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Contact angle of a hemispherical bubble: an analytical approach
M A C Teixeira1, P I C Teixeira
1University of Lisbon, CGUL, IDL, Edifício C8, Campo Grande, P-1749-016 Lisbon, Portugal.
Journal of Colloid and Interface Science
|June 23, 2009
Summary
We analytically calculated the equilibrium shape of Plateau borders for bubbles on a flat surface, considering gravity. Gravity has a minor effect on bubble contact angle and Plateau border shape.
Area of Science:
- Fluid dynamics
- Surface science
- Physics of interfaces
Background:
- Plateau borders are crucial in understanding bubble behavior and foam stability.
- The shape of Plateau borders influences macroscopic properties like contact angles.
- Previous studies often relied on numerical methods or ignored gravitational effects.
Purpose of the Study:
- To analytically determine the equilibrium shape of an axially symmetric Plateau border.
- To investigate the influence of gravity on Plateau border geometry and bubble contact angles.
- To provide closed-form expressions for Plateau border surfaces.
Main Methods:
- Analytical integration of Laplace's equation for small Plateau border sizes.
- Incorporation of gravitational effects into the theoretical model.
- Comparison of analytical results with numerical solutions and experimental data.
Main Results:
- Closed-form expressions derived for Plateau border positions and orientations.
- Good agreement between analytical, numerical, and experimental results.
- Gravity's effect on Plateau border shape is minimal for typical bubble sizes.
Conclusions:
- The analytical model accurately predicts Plateau border equilibrium shape.
- Gravity causes minor widening of Plateau borders for sessile bubbles and narrowing for pendant bubbles.
- Bubble contact angle is found to be weakly dependent on gravity.
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