Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel

In this paper, the viscous fingering phenomenon of two immiscible fluids in a channel is studied by applying the lattice Boltzmann method (LBM). The fundamental physical mechanisms of a finger formation or the interface evolution between immiscible fluids are described in terms of the relative importance of viscous forces, surface tension, and gravity, which are quantifiable via the dimensionless quantities, namely, capillary number, Bond number and viscosity ratio between displaced fluid and displacing fluid. In addition, the effect of wettability on flow behaviour of fluids is investigated for the cases with and without consideration of gravity, respectively. The numerical results provide a good understanding of the mechanisms of viscous fingering phenomenon from a mesoscopic point of view and confirm that the LBM can be viewed as a promising tool for investigating fluid behaviour and other immiscible displacement problems.