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Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow
Liam C Morrow1, Michael C Dallaston2, Scott W McCue1
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4001, Australia.
Physical Review. E
|December 25, 2019
Summary
Axially symmetric bubbles in porous media can pinch off and break apart, a phenomenon not seen in 2D Hele-Shaw flow. Numerical simulations confirm a predicted power-law behavior near pinch-off.
Area of Science:
- Fluid dynamics
- Porous media physics
- Mathematical modeling
Background:
- The study investigates a moving boundary problem modeling fluid interfaces in porous media, analogous to Hele-Shaw flow.
- Focuses on pinch-off singularities, where interface curvature blows up, leading to bubble breakup.
- Highlights that these singularities differ from those in the 2D Hele-Shaw problem.
Purpose of the Study:
- To model and analyze the pinch-off behavior of axially symmetric bubbles in porous media.
- To investigate the occurrence and characteristics of pinch-off singularities in a higher-dimensional analog of Hele-Shaw flow.
- To compare the behavior of 3D bubbles with 2D Hele-Shaw flows.
Main Methods:
- Developed a numerical scheme utilizing the level set method to simulate bubble evolution.
- Applied similarity analysis to predict the scaling behavior of the bubble radius near pinch-off.
- Simulated time-dependent development of Saffman-Taylor fingers and Taylor-Saffman bubbles.
Main Results:
- Demonstrated that axially symmetric bubbles in porous media can undergo pinch-off in various geometries.
- Numerical results support the similarity analysis prediction of a power-law behavior (exponent α=1/3) near pinch-off.
- Identified similarities and differences between 3D bubble dynamics and 2D Hele-Shaw finger/bubble phenomena.
Conclusions:
- Pinch-off singularities are a key feature of 3D axially symmetric bubble evolution in porous media, unlike their 2D counterparts.
- The power-law scaling of bubble radius near pinch-off is robust and independent of initial conditions.
- The study provides valuable insights into fluid dynamics in porous media and extends Hele-Shaw flow analogs.
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