# Valve-based flow focusing for drop formation

Original entry: Sorell Massenburg, APPHY 226, Spring 2009

Adam R. Abate, Mark B. Romanowsky, Jeremy J. Agresti, and David A. Weitz, Appl. Phys. Lett. 94, 023503 (2009).

# Soft Matter Keywords

Dripping, Droplets, surface tension, drop formation, emulsion, microfluidics

# Overview

The authors here have developed a method to change the production of droplets via produced by microfluidic devices in real time. The method uses valves to capitalize on the flexibility the PDMS which are used to make the devices. The authors demonstrate that the droplet size can be altered by decreasing the nozzle size while the dripping frequency can be altered by changing the width of the side channels.

# How Soft is This?

## Motivation

Droplets made in flow focusing microfluidic devices can be thought of a tug-of-war between two continuously flowing, immiscible liquids that clash a t-junction where only one may pass at a time. The outer phase approaches horizontally (external liquid) and forms a continuous sheet until the inner phase (interior liquid) punches through vertically. The movement of outer phase is stymied by the flow inner phase. Since the outer phase is continually supplied it builds up pressure which eventually overcomes the inner fluid and pinches it off. The outer phase is now flowing from the horizontal arms of the t-junction and surrounds the inner phase, creating a droplet. Meanwhile the inner phase is backing up in the top, vertical channel. Eventually enough pressure builds up in the inner phase that it punches through once more, restarting the process.

Intuitively, if one wanted to change the dimensions of the droplet one would alter ratio of inner to outer flow rate, which would change the of inner phase liquid that pinched through each time. This process can be cumbersome and counter productive for some processes. Instead the authors have devised a novel method for quickly altering droplet size without changing the flow rates of the phases.

## Devices

Devices consist of a single PDMS layer fabricated using soft lithography techniques. In addition to an intersection to make the droplets, there are valves that approach the nozzle at a 45 degree angle from from direction of droplet egress and there are also valves that run parallel to the horizontal continuous phase channels. The valves are just regions devoid of PDMS in which the authors filled with water to varying degrees. Here the valve membrane is about $13 \mu m$ wide.

Left: Device design for changing size of droplets, Right: Device Design for changing frequency.

## Results

Top: Graph illustrating the variation of droplet size d, with channel width w. Bottom: Variation of droplet size with pressure.
Top: Graph that illustrates the effect of of channel width on droplet production frequency. Bottom: Variation of production frequency with applied pressure.

As one might intuitively expect from a dripping faucet, the size of droplets produced here is proportional to the size of the nozzle. Intuitively, the size of the nozzle limits the amount of water that gushes through the continuous phase before being pinched off. Regarding frequency, oscillating the the pressure in the valve changes the frequency at which the continuous phase pinches off the inner phase.

Previously for systems of this type, the nozzle size was considered to be a parameter fixed in the fabrication process. Initially the nozzle is 20$\mu m$ wide by 50$\mu m$ tall. For this initial nozzle size, the authors demonstrate the ability to control droplet size from 200$\mu m$ on down to 7$\mu m$. This ability is shown pictorially and the correlations between nozzle size and droplet diameter and pressure to droplet diameter are also shown. The authors report a nonlinear response in droplet size to nozzle width. The authors also credit two reasons for the change in droplet size with decreasing nozzle width: 1) smaller nozzle size and 2) increased local flow velocity. Additionally, the droplet size distribution over for a given pressure is relatively small for most pressures tried.

Top Left: Droplet production before valve actuation. Top Right: Example of droplet frequency change with valve pressure increase. Bottom: Examples of different size droplets that are possible.

In the case of frequency control, the response is linear and negative; the frequency increases with smaller channel sizes.

Top Left: Droplet production before valve actuation. Top Right: Example of droplet frequency change with valve pressure increase. Bottom: Examples of different size droplets that are possible.

The changes reported happen in real time since the oscillation of the channel width is shown to be in phase with the droplet production.

Overlay of channel width oscillations (applied pressure) and droplet production frequencies.