(93d) Lattice Boltzmann Simulations of a Single n-Butanol Drop Rising in Water

Emulsions, suspensions, and dispersions of immiscible liquids are widely encountered throughout engineering processes and everyday life. Knowledge of dispersed systems characteristics (apparent viscosity, rheology, terminal drop velocity, mass transfer rate) is required for safe and efficient operation of equipment dealing with these systems. The nature of liquid-liquid flows where millions of droplets interact with each other, break up and merge, and form swarms, makes the determination of these characteristics complicated. To get fundamental understanding of complex dispersed system behavior, simplified problems are studied experimentally and numerically: single drop motion and breakup under shear flow or gravity, head-on drop collision and coalescence. The findings of these investigations can be scaled on the real systems and also utilized in engineering models and correlations describing the dispersions.

In the present study the motion of an organic n-butanol drop in water under the influence of gravity was simulated using a diffuse interface free energy lattice Boltzmann method (LBM). Simulation results are useful for liquid-liquid extraction processes, since an important design parameter - terminal drop velocity - was determined. A pure two-liquid system without mass transfer between phases was considered. To reduce the computational cost while studying the long-term behavior of a moving interface, all calculations were carried out in a moving reference frame. A wide range of drop diameters that covered the flow conditions relevant to extraction process was examined. For each drop diameter the evolution of drop velocity in time, the terminal rise velocity and drop's shape were determined. The results were compared to the experimental and numerical results obtained with other numerical techniques and to semi-empirical correlations: the deviation of simulated terminal velocity from other results is within 5% for smaller drops and below 15% for large oscillating drops. The capability of the method to capture the drop shape deformation especially in oscillating regime was also demonstrated. As an example of computational results, the n-butanol drop deformation with velocity streamlines at different time steps is shown in the figure below.