Both numerical and analytical models have been developed to explore the viscosity effect of the continuous phase on drop formation at a T-shaped junction in immiscible liquids. The effects of the generalized power law coefficient, the power law exponent and the yield stress on the mechanism of drop breakup, final drop size and frequency of drop formation are studied by using the numerical three-dimensional volume of fluid model. Droplets coalescence in Bingham fluids is observed in the beginning transient period. The effect of yield stress on drop extension is also discussed. Predictions of drop size by using an analytical force balance show satisfactory agreement with simulation results for Newtonian and power law fluids with different viscosity ratios. The approximation error associated with the analytical model for Bingham fluids is also acceptable. This analytical model can greatly shorten the prediction time as compared with the numerical model, which is helpful for on-line control.
Droplet formation in a co-flowing microfluidic device is investigated with the lattice Boltzmann method (LBM). This LBM code was validated with two benchmarks such as Poiseuille flow through a straight duct and Taylor deformation on droplets between two shearing plates. A comparison of experimental droplet formation in a microchannel (Cramer et al, 2004) showed good quantitative agreement with our modeling results. With this code, a large number of simulations were carried out with various inlet flow rate ratios at various Re and various interfacial tensions in the co-flowing microfluidic system. All resulting droplet sizes are discussed quantitatively with the nondimensional parameters, which is helpful for droplet control in different co-flowing devices.
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