Elasticity Marangoni

The oscillating bubble method proves to be very convenient and precise for the evaluation of the non-equilibrium elasticity of surfaces in a wide range of frequencies of external disturbances and surface coverage (adsorption of surfactant) [103-105]. It is based on registration of the sinusoidal variation of bubble volume. The bubble is situated in a capillary containing surfactant solution in which oscillations of different frequencies and amplitudes are created. The treatment of the U = f(ft)) curves (where U is the tension needed to initiate oscillations of constant amplitude) allows the determination of Marangoni elasticities [105]. 

Two types of elasticity could be distinguished equilibrium (Gibbs elasticity) and dynamic (Marangoni elasticity). According to Gibbs the modulus of elasticity of the film is... 

The elasticity that is determined from nonequilibrium dynamic measurements depends upon the stresses applied to a particular system, is generally larger in magnitude, and is termed the Marangoni surface elasticity, jEm (6, 22) (equation 12). The time-dependent Marangoni elasticity is il-... 

The Marangoni elasticity can be determined experimentally from dynamic surface tension measurements that involve known surface area changes. One such technique is the maximum bubble-pressure method (MBPM), which has been used to determine elasticities in this manner (24, 26). In the MBPM, the rates of bubble formation at submerged capillaries are varied. This amounts to changing A/A because approximately equal bubble areas are produced at the maximum bubble pressure condition at all rates. Although such measurements include some contribution from surface dilational viscosity (23, 27), the result will be referred to simply as surface elasticity in this work. 

Marangoni Elasticity See Film Elasticity, Marangoni Effect. 

The relative stability of soap films is partially due to their elasticity. To see this, we consider a film with an equilibrium state represented by the surface excess T and the dissolved surfactant concentration c. A local stretching disturbs these parameters. If the disturbance occurs on a short time scale, the soap molecules do not have time to diffuse out from the inner fluid to the surface, so the same number of soap molecules remains both inside and at the surface. As the area increases, Tg decreases, which results in an increase of the surface tension according to Eq. (2.11), thus opposing the stretching. This process is called the Marangoni elasticity and explains the film stability to rapid disturbances. If the time scale of the stretching is... 

In principle, the limit between the Marangoni and the Gibbs elasticity is given by the time scale % = h /D, which characterizes the time needed to diffuse away by the thickness h. Since the diffusion coefficienf is D 4 x 10-1° mVs, for films of 1 pm thick is in the order of 0.01 s. However, it is arguedi that impurities make the equilibrium more difficult to reach, so that Marangoni elasticity can be observed up to tiie order of a second. 

A is the area of the surface. In a foam, where the surfaces are interconnected, the time-dependent Marangoni effect is important. A restoring force corresponding to the Gibbs elasticity will appear, because only a finite rate of absorption of the surface-active agent, which decreases the surface tension, can take place on the expansion and contraction of a foam. Thus the Marangoni effect is a kinetic effect. 

It is also important that the emulsifier films have sufficient elasticity to enable recovery from local disturbances (see Gibbs-Marangoni effect page 274). 

In concentrated emulsions and foams the thin liquid films that separate the droplets or bubbles from each other are very important in determining the overall stability of the dispersion. In order to be able to withstand deformations without rupturing, a thin liquid film must be somewhat elastic. The surface chemical explanation for thin film elasticity comes from Marangoni and Gibbs (see Ref. [199]). When a surfactant-stabilized film undergoes sudden expansion, then immediately the expanded... 

Although many factors, such as film thickness and adsorption behaviour, have to be taken into account, the ability of a surfactant to reduce surface tension and contribute to surface elasticity are among the most important features of foam stabilization (see Section 5.4.2). The relation between Marangoni surface elasticity and foam stability [201,204,305,443] partially explains why some surfactants will act to promote foaming while others reduce foam stability (foam breakers or defoamers), and still others prevent foam formation in the first place (foam preventatives, foam inhibitors). Continued research into the dynamic physical properties of thin-liquid films and bubble surfaces is necessary to more fully understand foaming behaviour. Schramm et al. [306] discuss some of the factors that must be considered in the selection of practical foam-forming surfactants for industrial processes. 

The simplest model assumes ideal elastic behavior (Figure 7.12A). At a stress below the yield stress (Fy), the sample behaves perfectly elastically. In this region, a modulus of elasticity can be determined. At the yield stress, the sample flows. It continues to flow until the stress is lowered again to below the yield stress value. Therefore, both the elastic modulus and yield stress describe the behavior of a plastic material. They can be determined easily by compression testing. The continuous network of fat crystals in a fat bears the stress below the yield stress and therefore contributes solid or elastic properties to the material (Narine and Marangoni, 1999a). 

Awad, T.S., Rogers, M.A., Marangoni, A.G. 2004. Scaling behavior of the elastic modulus in colloidal networks of fat crystals. J. Phys. Chem.B. 108, 171-179. 

Marangoni, A.G. 2000. Elasticity of high-volume-fraction fractal aggregate networks A thermodynamic approach. Phys. Rev. B. 62, 13951-13955. 

The elasticity depends on the rate of film expansion. Under quasistatic equilibrium conditions its values are very low and in such a case it is called Gibbs elasticity. When there is no equilibrium it is called Maiangoni elasticity. The largest value of the elasticity modulus, acquired when the adsorption layer behaves as insoluble one, is called Marangoni dilatation modulus Em). 

Under dynamic conditions, where equilibrium between the surface and the film bulk cannot be realised, some specific elasticity properties are expressed. This is Marangoni s effect. Assuming that under such conditions there is an equilibrium only in some parts between the film bulk and its surface, it is possible to employ Eq. (7.6) for the material balance to calculate the modulus of elasticity. Hence, instead of the whole film volume, only the zone where equilibrium with the film surface is established, should be considered. The faster the process of film thinning, the smaller this volume is and the larger the modulus of film elasticity. In the limiting case, when it is completely impossible to achieve equilibrium between the film bulk and its surface, the elasticity of the adsorption surfactant layers takes place. 

The mechanism of the equilibrium elasticity acts until it is possible to provide a surfactant re-partition between the exterior and interior of the film. In a NBF such a repartition is not possible and this mechanism of elasticity ceases to act. The elasticity properties of bilayer films, in which the hydrodynamic and adsorption processes are characterised with normal time of relaxation, are due to Marangoni effect in the insoluble adsorption layers. That is why stable foams with black films are very sensitive to different local disturbances (heating, vibration, etc.). 

Marangoni s group has since advanced the fractal theory applying Shih et al. s weak link regime with Vreeker s rheological findings to develop a fractal theory for fat crystal networks. Fat crystal networks are considered as cross-linked fractal clusters formed by aggregating fat crystals. Self-similarity is assumed to exist within the clusters, from the primary fat crystals to the clusters. If the force-constant of the links between micro structures was expressed as k/, then the macroscopic elastic constant K (in one dimension) of the network could be modeled as ... 

Narine, S.S., and Marangoni, A.G. (2001). Elastic modulus as an indicator of macroscopic hardness of fat crystal networks. Lebensmittel Wissenschaft und Technologie. 34 33 0. 

To illustrate the relevance of Marangoni effects, let us consider a simple Langmuir monolayer without network-type elasticity distinguishing two counterparts ... 

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