Marangoni damping

Marangoni damping) relatively fast time scale hours or few days (=> soluble, highly polar substances that disappear in the bulk water)... 

It is obvious that this model can well reproduce the measured damping ratios and, moreover, that the absence of the expected Marangoni damping maximum at intermediate Bragg wave numbers (approx. 100 rad m"1) can... 

The basis for our present models describing wave damping by monomolecu-lar surface films was formed by a paper published by Marangoni in 1872 ... 

As is well known, a lot of effects of surfactants, like damping of surface waves, the rate of thinning of liquid films, foaming and stabilisation of foams and emulsions, cannot just be described by a decrease in interfacial tension or by van der Waals and electrostatic interaction forces between two interfaces. The hydrodynamic shear stress at an interface covered by a surfactant adsorption layer is a typical example for the stimulation of an important surface effect. This effect, shown schematically in Fig. 3.9., is called the Marangoni effect. 

Here, is the so called foam parameter, and t is the viscosity m the surfactant-containing phase (Liquid 1 in Fig. 15) the influence of the transition zone film - bulk liquid is not accounted for in Eq. (76). Note that the bulk and surface diffusion fluxes (see the terms with and Z) in the latter equation), which tend to damp the surface tension gradients and to restore the uniformity of the adsorption monolayers, accelerate the film thinning (Fig. 1). Moreover, since Din Eq. (76) is divided by the film thickness h, the effect of surface diflhsion dominates that of bulk diffusion for small values of the film thickness. On the other hand, the Gibbs elasticity Eq (the Marangoni effect) decelerates the thinning. Equation (76) predicts that the rate of... 

If, however, SDS or DTAB is added to the aqueous phase Marangoni convection is seen to have been induced in the case the aniline/water interface, as can be seen in Figure 2, cases lb,c. In the other two systems (cases 2b,c and 3b,c), the addition of SDS or DTAB produces an increase in the convection intensity in comparison to the one observed when the water was clean . On the other hand, the addition of ATLAS G1300 has either no effect (case Id) on the interfacial stabihty or damps (cases 2d and 3d) any convection present in the clean system. 

A surfactant monolayer (or thin layer of oil) spread at a fluid interface damps the surface waves. This phenomenon is due to the fact that as the surfactant monolayer is compressed and expanded during the wave motion, the oscillations of the local surfactant concentration result in oscillations of the local interfacial tension. As a result, a combination of Marangoni and interfacial viscosity effects damp the surface waves. Following the classical approach of small-amplitude waves, Hansen and Ahmad [495] and Hedge and Slattery [496] derived the dispersion relation between the wave number k and wave frequency o) (see also Ref. 58) ... 

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