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Excess Pressure Inside a Drop and a Bubble

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The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.

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Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method

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Published on: June 14, 2019

Interfacial tension measurements using a new axisymmetric drop/bubble shape technique.

M A Cabrerizo-Vilchez¹, J R Fernández², M A Fernández-Rodríguez³

¹Biocolloid and Fluid Physics Group, Applied Physics Department, Faculty of Sciences, University of Granada Avda. de la Fuente Nueva s/n E-18071 Granada Spain.

|May 6, 2022

Summary

A new mathematical model accurately computes interfacial tension for drops and bubbles using the Young-Laplace equation and Newton

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Area of Science:

Fluid dynamics
Interfacial phenomena
Mathematical modeling

Background:

Accurate computation of interfacial tension is crucial for understanding fluid behavior.
Existing models may have limitations in handling specific geometries or conditions.

Purpose of the Study:

To introduce a novel mathematical model for calculating interfacial tension.
To provide a versatile and reproducible method for analyzing drops and bubbles.

Main Methods:

The Young-Laplace equation is employed to describe interface shape.
Numerical differentiation and the Newton method are used for solving the equations.
Boundary conditions ensure prescribed volume and fixed position.

Main Results:

The model was validated using theoretical bubble and drop data.
Numerical results were obtained for water and surfactant solutions.
Demonstrated applicability for both pendant/sessile drops and pendant/captive bubbles.

Conclusions:

The proposed mathematical model offers a reliable approach for interfacial tension computation.
The methodology is versatile, applicable to various fluids and bubble/drop configurations.
The approach is reproducible and suitable for scientific research.