Marangoni effect Gibbs elasticity

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 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... 

In the opposite case, when the surfactant is soluble in the continuous phase, the Marangoni effect becomes operative and the rate of film thinning becomes dependent on the surface (Gibbs) elasticity (see Equation 5.282). Moreover, the convection-driven local depletion of the surfactant monolayers in the central area of the film surfaces gives rise to fluxes of bulk and surface diffusion of surfactant molecules. The exact solution of the gives the following... 

For maximum mechanical stability, the interfacial film resulting from the adsorbed surfactants should be condensed, with strong lateral intermolecular forces, and should exhibit high film elasticity. The liquid film between two colliding droplets in an emulsion is similar to the liquid lamella between two adjacent air sacs in a foam (Chapter 7) and shows film elasticity for the same reasons (Gibbs and Marangoni effects). 

Many surfactant solutions show dynamic surface tension behavior. That is, some time is required to establish the equilibrium surface tension. If the surface area of the solution is suddenly increased or decreased (locally), then the adsorbed surfactant layer at the interface would require some time to restore its equilibrium surface concentration by diffusion of surfactant from or to the bulk liquid. In the meantime, the original adsorbed surfactant layer is either expanded or contracted because surface tension gradients are now in effect, Gibbs—Marangoni forces arise and act in opposition to the initial disturbance. The dissipation of surface tension gradients to achieve equilibrium embodies the interface with a finite elasticity. This fact explains why some substances that lower surface tension do not stabilize foams (6) They do not have the required rate of approach to equilibrium after a surface expansion or contraction. In other words, they do not have the requisite surface elasticity. 

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... 

In view of the term (jJl in Eq. (9), the Marangoni effects are hidden in the left-hand side of the interfacial momentum balance equation (8) through the surface gradients of (Ja. The thermodynamic surface tension, dJa, depends on the adsorption and temperature. The derivatives of with respect to In and InT define the Gibbs elasticity for the i-th surfactant species, Et, and the thermal analogue of the Gibbs elasticity, Ef. 

In a foam where the films are interconnected, the related time-dependent Marangoni effect is more relevant. A similar restoring force to expansion results because of transient decreases in surface concentration (increases in surface tension) caused by the finite rate of surfactant adsorption at the surface. Such nonequilibrium surface tension effects are best described in terms of dilatational moduli. The complex dilatational modulus e of a single surface is defined in the same way as the Gibbs elasticity as in equation (2) (the factor 2 is halved as only one surface is considered). 

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