Parametric Analysis of Microdroplet Formation in Co-Axial Co-Flowing Immiscible Liquids in Microtubes

This paper presents numerical results of disperse liquid droplets forming in the dripping regime at the tip of a microtube into another co-flowing immiscible liquid in a coaxial microtube of larger diameter. Investigated are the effects of the interfacial surface tension, velocities and viscosities of the liquids and the diameters of the coaxial microtubes on the forming dynamics and the size of the droplet. The 2-D, transient Navier-Stockes equations, in conjunction with the momentum jump condition across the interface between the co-flowing liquids are solved using a finite element method. The solution tracks the interface and the growth of the droplet and predicts droplet size and forming frequency. The droplet’s dimensionless radius (⁠$rd*$⁠) is correlated within ± 10% in terms of the continuous liquid capillary number (Ca_c) and ratios of Reynolds numbers (Re_d/Re_c) and microtube radii (R_c/R_d) of the co-flowing liquids as: