Drop-Carrier Particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution from an immiscible mixture (e.g.: oil and water) without using costly microfluidic equipment and techniques. Surface energy minimization with volume constraints provides a theoretical prediction for the configuration of fluids around a single DCP. Energy minimization also predicts the volume distribution in pairwise droplet splitting, showing good agreement with macro-scale experiments. We develop a probabilistic pairwise interaction model for a system of such DCPs exchanging fluid volume to minimize surface energy.  This leads to a theory for the number of pairwise interactions of DCPs needed to reach a uniform volume distribution. Heterogeneous mixtures of DCPs with different sized particles require fewer interactions to reach a uniform distribution.

 

For more information about DCPs, here are two papers that come from the collaboration group of Mathematicians and Bioengineers at UCLA that I was a part of: