**4. Conclusions**

We investigated the deformation index of various patterns such as circular, finger-like, and annular-like patterns during fluid displacement, while changing the progression of phase separation using the newly defined dimensionless number, Bf. The fully miscible cases under the hydrodynamically stable displacement condition, where the more viscous PEG solution displaces the less viscous Na2SO4 solution, show constant circular patterns. For the partially miscible systems, phase separation occurs at the interface between displacing and displaced solutions, creating a separated region with domain growth for the annular patterns and creating a deformed interface for the finger pattern. Moreover, the deformation index of the patterns can be scaled with Bf, which involves viscous dissipation, molecular diffusion, and phase separation. Therefore, the patterns in the partially miscible systems are proved to be formed by the competition of viscous dissipation and phase separation. Bf is a crucial factor to describe the complex morphologies induced by the fluid displacement in partially miscible systems. The investigated morphologies and Bf will directly contribute to predicting and/or controlling CO2-enhanced oil recovery, where more viscous water displaces less viscous CO2 under the ground, the conditions of which are partially miscible.

**Author Contributions:** Experiments, R.T. and R.X.S.; discussion and review, R.X.S., R.T., Y.N., M.M., and T.B.; writing, R.X.S. and T.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This is study was supported by JSPS KAKENHI Grant No. 19J12553.

**Conflicts of Interest:** The authors declare no conflict of interest.
