Breakup dynamics and scaling laws of liquid metal droplets formed in a cross junction

Abstract

The formation of liquid metal droplets in a microfluidic cross junction with different viscosities of the continuous phase is experimentally and theoretically investigated. The flow pattern is distinguished into squeezing and dripping by the presence of gaps. The differences in driving forces between the two patterns are analyzed theoretically and confirmed experimentally by Micro-PIV results. Roles of the squeezing force and the shear force in droplet formation are varying due to the dynamic evolutions of the gap width which reduces with time. Therefore, critical values of the initial gap width are obtained which are the outcome of the competition between neck thinning and tip growing. Compared to water–oil systems, gaps are more difficult to be formed due to the extremely high interfacial tension. Moreover, universal flow pattern maps are constructed using dimensionless parameters of Wed, Cac, and Rec, proving the important roles of both the squeezing force and the shear force. A scaling law of the droplet volume considering the influence of the viscosity ratio is proposed and a very good agreement between experimental data and theoretical predictions is obtained for different liquid systems.