Effect of geometry ratios on droplet breakup in a T-junction microchannel: A theoretical predictive model

Abstract

Understanding and predicting droplet breakup is essential in droplet-based microfluidic systems, as it enables precise control over droplet manipulation for various applications. In this study, droplet breakup behavior in a T-junction microchannel is investigated under the influence of microchannel geometry using three-dimensional numerical simulations. A theoretical model is developed based on the balance between surface tension and viscous drag forces acting on the droplet, incorporating the effects of geometric parameters on droplet length. This model predicts the critical Capillary number required for breakup to occur. The theoretical predictions are validated using both previous research data and the present numerical simulations. The results show that the model accurately predicts the transition between breakup and non-breakup regimes. Specifically, an increase in sidearm length ratio inhibits droplet breakup and leads to an asymmetric breakup regime. Furthermore, increasing the outlet-to-inlet width ratio also reduces the likelihood of droplet breakup. These findings provide a predictive framework for understanding and controlling droplet dynamics in microfluidic T-junctions, with potential applications in lab-on-a-chip technologies.

1. Introduction

In recent decades, droplet-based microfluidics has gained a lot of attention because of its numerous uses in the food, chemical, medicinal, and environmental sectors [1,2]. Rapid analysis times, accurate control over small droplet volumes, and dependable manipulation of individual droplets are only a few of the benefits that have driven its broad usage [3]. For droplet formation [4], mixing [5], merging [6], and breakdown [7], T-junction microchannels are essential parts of droplet-based microfluidic systems.

The study of droplet breakup in T-junctions is particularly important for applications requiring the mass production of microdroplets through sequential T-junctions [8]. This behavior was first investigated by Link et al. [8], followed by Jullien et al. [9], who identified three distinct breakup regimes: non-breakup (NB), breakup with tunnels (TB), and breakup with permanent obstruction (POB). In the TB regime, the droplet splits while leaving a gap or 'tunnel' between itself and the microchannel walls, allowing continuous flow of the outer fluid. This tunnel may exist either from the start or form gradually before breakup. In contrast, the POB regime involves the droplet fully blocking the channel branches throughout the breakup process, with no tunnel formation. Breakup in this case occurs through necking in the central region. Further exploration of these behaviors has been conducted, such as Chen and Deng [10] study on droplet non-breakup through hydrodynamics and shear stress, and Sun et al. [11] in-depth examination of the tunnel breakup regime. The permanent obstruction breakup mode has been studied by Leshansky et al. [12] and Hoang et al. [13].