Drops Marangoni effects

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

For all phenomena the assumption has been made that there Is no charge transfer through the particle surface. In fact, often the particles are taken as dielectric solids through which the lines of electric flow do not pass. For fluid drops, as in emulsions, this may be a poor approximation because internal flow inside the drops may occur. However, practice has shown that, due to Marangoni effects, the liquid-liquid Interface also often behaves as if it were inextenslble. Absence of ion transfer across the phase boundaiy means that there the normal component of J is zero... 

Electrophoresis of bubbles and drops is a story on its own. As long ago as 1861 Quincke ) observed the electrophoresis of small air bubbles in water. Such a motion is possible only when there is a double layer at the Interface, containing free ions. It is extremely difficult to keep oil-water or air-water Interfaces rigorously free from adsorbed ionic species. When these are present, especially for surfactants, Marangoni effects make the surface virtually inexten-slble then the drops or bubbles behave as solid spheres. Electrophoretic studies... 

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. 

Closely related to the above mechanism is the Gibbs-Marangoni effect [13-17], which is represented schematically in Figure 10.19. The depletion of surfactant in the thin film between approaching drops results in a y-gradient without Hquid flow being involved. This results in an inward flow of liquid that tends to drive the drops apart. 

The Gibbs-Marangoni effect also explains the difference between surfactants and polymers for emulsification. When compared to surfactants, polymers produce larger drops and also give a smaller value of e at low concentrations (Figure 10.19). 

Y. Pawar and K. J. Stebe, Marangoni effects on drop deformation in an extensional flow The role of surfactant physical chemistry. I. Insoluble surfactants, Phys. Fluids 8, 1738-51 (1996). 

A more common source of Marangoni effects in systems of interest to chemical engineers is surfactants, as discussed in Chap. 2. This is particularly pertinent to the motion of gas bubbles (or drops) in water, or in any liquid that has a large surface tension (the surface tension of a pure air-water interface is approximately 70 dyn/cm). Experiments on the motion of gas bubbles in water at low Reynolds numbers show the perplexing result illustrated in Fig. 7-18. For bubbles larger than about 1 mm millimeter in diameter, the translation velocity is approximately equal to the predicted value for a spherical bubble with zero shear stress at the interface, that is,... 

This is in qualitative accord with the experimental observation that the bubble reverts to noslip behavior for small radii below some critical threshold value. This effect of nonuniform surfactant concentrations is one of the most easily observed manifestations of Marangoni effects in the motion of bubbles or drops. 

The first term Fy in (5.10.8) is just Hadamard-Rybczynski s result (2.2.15) for the drag of a drop in a translational flow. The second term Ft is the thermocapillary force acting on the drop in the external temperature gradient due to the Marangoni effect. 

All the above cases of the Marangoni effect for a drop have one common feature, namely, the presence of an exterior asymmetry, which is not connected with motion. Essentially different situations are investigated in [270, 419], when the surface tension gradient is produced only in the motion of the liquid inside and outside the drop and, in turn, affects the motion. 

In practical systems, the motion of bubbles or droplets in surfactant solutions is strongly retarded by gradients of the surface tension. The schematic in Fig. 3.11. clearly demonstrates the retardation effect on rising bubbles or sinking drops. In surfactant solutions gravitation and the Marangoni effect move in the opposite direction. 

Thin liquid films in foam and emulsion systems are usually stabilised by soluble surfactants. During the formation of such films the flow-out process of liquid disturbs the surfactant equilibrium state in the bulk and film surfaces. The situation of drainage of a surfactant containing liquid film between two oil droplets is shown in Fig. 3.15. (after Ivanov Dimitrov 1988). Here j" and are the bulk fluxes in the drops and the film, respectively, j and j are the fluxes due to surface diffusion or spreading caused by the Marangoni effect, respectively. 

If a solid particle crosses the diffusion layer of a bubble or drop it also includes the long range interaction caused by a local disturbance of the adsorption layer. This leads to Marangoni effects and influences the film drainage between particle and bubble or drop. Local desorption of surfactant from one surface and its adsorption on the other also causes interaction. 

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