# Jetting to dripping transition: critical aspect ratio in step emulsifiers

## TL;DR

This study uses 3D simulations to identify a critical aspect ratio in step emulsifiers that determines whether a jet breaks into droplets or remains stable, aligning well with experimental observations.

## Contribution

The paper reveals the critical $w/h$ ratio (~2.56) that governs droplet formation in step emulsifiers through detailed fluid dynamics simulations.

## Key findings

- Droplet breakup occurs above a $w/h$ ratio of approximately 2.56.
- Below this threshold, the fluid undergoes a smooth transition without droplet formation.
- Simulations agree with experimental data on the critical aspect ratio.

## Abstract

Fully three-dimensional, time-dependent, direct simulations of the non-ideal Navier-Stokes equations for a two-component fluid, shed light into the mechanism which inhibits droplet breakup in step emulsifiers below a critical threshold of the the width-to-height ($w/h$) ratio of the microfluidic nozzle. Below $w/h \sim 2.6$, the simulations provide evidence of a smooth topological transition of the fluid from the confined rectangular channel geometry to an isotropic (spherical) expansion of the fluid downstream the nozzle step. Above such threshold, the transition from the inner to the outer space involves a series of dynamical rearrangements which keep the free surface in mechanical balance. Such rearrangements also induce a backflow of the ambient fluid which, in turn, leads to jet pinching and ultimately to its rupture, namely droplet formation. The simulations show remarkable agreement with the experimental value of the threshold, which is found around $w/h \sim 2.56$.