  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.
