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Numerical study of pattern formation in miscible rotating Hele-Shaw flows.
Ching-Yao Chen1, Chen-Hua Chen, José A Miranda
1Department of Mechanical Engineering, National Yunlin University of Science & Technology, Yunlin, Taiwan, Republic of China. chingyao@yuntech.edu.tw
Summary
Miscible fluid interfaces in rotating Hele-Shaw cells exhibit patterns similar to immiscible fluids. Korteweg stresses create an effective interfacial tension, quantitatively matching surface tension in immiscible displacements.
Area of Science:
- Fluid dynamics
- Interface phenomena
- Complex systems
Background:
- Hele-Shaw cells are crucial for studying fluid displacement dynamics.
- Miscible fluid interfaces present complex morphological behaviors.
- Korteweg stresses influence interfacial patterns in fluid systems.
Purpose of the Study:
- To investigate the dynamics of miscible fluid interfaces in a rotating Hele-Shaw cell.
- To analyze the impact of viscosity contrast and Korteweg stresses on interfacial patterns.
- To establish the quantitative equivalence between Korteweg stresses and surface tension.
Main Methods:
- Intensive and highly accurate numerical simulations were employed.
- Experiments were conducted across a wide range of parameters.
- Interfacial pattern formation, finger competition, and filament stretching were analyzed.
Main Results:
- Miscible patterns strongly resemble immiscible counterparts at higher Korteweg stresses.
- An effective interfacial tension was identified for miscible displacements.
- Simulations showed excellent agreement with existing experiments for immiscible displacements.
Conclusions:
- Korteweg stresses provide an effective interfacial tension for miscible fluids.
- This effective tension is quantitatively and qualitatively equivalent to immiscible surface tension.
- The study reveals striking similarities between miscible and immiscible pattern morphologies.