Bézier Curve Method to Compute Various Meniscus Shapes

Area of Science:

• Fluid dynamics
• Computational physics
• Surface science

Background:

• The Young-Laplace equation is crucial for understanding capillary phenomena.
• Previous methods for solving the Young-Laplace equation often involve complex numerical techniques.
• Accurate prediction of meniscus shape is vital in various scientific and engineering applications.

Purpose of the Study:

• To extend a previously developed Bézier curve optimization method for calculating meniscus shapes.
• To demonstrate the method's applicability to diverse capillary geometries beyond cylindrical tubes.
• To validate the Bézier curve approach against established solutions for the Young-Laplace equation.

Main Methods:

• Utilizing Bézier curves for optimizing solutions to the Young-Laplace equation.
• Applying the method to predict meniscus shapes in cylindrical capillaries, tilted plates, parallel plates, and sessile drops.
• Investigating the impact of Bézier curve degree on prediction accuracy.

Main Results:

• The Bézier curve method successfully predicts meniscus shapes across multiple geometries.
• The method demonstrates computational simplicity compared to traditional approaches.
• A 4th-degree Bézier curve accurately models menisci in cylindrical capillaries, tilted plates, and between plates.
• A 5th-degree Bézier curve is necessary for precise sessile drop shape prediction.

Conclusions:

• The Bézier curve optimization method provides a computationally simple and versatile tool for solving the Young-Laplace equation.
• This approach can be adapted for solving other complex differential equations.
• The study validates the effectiveness of Bézier curves in accurately modeling fluid interfaces.