Universality in microdroplet nucleation during solvent exchange in Hele-Shaw like channels

TL;DR

This study investigates the universal scaling behavior of droplet nucleation during solvent exchange in Hele-Shaw channels, combining experiments and theory to reveal a power-law relationship between droplet volume and Péclet number.

Contribution

It introduces a theoretical model explaining the $V \,\propto \, Pe^{1/2}$ scaling law for droplet volume, unifying data across different geometries and compositions.

Findings

Droplet volume scales as $Pe^{0.50}$.

Universal curve collapses data from various conditions.

The model accurately predicts the observed scaling law.

Abstract

Micro and nanodroplets have many important applications such as in drug delivery, liquid-liquid extraction, nanomaterial synthesis and cosmetics. A commonly used method to generate a large number of micro or nanodroplets in one simple step is solvent exchange (also called nanoprecipitation), in which a good solvent of the droplet phase is displaced by a poor one, generating an oversaturation pulse that leads to droplet nucleation. Despite its crucial importance, the droplet growth resulting from the oversaturation pulse in this ternary system is still poorly understood. We experimentally and theoretically study this growth in Hele-Shaw like channels by measuring the total volume of the oil droplets that nucleates out of it. In order to prevent the oversaturated oil from exiting the channel, we decorated some of the channels with a porous region in the middle. Solvent exchange is performed with various solution compositions, flow rates and channel geometries, and the measured droplets volume is found to increase with the P\'eclet number $Pe$ with an approximate effective power law $V\propto Pe^{0.50}$. A theoretical model is developed to account for this finding. With this model we can indeed explain the $V\propto Pe^{1/2}$ scaling, including the prefactor, which can collapse all data of the "porous" channels onto one universal curve, irrespective of channel geometry and composition of the mixtures. Our work provides a macroscopic approach to this bottom-up method of droplet generation and may guide further studies on oversaturation and nucleation in ternary systems.