Gibbs-Plateau border

Mueller et al. [6] discovered in 1962 that when a small quantity of a phospholipid (2% wt/vol alkane solution) was carefully placed over a small hole (0.5 mm) in a thin sheet of Teflon or polyethylene (10-25 pm thick), a thin film gradually forms at the center of the hole, with excess lipid flowing towards the perimeter (forming a Plateau-Gibbs border ). Eventually, the central film turns optically black as a single (5 nm-thick) bilayer lipid membrane (BLM) forms over the hole. Suitable lipids for the formation of a BLM are mostly isolated from natural sources, e.g.,... 

Fig. 61. Schematics of pressure-induced and applied-potential-induced BLM deformations. Application of hydrostatic pressure (by lowering a piston into the aqueous solution bathing the cis side of the BLM) displaces the BLM from position 1 to position 2. The displacement involves both translational (lateral) motion (Ft) and curvature increase (Fc). As indicated, deformation of the BLM is accompanied by a change in its torus (Plateau-Gibbs border). 2R and 2Rm represent the diameters of the aperture of the pinhole in the Tefzel film and that of the membrane (excluding the torus). The object laser beam, incident upon the trans side of the BLM and reflected by it at 45° at a shortened wavelength produces concentric optical interference fringes with the reference laser beam. Ag/AgCl electrodes, placed in the cis and trans sides of the BLM, allow for continuous electrical measurements [413]...

Bilayer lipid membranes (BLMs) 2D, 3D 30- to 50- Painting of the surfactant (or A-thick, 1- to 2- lipid), dissolved in a hydrocarbon mm-diameter mem- solvent, across a teflon pinhole brane, supported which separates two by a solvent compartments of aqueous solution surfactant reservoir the Plateau-Gibbs border or torus) and separating two aqueous solutions macroscopically Hours Convenient system for fundamental studies as simultaneous electrical and spectroscopic measurements were possible 385, 387... 

Plateau-Gibbs border P-G border, the edge where the lipid film (or BLM) is terminated. 

Procedure. To form a BLM, a small amount (.— 0.005 ml.) of lipid solution was applied via a Teflon capillary attached to a micrometer syringe. The formation characteristics leading to the black state were observed under reflected light at 20-40 X magnification. Other precautions that should be exercised are essentially those described previously (10). The bifacial tension of BLM was measured as follows. After the membrane had become completely black (except at the Plateau-Gibbs border), the infusion-withdrawal pump was started. The pressure difference across the BLM was continuously monitored and reached a maximum when the membrane was hemispherical. The interfacial tension was calculated from this point using Equation 3. 

Our objective in this study is to elucidate the complex phenomena occurring during the process of three phase foam thinning, to identify the interaction mechanisms between the oil droplets, the thinning foam film and the Plateau-Gibbs borders and the role of surface and interfacial tension gradients in foam stability, and to examine the implications upon crude oil displacement by foam in pourous media. 

Khristov et al. (1984) on the dependence of lifetime of foams on the pressure difference in the Plateau-Gibbs borders are shown in Fig. 3.19. 

Apart from its biomolecular thickness, a BLM is a liquid-like, dynamic structure in a metastable state from a self-assembling point of view we conclude that it is difficult to envision how a BLM separating two aqueous solutions can be made from two rigid, solidlike monolayers of lipids without a Plateau Gibbs border. For biosensor development, it is our opinion that a fluid bilayer is of crucial importance. The aim of this section is to describe in sufficient detail how to set up a simple BLM system using the self-assembling techniques [5 10]. 

Fig. 1 Two basic types of BLMs (planar lipid bilayers), (a) A conventional BLM separating two aqueous solutions in formation [1] (a short movie illustrating the BLM-forming process) may be seen by visiting the URL http //ivwiv.msu.edu/user/ottoval soapJtubble.html] (b) supported BLMs (c) a BLM on metal substrate (s-BLM) (d) a salt-bridge supported BLM (sb-BLM). P-G stands for Plateau-Gibbs border that supports the BLM [2, 3].

Figure 2. Plateau-Gibbs (P-G) border and bimolecular lipid membrane (BLM).. N is the line of intersection of three interfaces, /, II, and III...

Foam is produced when air or some other gas in introduced beneath the surface of a liquid that expands to enclose the gas with a film of liquid. Foam has a more or less stable honeycomb structure of gas cells whose walls consist of thin liquid films with approximately plane parallel sides. These two-sided films are called the lamellae of the foam. Where three or more gas bubbles meet, the lamellae are curved, concave to the gas cells, forming what is called the Plateau border or Gibbs triangles (Figure 7-1). 

The edges of foam cells are the Gibbs-Plateau borders (channels) filled with dispersion medium (see Chapter VII, 1). It was shown by Plateau that only three films may be joined by one border, and that the films must meet at 120°. The surface of Gibbs- Plateau border has a complex concave shape dictated by the condition requiring that the sum of two main curvatures remains constant. The capillary pressure under a concave surface is the reason for the lowered pressure in the Gibbs-Plateau border. 

In foams with high foam numbers the surface in Gibbs- Plateau borders is close to cylindrical, i.e. has a constant triangular-shaped cross-section with concave sides. The pressure in such cross-section is lowered in comparison with the pressure in foam cells by the amount of o/rcurv, where rcurv is the curvature radius of the border surface (i.e., of the side of triangle). 

Figure 5. Gibbs—Marangoni effect in the thin-film drainage process. Surfactant is swept to the Plateau borders by flow in the film and droplet phases, and thereby create surface concentration gradients that engender surface tension gradients.

Plateau Border The region of transition at which thin fluid films are connected to other thin films or mechanical supports such as solid surfaces. For example, in foams Plateau borders form the regions of liquid situated at the junction of liquid lamellae. Sometimes referred to as a Gibbs ring or Gibbs—Plateau Border. 

---