Title: Lattice Boltzmann simulation of viscous fingering of immiscible displacement in a channel using an improved wetting scheme,
Abstract: An improved wetting boundary implementation strategy is proposed based on
lattice Boltzmann color-gradient model in this paper. In this strategy, an
extra interface force condition is demonstrated based on the diffuse interface
assumption and is employed in contact line region. It has been validated by
three benchmark problems: static droplet wetting on a flat surface and a curved
surface, and dynamic capillary filling. Good performances are shown in all
three cases. Relied on the strict validation to our scheme, the viscous
fingering phenomenon of immiscible fluids displacement in a two-dimensional
channel has been restudied in this paper. High viscosity ratio, wide range
contact angle, accurate moving contact line and mutual independence between
surface tension and viscosity are the obvious advantages of our model. We find
the linear relationship between the contact angle and displacement velocity or
variation of finger length. When the viscosity ratio is smaller than 20, the
displacement velocity is increasing with increasing viscosity ratio and
reducing capillary number, and when the viscosity ratio is larger than 20, the
displacement velocity tends to a specific constant. A similar conclusion is
obtained on the variation of finger length.