Injection of Newtonian fluids to displace pseudoplastic and dilatant fluids, governed by the power-law viscosity relationship, is common in many industrial processes. In these applications, changing the viscosity of the displaced fluid through velocity alteration can regulate interfacial instabilities, displacement efficiency, the thickness of the static wall layer, and the injected fluid’s tendency to move toward particular parts of the channel. The dynamic behavior of the fluid–fluid interface in the case of immiscibility is highly complicated and complex. In this study, a code was developed that utilizes a multi-component model of the lattice Boltzmann method to decrease the computational cost and accurately model these problems. Accordingly, a 2D inclined channel, filled with a stagnant incompressible Newtonian fluid in the initial section followed by a power-law material, was modeled for numerous scenarios. In conclusion, the results indicate that reducing the power-law index can regulate interfacial instabilities leading to dynamic deformation of static wall layers at the top and the bottom of the channel. However, it does not guarantee a reduction in the thickness of these layers, which is crucial to improve displacement efficiency. The impacts of the compatibility factor and power-law index variations on the filling pattern and finger structure were intensively evaluated.</p
