Translation:Essay on the theory of capillary phenomena. Theory of surface adhesion of liquid

Essay on the theory of capillary phenomena. Theory of surface adhesion of liquid (1879)
by Ippolit S. Gromeka, translated from Russian by Wikisource

4438121Essay on the theory of capillary phenomena. Theory of surface adhesion of liquid1879Ippolit S. Gromeka

Essay on the theory of capillary phenomena.

Theory of surface adhesion of liquid.

Read at the Mathematical Society on October 21, 1878

I. S. Ippolit

Newton drank in his "Optics" that as the water rose inside a capillary tube or between parallel plates and gave an explanation of the law found by Jurin's experiment, according to which the rise is inversely proportional to the tube diameter or the distance between the plates. Newton's explanation is based on considerations whose validity is doubtful, but he did not give them sufficient development. Earliest attempts to construct a mathematical theory of capillary phenomena were undertaken by Daniel Bernoulli^[1] and Alexis Clairaut^[2]. Bernoulli himself admits that he could not determine the law of the rise. Clairaut did not give an analytical conclusion of Jurin's law, and the conclusions he came to were still too vague. The first successful explanation of the theory capillary phenomena belongs to Seiner^[3], who suggested that the interaction between liquid particles extends only to inaccessible distances. He studied for a clean liquid the type of surface that liquids take on drops and proved that the height of such a surface is inversely proportional to the radius of the curvature.

In 1805 Thomas Young^[4] presented to the Royal Society of London a discussion on the cohesion of liquids. Assuming the existence of a special force on the surface layer of the liquid, Young brought out the surface equilibrium, limiting heavy liquid, and found a constant the angle at which this surface meets with the walls of the tube. In addition, he examined many specific questions of this theory, and reached almost all those you conclude; to which scientists were subsequently led further research in this area. I was stopped in my research to give a detailed deveelopment of Young's by the appearance of world of Lalapce's theory of capillarity^[5], to which I limited only some comments.

Laplace explained the capillarity phenomena by the mutaul attaction of particles and therefore created a theory that is completely consistent with the general principles of classical mechanics. But he did not find the constant angle at which the liquid surface meets the surface of the vessel. This gap was filled by Gauss^[6], who retaining the basic assumptions of Laplace,derived the theory of capillary phenomena from the principle of possible speeds.

In 1831, Poisson published his Nouvelle theorie del'action capillaire, also based on the assumption of partial interactions. In this work, consideration was given to the rapid change in density that must necessarily exist relative to the liquid particles lying on the surface. Various questions of the theory were examined and studied by Poisson with such completeness that the whole theory seemed exhausted in his labour. All that remained was to connect this theory with the general theory of equilibrium of liquids using the principle of possible speeds. This task was completed by August Yu. Davidov^[7] in his dissertation related to this subject. A. Yu. Davidov studied the theory of capillarity with the general rules of analytical mechanics, and also took into account physical circumstances that are significantly related to this subject.

In 1859, Paul du Bois-Reymond^[8] defended his dissertation in Berlin, which is also devoted to thermal capillarity. Having laid out with particular care the theory of the potential of capillary forces, he then gave in his dissertation a number of preparatory formulas^[9] representing the formation of certain integrals extended to the surface, through integrals extended to its contour. Some of these curious formulas can be found in Laplace's and Poisson's; however, in my view, du Bois-Reymond brought them out in an independent way. Questions concerning thermal capillarity, Du Bois-Reymond leads to four main problems. The solution to the last of them, which relates to an equally floating body, is based on the erroneous assumption and led the author to incorrect conclusions about the relationship that exists between the entire volume of floating body and that part of it that is wetted liquid^[10].

Meanwhile, how the theory founded by Laplace, in the works of the mentioned scientists and some others, reached significant development and well-known completeness, the method proposed by Young, developed much more slowly and for some time found only few followers.

In 1845 and 1846 Hagen^[11] in a number of articles again examined from this point of view both the general theory of capillarity and its particular questions. Since then, many physicists (Plateau, Lamarle, Van der Mensbrugghe and others) have used the hypothesis of surface cohesion of liquids when considering capillary phenomena. The number of such followers of Young has been constantly increasing in recent times. Flipping through the first books of the magazine Almeida, dedicated to physics, we find several notes concerning the theory of capillarity and a whole polemic between followers of both directions. At first Moutier^[12] placed a note in order to show the advantage Laplace theory. Renewing the reproach that Young's theory had not criticized before, as if it was founded only on the analogy between the surface layer of a liquid and an elastic plate, Moutier proves that the theory of partial attractions can explain all capillary phenomena without possible hypotheses about the existence of an elastic plate on the surface of a liquid. In the same volume there is a letter from Van der Mensdrugghe, who hotly disputes Moutier's opinion that the concept of tension, if any, exists, at the very least, uselessly. Understanding that this does not exclude the validity of Laplace's theory, and having mentioned Lamarle's attempt^[13] to explain tension precisely on the basis of this theory, Mensbrugghe points to the works of Quincke, Ludtge and many others. "So numerous questions,” writes Mensbrugghe, “considered, if not resolved, by these scientists, sufficiently proved the greatest benefit of this view, which will not hesitate to be accepted in physics courses.” I bring an excerpt from this controversy, as a characteristic of those opinions that have been expressed about this subject recently. In the same edition of Almeida we meet an attempt made by Duclaux^[14] to implement the idea expressed by Mensbrugghe is to base the elementary method on the principle of surface adhesion of a liquid. A similar elementary theory presented in the Grashoff's textbook.

