A lattice boltzmann simulation of three-dimensional displacement flow of two immiscible liquids in a square duct

A three-dimensional, multiphase lattice Boltzmann approach is used to study a pressuredriven displacement flow of two immiscible liquids of different densities and viscosities in a square duct. A three-dimensional, 15-velocity (D3Q15) lattice model is used. The effects of channel inclination, viscosity, and density contrasts are investigated. The contours of the density and the average viscosity profiles in different planes are plotted and compared with those obtained in a two-dimensional channel. We demonstrate that the flow dynamics in a three-dimensional channel is quite different as compared to that of a two-dimensional channel. We found that the flow is relatively more coherent in a three-dimensional channel than that in a two-dimensional channel. A new screw-type instability is seen in the three-dimensional channel that cannot be observed in the two-dimensional channel.