract

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