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

Abstract

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 h = 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.

Feedback control of inertial microfluidics using axial control forces

“…Most importantly, small particles at high Reynolds numbers have their stable equilibrium positions on the main axes, while larger particles at lower Reynolds number move to the equilibrium positions on the diagonals. This is a new result compared to previous treatments 6,8,9 .…”

“…In square channels they are typically found halfway between the channel center and the centers of the channel walls 7 . In numerical studies also migration to positions on the diagonals are observed 8,9 . In rectangular channels the number of equilibrium positions is further reduced to…”

“…7 In numerical studies, migration to positions on the diagonals are also observed. 8,9 In rectangular channels, the number of equilibrium positions is further reduced to two when the aspect ratio strongly deviates from one. 1,10 The particles all gather in front of the long channel walls.…”

“…In literature equilibrium positions in square channels have been reported along the main axes 6 , along the diagonals for large deformable drops 8 or on both axes 9 . In contrast to 9 we observe that particles move either to the diagonal equilibrium positions or to fixpoints on the main axes but the equilibrium positions are never stable at the same time as illustrated in Fig.…”

Stability of the lattice kinetic scheme and choice of the free relaxation parameter

“…The LKS, initially developed as a way to reduce memory consumption in LBM 67 , is a modified version of the SRT collision operator which allows for an additional relaxation coefficient (called second relaxation coefficient throughout this manuscript) for higher-order kinetic moments. This approach has mostly been applied to cases involving large variations in the diffusion coefficient (viscosity for flow solvers), such as non-Newtonian flows [68][69][70] , multi-phase flows [71][72][73][74] , thermal flows 75 and viscous fingering in porous media 76,77 . In all these examples the viscosity (or species and thermal diffusion coefficient) spans a rather large interval of values.…”