Numerical simulation of radial viscous fingering in a partially miscible system

When a displacing fluid is less viscous, the interface of two fluids gives a finger-like pattern in porous media. This phenomenon is called Saffman-Taylor instability or viscous fingering (VF). In addition to the importance of viscosity differences, fluid-fluid miscibility plays an important role in the VF dynamics. Miscibility has been traditionally classified into two types: fully miscible and immiscible systems. Recently a partially miscible system, in which two fluids mixed and the composition of solutions is finally different from that of initial solutions, has newly studied. It has been reported that diffusion and phase separation affect the VF dynamics in this case, and the partially miscible VF shows multiple droplets formation which cannot be explained by only hydrodynamic instability. Until now, the partially miscible cases have been studied with rectilinear numerical simulation and radial experiments. These two results show multiple droplets formation and the trend of changing the interface are consistent qualitatively. However, there is a clear difference between the displacement velocity between the rectilinear and radial geometries, and it is necessary to simulate partially miscible flows in a radial geometry. In this study, we simulate radial flows in partially miscible cases. We compare the results with the previous studies qualitatively and quantitatively, and investigate the effect of velocity in radial and rectilinear displacements in the partially miscible systems.