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, alpha, and growth exponent, beta, 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 alpha and beta 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.

Automated summary

The displacement of one fluid by another fluid is a significant process in various fields. Understanding the fluctuations at the interface under different miscibility conditions is crucial. The roughness exponent and growth exponent of the partially miscible case are larger, indicating the impact of Korteweg convection during phase separation. Despite miscibility conditions, fluctuations in the systems can be accurately predicted using a single curve, allowing for predictions at any scale and time.