In order to obtain consistency with the force balance theory of Young and Laplace, which quantitatively predicts the height of capillary rise from the contact angles of drops on solid surfaces, Gibbs made chemical potentials in interface functions of the integral interface free energies. We cite evidence that equilibrium chemical potentials in one-component systems are identical at interfaces to equilibrium chemical potentials in bulk phases. We evaluate two postulates. Partial free energies of liquids at an interface with a solid are functions of the strength and range of attractive fields outside solid phase boundaries. At equilibrium, the chemical potentials in all interfaces of a one-component liquid equal the chemical potential in its interior when the liquid is bonded to one or more immiscible solids. These postulates yield equations for partial equilibrium - PE - states of drops, films, and liquids. The PE equations yield the same prediction of the height of a meniscus from the contact angle of drops as does Young–Laplace theory and also the same dependence of the volume of capillary condensate on vapor pressure as does the Kelvin equation. But our measurements of the contact angles of water on glass and Teflon and between their close-spaced surfaces contradict the YL supposition that meniscus angles are the same as angles of drops on glass and Teflon surfaces and support the PE postulate that attraction by the external fields of solids, not meniscus curvature, is responsible for capillary rise. We use published data to illustrate the validity of the PE conclusion that divergence or convergence at the saturation pressure of a parent liquid depends on whether or not the attractive field of a solid surface imparts to the liquid more than twice the energy required to create two liquid-vapor interfaces. For divergent water films on quartz, the PE equation provides a quantitative fit to experimental data for films of any thickness greater than 1.5 nm. No previous theory has accomplished that. In an appendix, we illustrate applications of PE theory to evaluating the complex interactions between inherently reversible chemical diffusion and inherently irreversible forces introduced by strains.
A Partial Equilibrium Theory For Liquids Bonded to Immobile Solids
BERUTO, DARIO;BARBERIS, FABRIZIO
2009-01-01
Abstract
In order to obtain consistency with the force balance theory of Young and Laplace, which quantitatively predicts the height of capillary rise from the contact angles of drops on solid surfaces, Gibbs made chemical potentials in interface functions of the integral interface free energies. We cite evidence that equilibrium chemical potentials in one-component systems are identical at interfaces to equilibrium chemical potentials in bulk phases. We evaluate two postulates. Partial free energies of liquids at an interface with a solid are functions of the strength and range of attractive fields outside solid phase boundaries. At equilibrium, the chemical potentials in all interfaces of a one-component liquid equal the chemical potential in its interior when the liquid is bonded to one or more immiscible solids. These postulates yield equations for partial equilibrium - PE - states of drops, films, and liquids. The PE equations yield the same prediction of the height of a meniscus from the contact angle of drops as does Young–Laplace theory and also the same dependence of the volume of capillary condensate on vapor pressure as does the Kelvin equation. But our measurements of the contact angles of water on glass and Teflon and between their close-spaced surfaces contradict the YL supposition that meniscus angles are the same as angles of drops on glass and Teflon surfaces and support the PE postulate that attraction by the external fields of solids, not meniscus curvature, is responsible for capillary rise. We use published data to illustrate the validity of the PE conclusion that divergence or convergence at the saturation pressure of a parent liquid depends on whether or not the attractive field of a solid surface imparts to the liquid more than twice the energy required to create two liquid-vapor interfaces. For divergent water films on quartz, the PE equation provides a quantitative fit to experimental data for films of any thickness greater than 1.5 nm. No previous theory has accomplished that. In an appendix, we illustrate applications of PE theory to evaluating the complex interactions between inherently reversible chemical diffusion and inherently irreversible forces introduced by strains.
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