Capillary surfaces stability from families of equilibria with application to the liquid bridge by Brian J. Lowry

Cover of: Capillary surfaces | Brian J. Lowry

Published by Cornell Theory Center, Cornell University in Ithaca, N.Y .

Written in English

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Edition Notes

Includes bibliographical references.

Book details

StatementBrian J. Lowry, Paul H. Steen.
SeriesTechnical report / Cornell Theory Center -- CTC93TR150., Technical report (Cornell Theory Center) -- 150.
ContributionsSteen, Paul H., Cornell Theory Center.
The Physical Object
Pagination30, [33] p. :
Number of Pages33
ID Numbers
Open LibraryOL16960879M

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The experimental insights gained have, in Capillary surfaces book, strongly stimulated further theoretical and mathematical investigations.

Advancing and receding contact angles, wetting barriers, pinning of contact lines, oscillations of capillary surfaces and fluid sloshing are also discussed. In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different a consequence of being a surface, a capillary surface has no thickness in slight contrast with most real fluid interfaces.

Capillary surfaces are of interest in mathematics because Capillary surfaces book problems involved are very nonlinear and have interesting properties, such as.

This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of.

Equilibrium Capillary Surfaces. Authors: Finn, Robert Free Preview. Buy this book eB08 *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook.

Only valid for books with an ebook version. Equilibrium Capillary Surfaces (Grundlehren der mathematischen Wissenschaften) Softcover reprint of the original 1st ed. Edition by Robert Finn (Author) ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: Read this book if you are extremely interested in the reasons of capillary surfaces, the shapes they undergo, stability, and dynamics.

Moreover, weightlessness is a big Cited by: If one (at least) of the materials is a fluid, which forms with another fluid (or gas) a free surface interface, then the interface will be referred to as a capillary surface.

Keywords Calculation Surfaces behavior equation geometry identity plant proof stability theorem. For surfaces with zero capillary pressure, the length of the interval of canthotaxis varies in proportion to the cube of the angular interval.

Some details can be found in Langbein's book. Radial graphs and capillary surfaces in a cone are examples analogous to (vertical) graphs on a plane and capillary surfaces in a vertical cylinder if we move the vertex O of the cone to infinity. For a convex cone C Γ, Choe and Park have shown that if a parametric capillary surface S meets C Γ orthogonally, then S is part of a sphere [8].Cited by: 6.

Capillary forces can have a critical impact at the microscale. Capillary forces act at fluid-air-solid interfaces to minimize the surface energy of the interface. Surface tension or capillary forces scale with the perimeter of the wetted area ~[s 1].In the bulk region of a liquid, cohesive forces between the liquid molecules are balanced and shared with all the neighboring molecules.

History. Capillary bridges have been studied for over years. The question was Capillary surfaces book for the first time by Josef Louis Lagrange inand interest was further spread by the French astronomer and mathematician C.

Delaunay. Delaunay found an entirely new class of axially symmetrical surfaces of constant mean formulation and the proof of his theorem had a long story. Some mathematical aspects of capillary surfaces A. Mellet∗ April 9, Abstract This is a review of various mathematical aspects of the study of cap-illary surfaces.

A special emphasis is put on the behavior of the contact line, the three phases junction between the liquid, solid and vapor. 1 Introduction. Get this from a library. Capillary surfaces: shape-stability-dynamics, in particular under weightlessness. [Dieter W Langbein] -- This book is devoted to interfaces between two fluids, that is, between a liquid and a gas (such as water and air) or between two liquids (such as water and oil).

The main motivation for the book. ISBN: OCLC Number: Description: XIII, Seiten: Diagramme. Contents: 1 Introduction.- An interface constitutes an extensive, two‐dimensional defect in a system. This chapter is devoted to interfaces between a pure liquid and its vapor.

The interface is characterized by easy mechanical. Capillary action occurs because water is sticky, thanks to the forces of cohesion (water molecules like to stay close together) and adhesion (water molecules are attracted and stick to other substances).

Adhesion of water to the walls of a vessel will cause an upward force on the liquid at the edges and result in a meniscus which turns upward. Although surface tension is present at all interfaces, it is most important for small fluid bodies.

At length scales where surface tension does come into play the shape of an inter-face bears little relation to the gravitational equipotential surfaces that dominate the static shapes of large-scale systems analyzed in the preceding Size: KB.

This classification produces a unified approach to fluid interfaces in capillary tubes, sessile and pendent drops, liquid bridges, as well as exterior and annular capillary surfaces. Capillary surfaces are closely related to minimal surfaces.

In fact, capillary surfaces minimize a more general functional than do minimal surfaces. The standard mathematical model for volume constrained capillary problems is as follows: a set in is the region occupied by.

This book has been cited by the following publications. the effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering.

Les surfaces de glissement de Helmoltz at la résistance des fluides. Ann. de Chim. Phys. 23, – [23] Brodetsky, S. Cited by:   Capillary Surfaces: Shape, Stability, Dynamics, in Particular Under Weightlessness will be valuable to those working or having applications in this specialized area and useful as a reference to those with broader interests in capillary phenomena.

