Effect of curvature on the thermodynamics of surfaces

Scholberg, Harold M.

doi:10.1016/0039-6028(71)90096-3

Surface Science

1971

DOI: 10.1016/0039-6028(71)90096-3

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Effect of curvature on the thermodynamics of surfaces

Harold M. Scholberg

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Cited by 3 publications

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“…Lo que se produce es el efecto compensación de los escarnecedores escarnecidos, como demuestra la colación que, en cierta medida, es la visión ideal de los vejados, de esas "minorías oprimidas" (moriscos y judeoconversos) que "siempre se han refugiado en la risa para no caer por completo en la desesperación" 103 . Este autoescarnio -es decir, la cobardía del converso que reconoce burlesca y orgullosamente su autodegradación 104 -, "es a la vez una máscara para ocultar los verdaderos sentimientos ante ojos hostiles y un mecanismo defensivo para mantener el equilibrio en un mundo perverso y enemigo" 105 , cuya expresión cómica escarnecedora adquiere función defensiva en la línea "de dominar el automatismo psíquico" 106 .…”

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Guerras Y Polémicas en El “Aposentamiento en Juvera” Del Cancionero De Obras De Burlas Provocantes a Risa (1519)

COPPOLA

2023

MJS

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El Cancionero de obras de burlas provocantes a risa (1519) custodia una serie de composiciones sobre las animadas relaciones polémicas y satíricas que los letrados y políticos de España exhibían en su concurrida y conflictiva vida cultural. Dentro del contexto de la codicia de la comitiva papal y de la política del arzobispo Alonso Carrillo durante el difícil aposentamiento de la legación de Rodrigo Borja en Alcalá de Henares, nuestro trabajo estudiará cómo la primera composición dramático-histórica del “Aposentamiento en Juvera” encarna una codificación de la representación literaria del combate contra el infiel, como demuestran algunos fragmentos que, tratados con ambigüedad y polémica, nos han conducido al ciclo de los poemas fronterizos.

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Guerras Y Polémicas en El “Aposentamiento en Juvera” Del Cancionero De Obras De Burlas Provocantes a Risa (1519)

COPPOLA

2023

MJS

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“…In his equations (Scholberg, 1971), the term /a2 + y appears, where y is the surface tension and a is the radius of curvature of the interface. In the water-air system, varied…”

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“…Because the thickness of the duplex film is about two to three orders of magnitude greater than molecular dimensions, it is necessary to take the curvature energy into account. This has been done (Scholberg, 1971) with the definition of a new energy term, , which has the dimensions ergs per radian, and which, by analogy with the strength of materials, has been called the flexural rigidity. This is in accord with the terminology "surface tension" for the area dependent energy.…”

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A Hydrodynamic Mechanism for the Coalescence of Liquid Drops. Theory of Coalescence at a Planar Interface

Scholberg¹,

Lang²,

Wilke³

1972

Ind. Eng. Chem. Fund.

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SIR: In a recent issue, Lang and Wilke (1971) have described some theoretical and experimental work on the coalescence of liquid drops at a planar interface. A cursory glance at their Figure 1 shows that the model of Figure 2 is oversimplified. The correct model is shown in Figure 1 of this correspondence.For the quasi-equilibrium they assume both horizontal and vertical resolutions of the forces may be made. The horizontal resolution of the Keumann triangle gives the equationwhich shows that u1 is less than the sum of the other two tensions. This means that their eq 1 is incorrect. Therefore, the entire theoretical development is questionable. However, it is questionable not just because of some minor variations in the constant 3 and the function Q(p) in their eq 1, but because the correct model raises some question about the very basis of surface chemistry. That question is-how thick is the interfacial region? Gibbs (1931) assumed that it was of molecular dimensions and that therefore the curvature contribution to the total surface free energy could be set equal to zero. If it can be shown that the thickness of the interfacial region is large, Gibbs' assumption that the curvature energy is zero is no longer tenable. However, because of the equation above, it is evident that the two sides of the duplex film of the liquid drop, or of a foam bubble, influence each other; i.e., the thickness of the surface region is of the same order of magnitude as the thickness of the duplex film.SIR: Scholberg has raised questions concerning three parts of our theoretical development (Lang and M7ilke, 1971a) : (a) the geometry of the drop quasi-equilibrium, (b) the resolution of forces about the drop, and (c) the curvature energy of the phase-2 film.Scholberg has proposed a drop geometry in which the phase-2 film has been omitted so that the drop resembles a floating oil drop a t a water-air interface (a three-phase system). This model cannot represent a liquid drop in a liquidliquid system. The geometry shown in our Figure 2 is based on the idealization that the drop behaves like a solid sphere. More realistic drop shapes have been proposed by Chappelear (1961), Princen (1963), and others. As we discussed, all of these models predict a rate of film thinning proportional to the cube of the film thickness, differing from our eq 3 by small numerical constants. However, only the spherical drop geometry we used permits simple analytic stability analyses.The implied relationship between Scholberg's horizontal force balance and our vertical one is not a t all clear. However, because the phase-2 film was omitted from Scholberg's figure, it is not possible to derive from it a vertical force balance which included the force due to gravity. It is this latter force which causes the phase-2 film to thin and increases the likelihood of drop coalescence.Scholberg has also recommended the inclusion of a "curvature energy" term @, which he calls the 'flexural rigidity." I n his equations (Scholberg, 1971), the term @/a2 + y appears, where y i...

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Counting efficiency and detection limit of condensation nuclei counters for submicrometer aerosols

Scheibel

Porstendörfer

1986

Journal of Colloid and Interface Science

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Effect of curvature on the thermodynamics of surfaces

Cited by 3 publications

References 16 publications

Guerras Y Polémicas en El “Aposentamiento en Juvera” Del Cancionero De Obras De Burlas Provocantes a Risa (1519)

Guerras Y Polémicas en El “Aposentamiento en Juvera” Del Cancionero De Obras De Burlas Provocantes a Risa (1519)

A Hydrodynamic Mechanism for the Coalescence of Liquid Drops. Theory of Coalescence at a Planar Interface

Counting efficiency and detection limit of condensation nuclei counters for submicrometer aerosols

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