Marangoni effects/flows

All of these disturbances cause a many-fold increase in the rate of transfer of solute across the interface. If a chemical or thermal difference along an interface causes an interfacial tension gradient, violent flow in the direction of low a will result. This action is usually termed the Marangoni effect. 

The reverse situation is depicted in Figure 15.1(b). When the surfactant is dissolved in the dispersed phase, the surfactants also flow along the interface with the continuous phase flowing out of the slit, but the depletion on the interface is easily countered by diffusion and adsorption of surfactants from the bulk of the dispersed phase. Therefore, there is no Marangoni effect counteracting the outflow of continuous phase, and coalescence takes place much more easily. 

When surface tension differences appear or are produced between some points or some small regions of an interface, the flow produced is called the Marangoni flow or flow with Marangoni effect. The Marangoni number, used to characterize the flow shown on Fig. 6.9, is a combination of the Reynolds number, the Weber number and the Schmidt number ... 

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... 

The sketch and pertaining explanation are simplified. In practice the dynamics of film thinning also has to be considered. The flow can lead to Marangoni effects emanating from Vy s in the LG Interface. 

When a membrane expands and the concentration of a surfactant at the interface decreases, there exist two mechanisms to restore the surfactant surface concentration. The first mechanism, termed the "Marangoni effect" (16), refers to the fact that the surface flow can drag with it some of the underlying layers, i.e. the surface layer can flow from areas of low surface tension, thus restoring the film thickness. It is also a source of film elasticity or resilience. 

The hypothesis advanced here is that the observed enhancement is due to thermocapillarity arising from the temperature dependence of the interfacial tension. Although we know of no theory for such a Marangoni effect in binary condensation per se, theory does exist for both mass transfer (M. 11) and heat transfer (16, 12) aeross an interface in the absence of bulk flow. We note that the sign of the derivative of the interfacial tension with respect to temperature is positive near a lower consolute point and that this is in the correct direction to sustain disturbances in condensation rate. Thus, in retrograde condensation, provided a critical temperature gradient normal to the interface is exceeded, a local increase in condensation flux toward the vapor liquid interface will result in its cooling. 

Figure10.17 Interfacial tension gradients and flow nearan oil/water interface, (a) No surfactant (b) Velocity gradient causes an interfacial tension gradient (c) Interfacial tension gradient causes flow (Marangoni effect).

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. 

In the presence of liquid flow, the situation becomes more complicated due to the creation of surface tension gradients [17]. These gradients, described by the Gibbs dilational elasticity [17], e, initiate a flow of mass along the interface in direction of a higher surface or interfacial tension (the Marangoni effect), e is given by the... 

Now, from a qualitative point of view, the role of surfactant is twofold One is to simply reduce the interfacial tension everywhere by an amount that depends on the mean value of T, and the second is to produce Marangoni effects that are due to flow-induced nonuniformity in T. As a consequence, it is convenient to define T as being... 

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). 

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. 

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