Gibbs effect

Figure 2.10 Partial sums of Fourier components of the boxcar function up to p = 9. Convergence to the boxcar functions is achieved rapidly although ears appear next to discontinuities (Gibbs effect).

Addition of the first components up to p = 9 is shown in Figure 2.10. Reconstruction of the boxcar function is rapid although ears persist next to the edge, a feature characteristic of discontinuities and known as the Gibbs effect , o... 

This is an important stabilising effect in foams which are formed from solutions of soaps, detergents, etc. If a film is subjected to local stretching as a result of some external disturbance, the consequent increase in surface area will be accompanied by a decrease in the surface excess concentration of foaming agent and, therefore, a local increase in surface tension (Gibbs effect). Since a certain time is... 

In the second mechanism, the "Gibbs effect," the surface deficiency is replenished by diffusion from the interior and the surface tension is lowered to obtain a desirable level. For the best stabilization of a foam, an optimum concentration of surfactant as well as an optimum rate of diffusion is desirable (3). 

The second cause of coalescence is the film rupture between bubbles. This can easily be very significant. Physically, the film rupture stems from a depletion of surfactant at the film surface when the surface is stretched. The film stability is commonly ascribed in large measure to the so-called Marangoni effect and Gibbs effect. The Marangoni effect involves the inability of surfactant molecules to diffuse instantaneously to any locally stretched area in the film surface. The resulting lag permits the stretched surface to be momentarily depleted of surfactant. The Gibbs effect involves... 

The Gibbs effect can be evaluated quantitatively. Gibbs defined a coefficient of surface elasticity E as the stress divided by the strain per unit area, E = [2dy/(dA/A). The greater the value of E, the greater the ability of the film to withstand shocks on thinning. 

In solutions the surface tension may depend on the interfacial area due to the Gibbs effect (see Chapter VII, 3)... 

The effective elasticity of films with surfactant adsorption layers. An increase in film size related, for instance, to film deformation (flexure, stretching) due to the action of external force, leads to changes in equilibrium between adsorption layer and surfactant solution in the volume of film. If deformation occurs slowly, and the film thickness is small, the stretching causes some of surfactant molecules in the film to move from the depth onto the surface. As a result, the surfactant concentration in the bulk of film decreases, leading to a decrease in equilibrium adsorption. Consequently, the surface tension increases (the Gibbs effect) [6]. The dependence of surface... 

The effective film elasticity is especially important in emulsions in which the interfacial tension is small and can not ensure the stability of surfaces against the deformation due to random causes. The Gibbs effect is a thermodynamicfactorof colloid stability (this emphasizes only the nature of the effect, and one need not assume that this factor can ensure high stability of disperse systems). 

After the creation of a fresh surface (or an almost bare surface) the adsorption increases until equilibrium has been reached. Liquid flow lateral to the surface creates concentration and surface tension gradients which induce additional surface flow. This effect is called the Marangoni-Gibbs effect. 

These conclusions can change if micellisation in surfactant solutions is taken into account. If the surfactant concentration exceeds the critical concentration of micellisation (CMC) the surface tension does not change with surfactant concentration. It means that the Marangoni-Gibbs effect and the surface retardation of a bubble also disappear. 

Finally, the effect of the ionic character of the surfactant upon the surface forces. Let us consider first of all the diffusion - electric analog of the Marangoni-Gibbs effect. Since stretching of the film results in adsorption, both film surfaces are charged simultaneously and are pushed away from each other. This makes film thinning difficult. This repulsion of a nonequilibrium double layers takes place at distances which are many times greater than the double layer thickness. 

Gibbs Effect The decrease in surface or interfacial tension that occurs as surfactant concentration increases toward the critical micelle concentration. 

J WUard Gibbs (1839 to 1903) was an American mathematician best-known for the Gibbs effect seen when Fourier-analysing a discontinuous function. 

In order to enhance coalescence in systems stabilized by the Marangoni-Gibbs effect, the interfacial activity of the surfactant must be high enough to account for the interfacial tension gradient created [39,41,42-44]. Some researchers found that the emul-... 

The effect on surface tension by surfactant adsorption from the bulk solution (Gibbs effect) and by diffusion along an interface (Marangoni effect) is often referred to as the combined Gibbs-Marangoni effect (Figure 11.7). 

Figure 11.7. Schematic representation of the Gibbs-Marangoni effects, (a) Unstretched film, (b) Stretched film. Film stretching causes localized areas of high surface tension, y [1]. Surfactant molecules flow from the bulk phase [2] to the surface (Gibbs effect) and along the interface [3] (Marangoni effect) to heal the stretched film [IJ...

Clearly it is incorrect to consider the nonoxidative phase of the P.p.c. as a fixed, albeit fairly complex mechanism for the conversion of 3 molecules of pentose phosphate into a triose phosphate and 2 molecules of hexose phosphate. There exists a network of possible reactions, which can change in emphasis, depending on the tissue, and possibly on the physiological state of the tissue. Thus, in rat epididymal fat pad, isotopic labeling suggests that the older scheme of Horecker operates for the metabolism of pentose phosphates. Operation of the new scheme in plants would provide an explanation of the Gibbs effect (see). Other workers [T.Wood A. Gascon Archives of Biochemistry and Biophysics 2Q3 (1980) 727-733] have reported their failure to demonstrate the interconversion of D-arabinose S-phosphate and D-ribose S-phosphate, or the role of D-arabinose S-phosphate as an acceptor for transketolase in baker s yeast, Candida ulilis, or rat liver. 

The Ostwald-Freundlich equation, applied to solubility (known as the Thompson-Gibbs effect), is as follows ... 

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