Thermodynamics of Sessile Drops on a Rigid Substrate: A Comparison of Two Theories

Published

November 15, 2005

Author(s)

Jeffrey W. Bullard

Abstract

Minimization of free energy is used to calculate the equilibrium shapes of sessile liquid drops under different wetting conditions and under the influence of a gravitational body force. The total system free energy is assumed to obey an equation recently derived by Searcy [1], and the shapes of sessile drops of different sizes are calculated and compared with experimental measurements. Stationary states in the free energy are found using standard variational principles, which lead not only to an Euler-Lagrange differential equation for the drop shape, but also to the boundary conditions at the three-phase junction where the liquid, solid, and surrounding vapor meet. The analysis shows that the Searcy equation leads to the classical Young-Dupr equation for the thermodynamic contact angle. Drop shapes calculated by this approach are in excellent agreement with experimenta observations of drops of pure water resting on a clean Teflon substrate.

Citation

NIST Interagency/Internal Report (NISTIR) - 7272

Report Number

7272

NIST Pub Series

NIST Interagency/Internal Report (NISTIR)

Pub Type

NIST Pubs

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DOI Link

Keywords

building technology, contact angle, thermodynamics, wetting

Citation

Bullard, J. (2005), Thermodynamics of Sessile Drops on a Rigid Substrate: A Comparison of Two Theories, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.7272 (Accessed June 5, 2023)