Membranes soap film

As a point of interest, it is possible to form very thin films or membranes in water, that is, to have the water-film-water system. Thus a solution of lipid can be stretched on an underwater wire frame and, on thinning, the film goes through a succession of interference colors and may end up as a black film of 60-90 A thickness [109]. The situation is reminiscent of soap films in air (see Section XIV-9) it also represents a potentially important modeling of biological membranes. A theoretical model has been discussed by Good [110]. 

The schematic diagram of the experimental setup is shown in Fig. 2 and the experimental conditions are shown in Table 2. Each gas was controlled its flow rate by a mass flow controller and supplied to the module at a pressure sli tly higher than the atmospheric pressure. Absorbent solution was suppUed to the module by a circulation pump. A small amount of absorbent solution, which did not permeate the membrane, overflowed and then it was introduced to the upper part of the permeate side. Permeation and returning liquid fell down to the reservoir and it was recycled to the feed side. The dry gas through condenser was discharged from the vacuum pump, and its flow rate was measured by a digital soap-film flow meter. The gas composition was determined by a gas chromatograph (Yanaco, GC-2800, column Porapak Q for CO2 and (N2+O2) analysis, and molecular sieve 5A for N2 and O2 analysis). The performance of the module was calculated by the same procedure reported in our previous paper [1]. 

Small molecule size-c Ecluslon chrmutography 441 Soap-film meter (GC) 4, 235 Solid-phase extraction 777 cartridges 777 membranes 780 optimization 777, 783 sorbents 778, 785 trace enrichment 777, 783 Solubility parameters 460 Solvatochromic parameters GC 191... 

As a general physical example one may consider a flexible membrane like a thin rubber sheet or a soap film stretched over an irregular support, such as a distorted ring. 

Various other physical processes lead in their mathematical description to equations of the same form as Flq (2). especially in its steady-state form, Such processes include the conduction of electricity in a conductor, or the shape of a thin membrane stretched over a curved boundary. This situation has led to the development of analogies (electric analogy, soap film analogy) to heal conduction processes, which are useful because they often offer the advantages of simpler experimentation. 

Those researchers whose work have no direct connection with biomembranes perhaps are not acquainted with experimental lipid bilayers, commonly referred to as planar bilayer lipid membranes (BLMs) and spherical liposomes. These artificial systems have been extensively used in the past four decades as experimental models of cell membranes. The work began with D. O. Rudin and his associates in 1959 [1]. They first investigated lipid monolayers and multilayers of the Langmuir-Blodgett (L-B) type, and then they toyed with soap bubbles and films. It was realized that the structure of a soap film in air, in its final stage of thinning, has a structure that may be depicted as two lipid monolayers sandwiching an aqueous solution. That is a system which may be represented as ... 

For decades, colloid and surface scientists have known that amphiphilic molecules such as phospholipids can self-assemble or self-organize themselves into supramolecular structures of bilayer lipid membranes (planar BLMs and spherical liposomes), emulsions, and micelles [2-4]. As a matter of fact, our current understanding of the structure and function of biomembranes can be traced to the studies of these experimental systems such as soap films and Langmuir monolayers, which have evolved as a direct consequence of applications of classical principles of colloid and interfacial chemistry. As already mentioned in Section I, the seminal work on the self-assembly of planar lipid bilayers and bilayer or black lipid membranes was carried out in 1959-1963. The idea started while one of the authors was reading a paperback edition of Soap Bubbles by C. 

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. 

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. 

A soap film has many properties in common with an elastic membrane. If it is contained by a circular ring it can be made to vibrate transversely, in a direction perpendicular to the ring, like a drum skin. These vibrations are... 

A membrane is a two dimensional string . There are special frequencies of vibration, normal modes, of the membrane in which all elements vibrate with the same angular frequency, a>. Once all of these special motions are known it is possible to describe any general motion of the membrane. We shall begin the study of the vibrations of membranes by obtaining the equation of motion of the soap film membrane and hence obtain the normal mode frequencies. 

The determination of the normal modes of a membrane can be applied to membranes contained by any boundary. It can be extended to problems such as that of a kettledrum , in which air is trapped in the drum by a soap film membrane. The motion of the air in the drum must also be taken into account in this problem. 

The normal modes of a soap film membrane with a rectangular boundary, circular boundary, or a boundary of any shape, can be easily demonstrated experimentally.29.96-114 It is an advantage to use one of the long lasting recipes, section 1.7, for the soap film. However, solutions made from washing-up liquid can be used but will not have as long a lifetime. 

A uniformly stretched rubber membrane is similar in many respects to a soap film, or the interface between two fluids. It has a uniform tension and the thickness of the membrane is small compared with the dimensions of the surface area. The analysis of section 5.2, which derives the Laplace-Young equation for a fluid interface or soap film, applies equally to a uniformly stretched membrane with a transverse pressure load that is perpendicular to the surface. So the Laplace-Young equation for the membrane is... 

In section 5.1 it was emphasised that the Laplace-Young equation was a differential equation. Thus once the boundary curve of the membrane, or soap film, has been chosen the solution is unique. 

If it is not convenient to obtain the configuration of a membrane with a pressure load distribution, pm, and line tension, am, one can build an analogue system using a soap film. The Laplace-Young equation for the soap film, using a/ for the film tension and pf for the pressure difference across the film, is... 

Thus using the same boundary conditions for the soap film and the membrane, one can ensure that the solution to (6.48) is identical to (6.47) by setting... 

The differential equations of Poisson and Laplace occur in many branches of physics, other than the fields of membranes and soap films. We can thus use the soap film as an analogue method of solving these equations. It must be remembered that soap films satisfy (6.53) and (6.54) providing the small gradient conditions, (6.52), are satisfied at all points on the surface. 

The single gas permeation system is illustrated in Fig. 5.5. Pure O2 and pure N2 are introduced into the system at feed pressures of 1-5 bar at ambient temperature. The permeate side of membrane is maintained at atmospheric pressure. A soap film flow meter is used to measure the gas permeation rate. 

Thin film composite membranes were prepared on in-house fabricated porous supporting membranes made of either polyetherimide (Ultem ) or polyacrylonitrile (PAN). Gas fluxes of composite membranes were measured at 1-5 bar feed pressure (pure gases) and room temperature using a soap-film bubble flow meter. In this case, the permeate pressure was the ambient atmospheric pressure. 

Thermotropic smectic membranes are similar to the Newton black soap films in respecf to their structure, thickness, and because both are spanned on frames and can exchange molecules with the meniscus. However, the smectic membranes are more complex in the respect that the number N of monolayers is variable, whereas the Newton black films are usually bilayers. Smectic membranes are also similar to vesicles by means of their layered structures however, the vesicles are rather isolated unframed systems in the sense that the number of molecules is conserved, but the surface is free to evolve. ... 

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