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Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films

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Variable thickness model for fluid films under large displacement.

Pavel Grinfeld¹

¹Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19105, USA.

Physical Review Letters

|January 15, 2011

Summary

This study introduces dynamic nonlinear equations for thin fluid films, revealing dynamic thickening phenomena consistent with experimental observations under large deformations. The findings highlight the role of internal energy functions in capturing diverse fluid film behaviors.

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Area of Science:

Fluid dynamics
Nonlinear physics
Materials science

Background:

Understanding the behavior of thin fluid films under large deformations is crucial for various scientific and engineering applications.
Existing models may not fully capture the complex dynamic phenomena observed in experiments.

Purpose of the Study:

To develop and analyze dynamic nonlinear equations for free thin fluid films.
To explain experimental observations, such as dynamic thickening, in fluid films undergoing large deformations.

Main Methods:

Formulation of a two-dimensional model for thin fluid films.
Representation of film thickness using two-dimensional density (ρ).
Numerical solutions of the derived dynamic nonlinear equations.

Main Results:

The numerical solutions exhibit features consistent with experimental data for fluid films under large deformations.
Dynamic thickening was observed in the simulations.
Demonstration that a suitable internal energy function e(ρ) can capture a wide range of effects.

Conclusions:

The proposed dynamic nonlinear equations provide a robust framework for studying thin fluid films.
The model successfully explains dynamic thickening and other complex behaviors.
Internal energy functions are key to accurately modeling diverse fluid film dynamics.