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A finite element based algorithm for determining interfacial tension (gamma) from pendant drop profiles.

Nicole M Dingle¹, Kristianto Tjiptowidjojo, Osman A Basaran

¹School of Chemical Engineering, Forney Hall of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907-2100, USA.

Journal of Colloid and Interface Science

|May 18, 2005

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A new Galerkin finite element method (gamma-PD-FEM) accurately determines interfacial tension (gamma) from pendant drop profiles. This robust algorithm offers improved precision over traditional arc length-based methods.

Area of Science:

Fluid Mechanics
Materials Science
Computational Physics

Background:

Interfacial tension is a critical parameter in fluid dynamics and materials science.
Accurate measurement of interfacial tension is essential for understanding phenomena like wetting and droplet formation.
Existing methods, such as the Bashforth and Adams (gamma-PD-BA) approach, have limitations in precision and handling boundary conditions.

Purpose of the Study:

To introduce a novel algorithm, gamma-PD-FEM, for precise determination of interfacial tension from pendant drop profiles.
To compare the performance of gamma-PD-FEM against the established gamma-PD-BA method.
To validate the algorithm's ability to assess the static equilibrium of drop shapes.

Main Methods:

Solving the axisymmetric Young-Laplace equation using the Galerkin finite element method.

Related Experiment Videos

Generating theoretical pendant drop profiles by solving the Young-Laplace equation in spherical coordinates.

Minimizing the difference between theoretical and experimental surface functions (f(theta)) for parameter estimation.

Main Results:

The gamma-PD-FEM algorithm provides a robust method for interfacial tension determination.
Comparison with simulated and experimental data shows comparable or improved accuracy over the gamma-PD-BA method.
The algorithm successfully incorporates boundary conditions at the apex and contact line, enabling static equilibrium assessment.

Conclusions:

The gamma-PD-FEM algorithm offers a reliable and accurate alternative for interfacial tension measurement.
This method enhances the understanding of fluid behavior at interfaces.
The algorithm's ability to incorporate dual boundary conditions improves the physical realism of the analysis.