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Updated: Apr 27, 2026
07:57
Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
Published on: August 30, 2019
6.8K
Selection of the Taylor-Saffman bubble does not require surface tension.
Giovani L Vasconcelos1, Mark Mineev-Weinstein2
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife, Brazil.
Summary
This study reveals that Hele-Shaw cell bubble dynamics can be accurately modeled without surface tension. The findings demonstrate a new attractor for bubble patterns, challenging existing theories.
Area of Science:
- Fluid Dynamics
- Mathematical Physics
Background:
- Hele-Shaw cells are crucial for studying viscous fluid flows.
- Surface tension has been traditionally considered essential for bubble pattern selection.
Purpose of the Study:
- To present a new class of exact solutions for bubble evolution in Hele-Shaw cells.
- To investigate bubble selection mechanisms without surface tension.
Main Methods:
- Utilizing conformal mapping to transform the flow domain.
- Analyzing the dynamics of nonsingular bubble evolution.
Main Results:
- Exact solutions for arbitrary initial bubble shapes were derived.
- A stable fixed point (attractor) was identified for bubble dynamics.
- Bubble selection was shown to occur without surface tension.
Conclusions:
- Surface tension is not required for bubble selection in Hele-Shaw cells.
- The findings extend previous work from single to double connected geometries.
- A conjecture is proposed for Hele-Shaw flows of arbitrary connectivity.
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