Soap film properties

The fundamental property of liquid surfaces is that they tend to contract to the smallest possible area. This property is observed in the spherical form of small drops of liquid, in the tension exerted by soap films as they tend to become less extended, and in many other properties of liquid surfaces. In the absence of gravity effects, these curved surfaces are described by the Laplace equation, which relates the mechanical forces as (Adamson and Gast, 1997 Chattoraj and Birdi, 1984 Birdi, 1997) ... 

The composition of the soap solution used has a great influence on the stability and properties of the films. For good results very highly purified oleic acid must be used and the best results cannot apparently be obtained without the use of a trace of ammonia or an amine. Excess of alkali is said to be fatal this points to the hydrolytic equilibrium between acid and neutral soap being of great importance. A 5 per cent, solution of ammonium oleate in 50 per cent, glycerine makes a good solution for ordinary work details of this may be found in Lawrence s Soap Films. Perrin, however, used a 2 per cent, solution of ordinary soap ... 

The physicochemical properties of foam and foam films have attracted scientific interest as far back as a hundred years ago though some investigations of soap foams were carried out in the seventeen century. Some foam forming recipes must have been known even earlier. The foundations of the research on foam films and foams have been laid by such prominent scientists as Hook, Newton, Kelvin and Gibbs. Hook s and Newton s works contain original observations on black spots in soap films. 

The first systematic study of the various properties of soap films has been conducted by the Belgian scientist Plateau. Using the findings from investigations on the structure and properties of differently shaped films, he was the first to draw attention to that part of the film which contacts the surface holding the film. It came to be called Plateau border. Plateau studied the impact of various external effects (like the stream of air, evaporation, etc.) on the behaviour of... 

We shall examine properties of two systems of this type. Let the first system consist of a soap film stretched on two rings having the same diameter R (Fig. 28). 

This section begins with a qualitative description of thin liquid PU films. This initial investigation had five goals in mind to confirm that stable, vertically-oriented, thin liquid films could be prepared using mixtures of ingredients designed to model a PU foam, to study the hydrodynamic phenomena in the films, to compare the physical behaviour of these films to the behaviour of the more common aqueous soap films, to observe specific surfactant effects on the properties of these films, and to extrapolate conclusions about the behaviour of these films to operational PU foam. 

Some general references for surface and interfacial phenomenon are the books by Adamson and Gast [2] and Hiemenz and Rajagopalan [3]. An interesting scientific background to molecular and macroscopic properties of soap films and bubbles is provided in [4]. The fluid dynamics, heat transfer, and mass transfer of single bubbles, drops, and particles are covered in [5],... 

EXAMPLE 9.1 What is the fundamental equation when surface tension is important For experiments in test tubes and beakers, the surface of the material is such a small part of the system that surface forces contribute little to the thermodynamic properties. But for experiments on soap films in a dish pan, on cell membranes, or on interfaces, the surface properties can contribute significantly to the thermodynamics. 

Everyone has been fascinated, from an early age, by soap bubbles and soap films. This has been no less true of the scientific community. Biologists, chemists, mathematicians and physicists have all interested themselves in the properties of bubbles and films. 

His book was written primarily for students aged ten to fourteen years. Consequently it does not discuss in depth such subjects as molecular structure, interference phenomena, and mathematical properties. This book is intended for the older student, or adult, with an undergraduate background in science, or at least a sixth form education, who would like to gain a greater insight into the scientific explanations of the properties, and behaviour, of soap bubbles and soap films. In common with Professor Boys s book the demonstrations here, particularly in Chapters 3 and 4, are simple to perform using household materials. 

Chapter 5 investigates the shape of liquid drops, bubbles, and the liquid surface in the vicinity of a solid surface, using the Laplace-Young equation. The last chapter. Chapter 6, contains a number of interesting properties and applications, such as the vibrational oscillations of soap film membranes and the application of soap films to the analogue solutions of the differential equations of Poisson and Laplace. 

The author has visited numerous institutions in Britain and the United States giving lecture-demonstrations at all academic levels. Soap bubbles and soap films is a subject that can be appreciated by all ages. Primary school children can learn some simple geometrical properties and perform experiments for themselves. Older children will be able to appreciate some of the simpler scientific principles. At sixth form and undergraduate levels the more detailed explanations, presented in this book, can be given. For the researcher there are many questions that still remain to be resolved. 

