**Ryuta X. Suzuki 1, Risa Takeda 1, Yuichiro Nagatsu 1, Manoranjan Mishra <sup>2</sup> and Takahiko Ban 3,\***


Received: 16 September 2020; Accepted: 1 October 2020; Published: 6 October 2020

**Abstract:** The displacement of a less viscous fluid by a more viscous fluid in a radial Hele-Shaw cell makes a circular pattern because the interface is hydrodynamically stable in this condition. Very recently, it has been experimentally reported that the hydrodynamically stable displacement in a partially miscible system induces fingering patterns while stable circular patterns are made at fully miscible and immiscible systems. The fingering instability in the partially miscible system results from complex and entangled elements involving viscous dissipation, molecular diffusion, and phase separation. The analyzing mechanism requires a quantitative relationship between the hydrodynamic interfacial fingering patterns and underlying physicochemical properties. Here, we experimentally investigated the change in fluid patterns formed by the progression of phase separation in the partially miscible systems and categorized them into three patterns: finger-like pattern, annular-like pattern, and circular pattern. Moreover, we propose the mechanism of the pattern formation by an interfacial tension measurement and evaluate the patterns by modified capillary number and newly defined body force ratio, *B*f. Our analysis revealed that the deformation index of the pattern can be expressed as a function of *B*<sup>f</sup> on a single curve regardless of the miscibility.

**Keywords:** fluid displacement; inverse Saffman–Taylor instability; partially miscible; Korteweg force
