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Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
Growing Interface with Phase Separation and Spontaneous Convection during Hydrodynamically Stable Displacement.
Takahiko Ban1, Ryohei Tanaka2, Ryuta X Suzuki2
1Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka, Osaka 560-8531, Japan.
Fluid interface fluctuations during displacement processes are analyzed. Partially miscible systems exhibit greater roughness and growth exponents due to Korteweg convection, enabling unified predictions across miscibility conditions.
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Area of Science:
- Fluid dynamics
- Interfacial phenomena
- Thermodynamics
Background:
- Fluid displacement is crucial in industrial and environmental applications like enhanced oil recovery and CO2 sequestration.
- Even in stable displacement, interfaces between fluids exhibit fluctuations influenced by miscibility.
- Understanding these fluctuations is key to controlling processes in porous media and Hele-Shaw cells.
Purpose of the Study:
- To analyze interfacial fluctuations in fluid displacement across fully miscible, partially miscible, and immiscible systems.
- To calculate scaling exponents (roughness α and growth β) for each system.
- To investigate the impact of miscibility on interface dynamics and develop predictive models.
Main Methods:
- Utilized Family-Vicsek scaling theory to analyze interfacial fluctuations.
- Calculated roughness exponent (α) and growth exponent (β) for different miscibility conditions.
- Compared fluctuation dynamics across the three thermodynamic systems.
Main Results:
- Partially miscible systems showed higher roughness (α) and growth (β) exponents compared to immiscible and fully miscible systems.
- Korteweg convection effects during phase separation were identified as the cause for increased exponents in partially miscible cases.
- Fluctuations across all systems collapsed onto a single curve when plotted with steady α and β values.
Conclusions:
- Interfacial fluctuation dynamics in fluid displacement are significantly influenced by miscibility.
- The findings enable accurate, scale-independent predictions of interface behavior in Hele-Shaw flows, regardless of miscibility.
- This research provides a unified framework for understanding and modeling interfacial dynamics in diverse fluid displacement scenarios.