The scientific study of liquid surfaces, which has led to our present knowledge of soap films and soap bubbles, is thought to date from the time of Leonardo da Vinci - a man of science and art. Since the fifteenth century researchers have carried out investigations in two distinct camps. In one camp there are the physical, chemical and biological scientists who have studied the macroscopic and molecular properties of surfaces with mutual benefit. The other camp contains mathematicians who have been concerned with problems that require the minimization of the surface area contained by a fixed boundary and related problems. A simple example of such a problem is the minimum area surface contained by a circle of wire. The solution to this problem is well known to be the disc contained by the wire. 

The great popularizer of the properties of soap films and soap bubbles at the era around the turn of this century was Charles Vernon Boys (Fig. 1.4). He gave numerous lecture-demonstrations which delighted everyone, no matter their age or academic background, and his book Soap Bubbles and the forces which mould thern has been popular with young people since its publication in 1890. 

Another example of the minimum area property is obtained if a loop of cotton thread is joined to the circular ring and a soap film is formed in the ring. It will rest loosely in the plane of the soap film (Plate 1.1(a)). When the soap film inside the loop of thread is broken the surrounding soap film, contained between the loop of thread and the circular ring, will take up the surface of minimum area. This will occur when the area of the hole inside the loop of thread is a maximum. The maximum area of the hole can be shown mathematically to occur, for a fixed length of thread, when it forms a circle. This is seen to occur in Plate 1.1.(b). 

It is shown in Appendix IV, for a restricted class of problems, that Eq. (1.27) is the mathematical condition for a surface to have minimum area. This mathematical minimum area property can be shown to hold generally for any surface that has zero excess pressure across it and hence satisfies Eq. (1.27). We can verify this result on physical grounds by considering the energy of a soap film, as in section 1.3, and showing that the condition for stable equilibrium of a soap film requires that the area of the film be minimized providing that of is constant. 

Soap solutions have the remarkable property of forming stable bubbles and films. This property is a consequence of the surface structure of the soap solution and the soap film. The surface of a bath of soap solution and a soap film consists of a monomolecular layer of amphipathic] ions. These are ions... 

There are three important contributions to the molecular forces present in a soap film that have been investigated and explain some of the equilibrium properties of soap films, particularly the properties of the thicker equilibrium film, the common black film. These are the van der Waals attraction between molecules and ions, the electrostatic repulsion due to the double layers of charge at each surface, and the Born repulsion due to the hard cores of the molecules and ions. In addition there are other molecular forces in the soap film that are not fully understood. They are probably partly steric in nature, arising from the rigidity of the surfactant. The forces due to hydrogen bonding between the water molecules are not significant. They would become important if the equilibrium thickness of the soap film was less than 20 A. 

It is possible to use the result concerning the minimization of the surface area of a soap film to solve some mathematical minimization problems. In order to do this we must construct a boundary with the property that the solution to the mathematical problem will be given by the area of the soap film, when it is minimized, at equilibrium. In the case of a soap film contained by a circular ring the equilibrium configuration gives the solution to the mathe-... 

This is the shortest roadway encountered. Is it the shortest If it is the shortest road linking the four towns, how is it possible to prove that there is no shorter road system Alternatively, if it is not the shortest system, what is the shortest roadway configuration and what is its length This problem can be simply solved using an analogue method based on the minimization property of the area of a soap film. 

All the problems discussed in this chapter have been solved by analogue methods based on the minimization property of the surface area of soap films. We shall now solve using analytic means one of the simpler problems, the problem of finding the minimum path linking three points. 

In the previous chapter we applied the minimum area property of soap films to the solution of some two dimensional problems requiring the minimization of the path length linking a number of points. This was carried out by using two parallel plates in order to maintain a constant film width. In this chapter this constraint will no longer be imposed and more general three dimensional minimization problems will be examined. 

All the surfaces examined in this section have the property that there is no pressure difference across the soap film surface. Thus the Laplace-Young result of section 1.5 gives... 

The minimum surface area property of soap films has been shown to be a consequence of the minimization of the free energy of the soap films. This minimization condition leads to a differential equation for the surface the Laplace-Young differential equation for zero excess pressure. In the more general system of soap film surfaces and bubbles the free energy consists of two terms. One contribution from the area of the film. A, and another contribution from the air inside the bubble Fb- This total free energy F is thus given by... 

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