On the capillary self-focusing in a microfluidic system

TL;DR

This paper presents a computational model for capillary self-focusing in microfluidic Step Emulsification systems, validated by experiments, highlighting the importance of boundary conditions in predicting interface shapes and breakup regimes.

Contribution

The study introduces a reduced Hele-Shaw based computational framework and proposes a correction to the pressure boundary condition for better accuracy.

Findings

The interface forms a neck narrowing before entering the reservoir.

The boundary pressure assumption is valid when the neck width is small.

A corrected boundary condition improves agreement with experiments.

Abstract

A computational framework is developed to address capillary self-focusing in Step Emulsification. The microfluidic system consists of a single shallow and wide microchannel that merges into a deep reservoir. A continuum approach coupled with a volume of fluid method is used to model the capillary self-focusing effect. The original governing equations are reduced using the Hele-Shaw approximation. We show that the interface between the two fluids takes the shape of a neck narrowing in the flow direction just before entering the reservoir, in agreement with our experimental observations. Our computational model relies on the assumption that the pressure at the boundary, where the fluid exits into the reservoir, is the uniform pressure in the reservoir. We investigate this hypothesis by comparing the numerical results with experimental data. We conjecture that the pressure boundary condition becomes important when the width of the neck is comparable to the depth of the microchannel. A correction to the exit pressure boundary condition is then proposed, which is determined by comparison with experimental data. We also present the experimental observations and the numerical results of the transitions of breakup regimes.