Interaction Forces Between Microfluidic Droplets in a Hele-Shaw Cell

TL;DR

This paper derives exact solutions for interaction forces between microfluidic droplets in a Hele-Shaw cell, overcoming previous limitations of distance assumptions, and compares these with numerical and experimental data.

Contribution

It provides novel exact solutions for droplet interactions in microfluidics, including complex configurations, without relying on large-distance approximations.

Findings

Exact solutions for two droplets and droplet within droplet configurations.

Comparison with numerical, experimental, and dipole-based models.

Application to dynamics of dense droplet lattices.

Abstract

Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow micro-channels. Modeling the dynamics of such systems requires calculation of the forces of interaction between the moving droplets. These forces are commonly approximated by superposition of dipoles solutions, which requires an assumption of sufficiently large distance between the droplets. In this work we obtain exact solutions (in the Hele-Shaw limit) for two moving droplets, and a droplet within a droplet, located within a moving immersing fluid, without limitation on the distance between the droplets. This is achieved by solution of the pressure field in a bi-polar coordinate system and calculation of the force in a Cartesian coordinate system. Our results are compared with numerical computations, experimental data and the existing dipole-based models. We utilize the results to calculate the dynamics of a droplet within a droplet, and of two close droplets, located within an immersing fluid with oscillating speed. The obtained results may be used to study the dynamics of dense droplet lattices, common to many microfluidic systems.