Tunable Hydrodynamic Interfacial Instability by Controlling a Thermodynamic Parameter of Liquid-Liquid Phase Separation

Momentum transport of morphological instability in fluid displacement with changes in viscosity

Saffman-Taylor instability exhibits a stepwise unstable morphology from a stable interface to viscous fingering, eventually leading to tip splitting. The nonlinear dynamics of the destabilized interface depends on various flow properties. However, the physicochemical mechanism that determines the transition point of the flow state is unclear. We studied the interfacial instability transition in miscible displacement from a thermodynamic perspective by calculating the momentum transport and entropy production. Using numerical analysis based on Darcy's law coupled with the convection-diffusion equation, the observed flux-dependent flow state transitions were attributed to the selection of the flow state with a higher entropy production.

Hydrodynamic Fingering Induced by Gel Film Formation in Miscible Fluid Systems: An Experimental and Mathematical Study

Hydrodynamic fingering induced by gel formation shares common features with growing biofilms, bacterial colonies, and the instability of a confined chemical garden. Fluid displacement with gel formation is also essential in various engineering applications, including CO2 leakage remediation from storage reservoirs and enhanced oil recovery. We conducted Hele-Shaw cell displacement experiments for a miscible fluid system using skim milk and aqueous citric acid solution. This study aimed to investigate the effects of gel film formation on the fingering instability of a miscible fluid system and develop a mathematical model of the sequential growth of gel film formation at the fingertip. We found that the gel film formation thickens with time, resulting in instability at the interface. A distinctive fingering pattern, resembling tentacles, appears where miscibility is suppressed, and the growth of the finger is localized at the fingertip. The finger width remains constant with increasing flow rate, whereas the number of fingers increases linearly before the fingers merge. The gap width significantly limits the finger width. Finally, a mathematical model of sequential film thickness growth for a bubble-like fingertip structure was developed. This model is based upon the interplay between the diffusion of citric acid through the existing gel film formation and elongation of the fingertip. The model provides an understanding of the fundamental mechanism of the growth of the bubble-like fingertip.