Numerical simulations of the behaviour of a drop in a square pipe flow using the two-phase lattice Boltzmann method

The lattice Boltzmann method for multi-component immiscible fluids is applied to simulations of the behaviour of a drop in a square pipe flow for various Reynolds numbers of 10 < Re < 500, Weber numbers of 0 < We < 250 and viscosity ratios of eta = 1/5, 1, 2 and 5. It is found that, for low Weber numbers, the drop moves straight along a stable position on the diagonal line of the pipe section, and it moves along the centre axis of the pipe for larger Weber numbers. We obtain the boundary of the two different behaviours of the drop in terms of Reynolds number, Weber number and viscosity ratio.