Emulsion Formation in Dripping Regime of Co-Flowing Immiscible Liquids in Co-Axial Micro-Tubes

Numerical analysis is performed of the formation of an emulsion of disperse micro-drops in the dripping regime of co-flowing immiscible liquids in co-axial micro-tubes. This parametric analysis investigated the effects of changing the interfacial tension, velocities and viscosities of the two liquids and the diameters of the coaxial micro-tubes on the dynamics, frequency and radius of the forming droplets. The transient, 2-D axisymmetric Navier-Stockes equations of the two liquids and the advection equation for the interface, subject to the momentum jump condition, are solved using a finite element method. Semi-empirical correlations are developed for the dimensionless radius and formation frequency of the droplets, based on numerical results for wide ranges of parameters. The correlations are in good agreement (+10% to -14%) with recently reported experimental measurements for water (mono-disperse) droplets in a continuous flowing salad oil in a co-axial micro-tube.