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Macroscopic theory for capillary-pressure hysteresis.

Bhagya Athukorallage1, Eugenio Aulisa, Ram Iyer

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Summary

We developed a theory for macroscopic contact angle hysteresis by minimizing Helmholtz free energy. This model explains capillary pressure and volume relationships in drops, simplifying complex fluid behavior.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Materials Science

Background:

  • Contact angle hysteresis is crucial for understanding fluid behavior on surfaces.
  • Existing models often oversimplify the complex pinning effects at the contact line.
  • Macroscopic drops exhibit hysteresis, but a unified theoretical framework is lacking.

Purpose of the Study:

  • To present a novel theory for macroscopic contact angle hysteresis.
  • To model the relationship between capillary pressure and volume in sessile drops.
  • To simplify the understanding and modeling of capillary effects in fluid systems.

Main Methods:

  • Minimization of Helmholtz free energy for a solid-liquid-gas system under constant volume.
  • Application of calculus of variations to derive governing equations.
  • Utilizing a variational inequality to describe contact angle hysteresis for advancing/receding flow.

Main Results:

  • Derived the Young-Laplace equation for the drop surface and a variational inequality for contact angle hysteresis.
  • Developed a hysteresis operator linking capillary pressure and volume.
  • Validated the theoretical model using experimental data for macroscopic sessile drops.

Conclusions:

  • The Helmholtz free energy minimization provides a robust theory for macroscopic contact angle hysteresis.
  • The derived hysteresis operator simplifies the analysis of capillary pressure-volume relationships.
  • This approach offers a powerful tool for understanding and modeling fluid behavior on surfaces, analogous to magnetic hysteresis.