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Mode-coupling approach to non-Newtonian Hele-Shaw flow
Magdalena Constantin1, Michael Widom, José A Miranda
1Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Summary
This study explores viscous fingering in Hele-Shaw cells, revealing how fluid properties influence interface patterns. Mode-coupling dynamics explain tip splitting and sidebranching in non-Newtonian fluid displacement.
Area of Science:
- Fluid dynamics
- Non-Newtonian fluid mechanics
- Pattern formation
Background:
- The Saffman-Taylor problem describes fluid displacement in porous media.
- Understanding interfacial dynamics is crucial for various industrial processes.
- Non-Newtonian fluids exhibit complex flow behaviors not captured by standard models.
Purpose of the Study:
- Investigate viscous fingering for non-Newtonian fluid displacement by a Newtonian fluid in a radial Hele-Shaw cell.
- Analyze the morphology of the fluid-fluid interface using a mode-coupling approach.
- Examine the influence of fluid properties on pattern formation.
Main Methods:
- Employed a mode-coupling approach to analyze the Saffman-Taylor problem.
- Derived a differential equation for early nonlinear interface evolution.
- Introduced a vector potential for velocity due to vorticity from a modified Darcy's law.
- Analyzed interfacial patterns in both radial and rectangular Hele-Shaw cells.
Main Results:
- Mode-coupling dynamics were linked to tip splitting and sidebranching phenomena.
- The study addressed both shear-thinning and shear-thickening non-Newtonian fluid behaviors.
- Analytical results provide insights into the development of non-Newtonian interfacial patterns.
Conclusions:
- The mode-coupling approach effectively describes non-Newtonian viscous fingering.
- Fluid rheology significantly impacts the resulting interfacial morphology.
- The findings contribute to the understanding of complex fluid flow and pattern formation.
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