Instabilities Marangoni

The effect can be important in mass-transfer problems (see Ref. 57 and citations therein). The Marangoni instability is often associated with a temperature gradient characterized by the Marangoni number Ma ... 

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Should there be Marangoni instability in a layer of water 1.5 mm deep, with the surface 0.3°C cooler than the bottom What dimensions does the Marangoni number (Ma) have (Assume T 25°C.)... 

Kavehpour P, Ovryn B, McKinley GH. (2002) Evaporatively-driven Marangoni instabilities of volatile liquid films spreading on thermally conductive substrates. Colloids Surf 206 409 23. 

Numerous studies have shown that mass transfer of solute from one phase to the other can alter the behavior of a liquid-liquid dispersion—because of interfacial tension gradients that form along the surface of a dispersed drop. For example, see Sawistowski and Goltz, Trans. Inst. Chem. Engrs., 41, p. 174 (1963) BaWcer, van Buytenen, and Beek, Chem Eng. Sci., 21(11), pp. 1039-1046 (1966) Rucken-stein and Berbente, Chem. Eng. Sci., 25(3), pp. 475—482 (1970) Lode and Heideger, Chem. Eng. Sci., 25(6), pp. 1081—1090 (1970) and Takeuchi and Numata, Int. Chem. Eng., 17(3), p. 468 (1977). These interfacial tension gradients can induce interfaci turbulence and circulation within drops. These effects, known as Marangoni instabilities, have been shown to enhance mass-transfer rates in certain cases. 

Reichenbach, J. and Linde, H., Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability), J. Colloid Interface Sci., 84, 433 143, 1981. Nepomnyashchy, A.A., Velarde, M.G., and Colinet, R, Interfacial Phenomena and Convection, CRC Press/Chapman Hall, London, 2002. 

Linde, H. et al.. Interfacial wave motions due to Marangoni instability. I. Traveling periodic wave trains in square and annular containers, J. Colloid Interface Sci., 188, 16-26, 1997. 

In the last two sections, we considered mass transfer from the film toward the droplets and the reverse, from droplets toward the film. In both cases, the diffusion fluxes lead to stabilization of the film. Here we consider the third possible case corresponding to mass transfer from the first droplet toward the second one across the film between them. In contrast with the former two cases, in the last case the mass transfer is found to destabilize the films. Experimentally, the diffusion transfer of alcohols, acetic acid, and acetone was studied. - The observed destabilization of the films can be attributed to the appearance of Marangoni instability, which manifests itself through the growth of capillary waves at the interfaces, which eventually can lead to film rupture. 

Finally, we consider the problem of Marangoni instability, namely convection in a thin-fluid layer driven by gradients of interfacial tension at the upper free surface. This is another problem that was discussed qualitatively in Chap. 2, and is a good example of a flow driven by Marangoni stresses. 

Figure 2-21. A sketch of an intial flow perturbation that can lead to instability and strong cellular motion due to Marangoni instability in a fluid layer that is heated from below.

In this section, we consider the classic problem of a fluid layer of depth d, with an upper surface that is an interface with air that is maintained at an ambient temperature 7o. The fluid layer is heated from below, and we shall assume that the lower fluid boundary is isothermal with temperature T (> To). This problem sounds exactly like the Rayleigh-Benard problem with a free upper surface. However, we consider the fluid layer to be very thin (i.e., d small) so that the Rayleigh number, which depends on d3, is less than the critical value for this configuration. Nevertheless, as previously suggested, the fluid layer may still undergo a convective motion that is due to Marangoni instability. 

Figure 12-7. A schematic for Marangoni instability. Warm liquid is convected up to the surface, which causes the temperature at the upper surface warmer than the ambient air temperature 7o. The resultant surface-tension gradient drives motion in the same direction, thus producing instability.

The governing equations for the linear stability theory are the same as for the Rayleigh-Benard problem, namely (12-215), except that it is customary to drop the buoyancy terms because these are of secondary importance for very thin fluid layers where Marangoni instabilities are present but Ra <neutral state. Assuming that... 

Problem 12-11. Marangoni Instability (The Principle of Exchange of Stabilities). Following the procedure that was outlined in Section F for the Rayleigh-Benard problem, prove that the principle of exchange of stabilities is valid for the Marangoni instability problem (Section H). 

Probably the most striking phenomenon which is caused by adsorption dynamics is the Marangoni instability. A short introduction into this topic and few demonstrations of observed features are given in Appendix 3C. 

From the thermodynamical point of view the formation of dissipative structures is entropy driven as intensively explained by Prigogine Glansdorf (1971). The criteria for surface instabilities due to mass transfer across a liquid interface were evaluated by Stemling Scriven (1959). The typical Marangoni instability starts on surfactant concentration or temperature differences between two phases. Surface tension differences along the surface are... 

Example of autowaves of first-order roll-cells of Marangoni instability (left pictures) and of BZR (right pictures), a) concentric rings, b) spirals, according to Linde and co-workers... 

The field of Marangoni instabilities shows a large variety of dissipative structures, including the principle of stationary structures, hierarchical structures with limited self-similarity, relaxation oscillations and regular behavior of travelling autowaves with chaotic turbulence-like behaviour. There is also the oscillatory regime with trains of waves with soliton-like behaviour of each wave. Anormal as well as normal dispersion of these waves have recently... 

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