Breaking anchored droplets in a microfluidic Hele-Shaw cell

TL;DR

This paper investigates how anchored droplets in a microfluidic Hele-Shaw cell break up under flow, revealing a critical flow rate for breakup and modeling the shape of droplets using elastica equations.

Contribution

It introduces a new understanding of droplet breakup dynamics in microfluidic traps and models the shape transition using elastica equations based on capillary number.

Findings

Droplets break up at a critical flow rate.

Drop shape follows elastica equation below critical flow.

Array of anchors can produce stationary droplet arrays.

Abstract

We study microfluidic self digitization in Hele-Shaw cells using pancake droplets anchored to surface tension traps. We show that above a critical flow rate, large anchored droplets break up to form two daughter droplets, one of which remains in the anchor. Below the critical flow velocity for breakup the shape of the anchored drop is given by an elastica equation that depends on the capillary number of the outer fluid. As the velocity crosses the critical value, the equation stops admitting a solution that satisfies the boundary conditions; the drop breaks up in spite of the neck still having finite width. A similar breaking event also takes place between the holes of an array of anchors, which we use to produce a 2D array of stationary drops in situ.