The above brief overview of some of the most important works concerning capillary phenomena, clearly reveals two directions in it, which not not only differ significantly from each other in their counterparts, but even, in the interpretation of some authors, they become directly hostile to each other. In this I decide to offer my readers a special point of view on the theory of surface adhesion of liquid. This view is capable, it seems to me, of reconciling both of the abovementioned directions, and also of removing from Young’s theory the most important accusation that its opponents bring to it, claiming that it does not have a sufficient basis in general principles of rational mechanics. A theoretical consideration of those questions that lead to the idea of partial forces will significantly is facilitated through the introduction of the auxiliary concept of pressure. Kowu^[15] further defined as the resultant force of a certain system of partial interactions and showed that the influence of these interactions on the equilibrium of particles of any body can be determined as long as it is known further at every point inside the body. After that the concept of pressure was usefully used in the study of the equilibrium and movement of certain physical bodies, what are the solid ynpyria of the body, liquids undergoing destruction inside, etc. Applying this concept to the consideration of capillary phenomena leads to the theory of surface adhesion in the general principles of mechanics, including the elimination its disagreement with Laplace's theory.

This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.

Original:

This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.

Public domainPublic domainfalsefalse

Translation:

The standard Wikisource licenses apply to the original work of the contributor(s).

This work is licensed under the terms of the GNU Free Documentation License.

The Terms of use of the Wikimedia Foundation require that GFDL-licensed text imported after November 2008 must also be dual-licensed with another compatible license. "Content available only under GFDL is not permissible" (§7.4). This does not apply to non-text media.

Public domainPublic domainfalsefalse

This work is released under the Creative Commons Attribution-ShareAlike 4.0 International license, which allows free use, distribution, and creation of derivatives, so long as the license is unchanged and clearly noted, and the original author is attributed—and if you alter, transform, or build upon this work, you may distribute the resulting work only under the same license as this one.

Public domainPublic domainfalsefalse

↑ Hydrodynamique. 1738.
↑ Theorie de la figure de la terre. 1741.
↑ De figuris superficierum fluidorum. Comment, soc sclent. Gott. 1751.
↑ An essay on the cohesion of fluids, Phil. Transact. 1805.
↑ Mecanique celeste. T. lY
↑ Principia generalia theoriae fluidorum in statu aequlibrii. Gauss Werke. T. V.
↑ Опред^ленГе поверхности жидкости, заключенной въ сосуд'Ь. 1851.— Теор1я капиллярныхъ явлешй. А. Ю. Давидова. 1851
↑ De aequilibrio fluidorum. Dissertatio inauguralis. 1859
↑ Тамъ-же, § 6
↑ Тамъ-же, § 12, Problema 1У.
↑ Denkschriften der Berl. Ак. 1845, 1846
↑ Journal d'Almeida. Т. I.
↑ Comptes rendus, Т. 64, 1867. Зам-Ьтка Ath. Dupre
↑ Sur la capillarite. Duclaux. Extrait d'un travail inedit: „Theorie elementaire de la capillarite'*. Journal d'Almeida. 1872
↑ См. Статику Moignau стр. 616.

[1] Hydrodynamique. 1738.

[2] Theorie de la figure de la terre. 1741.

[3] De figuris superficierum fluidorum. Comment, soc sclent. Gott. 1751.

[4] An essay on the cohesion of fluids, Phil. Transact. 1805.

[5] Mecanique celeste. T. lY

[6] Principia generalia theoriae fluidorum in statu aequlibrii. Gauss Werke. T. V.

[7] Опред^ленГе поверхности жидкости, заключенной въ сосуд'Ь. 1851.— Теор1я капиллярныхъ явлешй. А. Ю. Давидова. 1851

[8] De aequilibrio fluidorum. Dissertatio inauguralis. 1859

[9] Тамъ-же, § 6

[10] Тамъ-же, § 12, Problema 1У.

[11] Denkschriften der Berl. Ак. 1845, 1846

[12] Journal d'Almeida. Т. I.

[13] Comptes rendus, Т. 64, 1867. Зам-Ьтка Ath. Dupre

[14] Sur la capillarite. Duclaux. Extrait d'un travail inedit: „Theorie elementaire de la capillarite'*. Journal d'Almeida. 1872

[15] См. Статику Moignau стр. 616.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]