Simulation of viscous fingering in microchannels with hybrid-patterned surface using lattice Boltzmann method

In recent years, a large effort has been devoted to the study of the viscous fingering phenomenon in microchannel flows. This phenomenon plays a crucial role in many fields of industry and occurs in geological sequestration of carbon dioxide (CO2), in the secondary and tertiary oil recovery stages. Viscous fingering, also known as the Saffman-Taylor instability, occurs at the unstable interface between two fluids when the less viscous fluid displaces the more viscous fluid which is originally residing in a porous medium. This paper studies viscous fingering occurring between two segregated immiscible fluids, such that the less viscous one is forced into a microchannel where the more viscous fluid initially resides. The 2D microchannel walls are present with a hybrid-patterned configuration such that the top wall is smooth, and the bottom wall is ribbed. The multiphase Shan-Chen Lattice Boltzmann Method (SC LBM) is implemented to capture the complex interfacial phenomenon since this method has proven to accurately describe multiphase interfacial entangling. The LBM is based on the discretization of micro- and mesoscopic kinetic equations and the SC LBM simulation allows us to study the viscous fingering phenomenon in terms of non-dimensional quantities, including capillary number and viscosity ratio. The effect of hybrid-patterned rough walls on fingering formation in a 2D microchannel is investigated and compared to the phenomenon when plain smooth walls are in place. The numerical results show that the SC Lattice Boltzmann multicomponent model provides insightful characteristics associated to the physical nature of the fingering phenomenon in microchannels and the role of adjacent walls.