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



Jeffrey W. Bullard


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.
NIST Interagency/Internal Report (NISTIR) - 7272
Report Number


building technology, contact angle, thermodynamics, wetting


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], (Accessed June 16, 2024)


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Created November 15, 2005, Updated June 2, 2021