The book is not recommended to those lacking significant background in fluid physics and applied Cited by: 7. An entry on capillary action first appeared in the Encyclopedia Britannica in (Maxwell ), reflecting the mathematical physicists’ wide interest in the subject at that time (e.g., Schrodinger ).

About one-third of the¨ page entry speaks to the stability of capillary surfaces. The entry remains in the encyclopedia untilatFile Size: 1MB.

Capillary Surfaces by Dieter W. Langbein,available at Book Depository with free delivery worldwide. Note: If you're looking for a free download links of Equilibrium Capillary Surfaces (Grundlehren der mathematischen Wissenschaften) Pdf, epub, docx and torrent then this site is not for you.

only do ebook promotions online and we does not distribute any free download of ebook on this site. dicates capillary rise; ˇ=2 0 are the surfaces u 0; if =0, the only such surfaces are u const:If. Thermodynamics of surfaces and capillary systems Soustelle, Michel This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of.

Read Capillary Surfaces: Shape Stability Dynamics in Particular Under Weightlessness (Springer. Zhu et al.: Shape and force analysis of capillary bridge between two slender structured surfaces Figure 1.

Change in contact angle caused by differences in wet-tability. the actual situation. Another study (Valencia et al., ) ad-dressed the morphology of the liquid phases within chemi-Cited by: 3. Students are presented with a short lesson on the difference between cohesive forces (the forces that hold water molecules together and create surface tension) and adhesive forces (the forces that causes water to "stick" to solid surfaces.

Students are also introduced to examples of capillary action found in nature and in our day-to-day lives. On capillary free surfaces in a gravitational field Concus, Paul and Finn, Robert, Acta Mathematica, ; A free boundary value problem for capillary surfaces. Gerhardt, Claus, Pacific Journal of Mathematics, ; On the existence of capillary free surfaces in the absence of gravity.

Chen, Jin Tzu, Pacific Journal of Mathematics, Cited by: Capillary effects are very important at small scales (see previous chapter [Physics_at_smaller_scales]). They appear at interfaces between a liquid and another material liquid, gas, or solid. The interfaces give rise to a surface tension that rules the dynamics of this interface.

Find Equilibrium Capillary Surfaces by Finn, Robert at Biblio. Uncommonly good collectible and rare books from uncommonly good booksellers This is an ex-library book and may have the usual library/used-book markings book has hardback covers.

In good all round condition. No dust jacket. Please note the Image in this listing is a. The above results describe a limiting case among corresponding properties that hold for surfaces defined over domains with smooth boundaries.

This extension is indicated, as well as a formal extension to n -dimensional surfaces; here the interest centers on the fact that it is the mean curvature of an (n -1)-dimensional boundary element that Cited by: dynamics of drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics.

Theoretical developments will be accompanied by classroom demonstrations. The role of surface tension in biology will be highlighted. associated with free surfaces. Young, surface tension, and wetting In his article on capillary action for the Encyclopedia Bri-tannica,4,5 James Clerk Maxwell wrote that Johann An-dreas von Segner, a Hungarian mathematician, first de-veloped the concept of surface tension, but Young is responsible for the bright idea of using that concept to ex.

Equilibrium capillary surfaces in zero gravity in cylindrical containers whose sections are (wedge) domains with corners are studied. Necessary and also sufficient conditions are developed for the existence or nonexistence of surfaces that are locally graphs over the base at the corner, with (prescribed) contact angles that may differ on the two by: @article{osti_, title = {High order finite element method for the calculation of capillary surfaces.

[Young--Laplace equation]}, author = {Brown, R A}, abstractNote = {A reduced quadratic finite element method on quadrilaterals is developed for discretizing the capillary equation in regular and irregular domains. Newton's method is used to solve the resulting set of nonlinear equations.

The cause of surface tension is said to be asymmetry in the forces experienced by the molecules at the surface due to different interactions with air and liquid, but then the same argument also applies for all other surfaces, where the fluid is in contact with the container then why isn't all strange surface tension phenomenon seen at those surfaces.

The movement of water (and other liquids) up or down capillary (narrow bore) tubes and confined spaces is due to the surface tension along the curved surfaces. a The meniscus is the curved liquid-gas surface b (shown right) with the water curving towards the surface at hydrophilic surfaces, or away at hydrophobic surfaces as shown on the far right.

To determine the surface tension of water by capillary rise method. Apparatus Three capillary tubes of different radii and a tipped pointer clamped in a metallic plate with a handle, travelling microscope, clamp and stand, a fine motion adjustable height stand, a flat bottom open dish, clean water in a beaker, thermometer.

the capillary are placed in the buffer reservoirs and the optical viewing window is aligned with the detector. After filling the capillary with buffer, the sample can be introduced by dipping the end of the capillary into the sample solution and elevating the immersed capillary a foot or so above the detector-side buffer reservoir.Capillary Bridges and Capillary-Bridge Forces Fig.

Liquid bridge between a spherical particle and a planar solid surface. constant mean curvature) and investigated their stability [].

The study of the instability of cylindrical fluid interfaces by Plateau was further extended by Rayleigh, who considered also jets of viscous fluid File Size: KB.Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to, external forces like effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin tube, in porous materials such as paper, in some non-porous materials such as liquefied carbon.

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