Anomalous patterns of Saffman-Taylor fingering instability during a metastable 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.

Growing Interface with Phase Separation and Spontaneous Convection during Hydrodynamically Stable Displacement

The displacement of one fluid by another is an important process, not only in industrial and environmental fields, such as chromatography, enhanced oil recovery, and CO2 sequestration, but also material processing, such as Lost Foam Casting. Even during hydrodynamically stable fluid displacement where a more viscous fluid displaces a less viscous fluid in porous media or in Hele-Shaw cells, the growing interface fluctuates slightly. This fluctuation is attributed to thermodynamic conditions, which can be categorized as the following systems: fully miscible, partially miscible, and immiscible. The dynamics of these three systems differ significantly. Here, we analyze interfacial fluctuations under the three systems using Family-Vicsek scaling and calculate the scaling indexes. We discovered that the roughness exponent, α, and growth exponent, β, of the partially miscible case are larger than those of the immiscible and fully miscible cases due to the effects of the Korteweg convection as induced during phase separation. Moreover, it is confirmed that fluctuations in all systems with steady values of α and β are represented as a single curve, which implies that accurate predictions for the growing interface with fluctuations in Hele-Shaw flows can be accomplished at any scale and time, regardless of the miscibility conditions.