Lattice Boltzmann simulations of a single n-butanol drop rising in water

The motion of an n-butanol drop in water under the influence of gravity was numerically studied using a diffuse interface free energy lattice Boltzmann method. A pure two-liquid system without mass transfer between the phases was considered. A range of drop diameters of 1.0–4.0 mm covered the flow conditions. Most calculations were carried out in a moving reference frame. This allowed studying of long-term drop behavior in a relatively small computational domain. The capability of the method to capture the drop shape especially in the oscillating regime was demonstrated. For each drop diameter the evolution of the drop velocity in time, the terminal rise velocity and drop's shape were determined. The results were compared to experimental and numerical results and to semi-empirical correlations. The deviation of the simulated terminal velocity from other results is within 5% for smaller drops and up to 20% for large oscillating drops. It was shown that beyond the onset of shape oscillations the binary system converges towards a constant capillary number of 0.056.