Diffusion surfactants

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

The adsorption and desorption kinetics of surfactants, such as food emulsifiers, can be measured by the stress relaxation method [4]. In this, a "clean" interface, devoid of surfactants, is first formed by rapidly expanding a new drop to the desired size and, then, this size is maintained and the capillary pressure is monitored. Figure 2 shows experimental relaxation data for a dodecane/ aq. Brij 58 surfactant solution interface, at a concentration below the CMC. An initial rapid relaxation process is followed by a slower relaxation prior to achieving the equilibrium IFT. Initially, the IFT is high, - close to the IFT between the pure solvents. Then, the tension decreases because surfactants diffuse to the interface and adsorb, eventually reaching the equilibrium value. The data provide key information about the diffusion and adsorption kinetics of the surfactants, such as emulsifiers or proteins. 

The reasons for this impeded foam formation by organic liquids are not completely clear. Probably either the weak surface activity of surfactants in the organic liquids causes it or the fact that the steady-state (described above) of film surfaces is established slowly due to decelerated surfactant diffusion towards the liquid/gas inteffaces. The much smaller thickness (100-300 nm) of the films formed compared to the typical initial thickness of aqueous films (1 pm) speaks in favour of this assumption. The latter increases with the increase in the bulk surfactant concentration [53,73],... 

Below, in Sections 5.2 and 5.3, we consider effects related to the surface tension of surfactant solution and capillarity. In Section 5.4 we present a review of the surface forces due to intermo-lecular interactions. In Section 5.5 we describe the hydrodynamic interparticle forces originating from the effects of bulk and surface viscosity and related to surfactant diffusion. Section 5.6 is devoted to the kinetics of coagulation in dispersions. Section 5.7 regards foams containing oil drops and solid particulates in relation to the antifoaming mechanisms and the exhaustion of antifoams. Finally, Sections 5.8 and 5.9 address the electrokinetic and optical properties of dispersions. 

The common nonionic surfactants are often soluble in both water and oil phases. In the practice of emulsion preparation, the surfactant (the emulsifier) is initially dissolved in one of the liquid phases and then the emulsion is prepared by homogenization. In such a case, the initial distribution of the surfactant between the two phases of the emulsion is not in equilibrium therefore, surfactant diffusion fluxes appear across the surfaces of the emulsion droplets. The process of surfactant redistribution usually lasts from many hours to several days, until finally equilibrium distribution is established. The diffusion fluxes across the interfaces, directed either from the continuous phase toward the droplets or the reverse, are found to stabilize both thin films and emulsions. In particular, even films, which are thermodynamically unstable, may exist several days because of the diffusion surfactant transfer however, they rupture immediately after the diffusive equilibrium has been established. Experimentally, this effect manifests itself in phenomena called cyclic dimpling and osmotic swelling. These two phenomena, as well as the equilibration of two phases across a film,568.569 3j.g described and interpreted below. 

FIGURE 5.46 Spontaneous cyclic dimpling caused by surfactant diffusion from the aqneous film toward the two adjacent oil phases, (a) Schematic presentation of the process, (b) Photograph of a large dimple just before flowing out the interference fringes in reflected light allow determination of the dimple shape. 

For small-molecule surfactants, D would be of the order of 3 10 10m2 s-1. For the above-mentioned quantities, Eq. (10.6) then predicts an adsorption time of about 30 ms, a time too short to measure r (or even y with common methods). The surfactant concentration can, however, be far smaller. Figure 10.6 shows that Na-stearate, a very surface active amphiphile, gives for c = 0.13mol-m a surface excess T = 9 10 6mol -m-2. This would lead to tads x 10 (9 10—6/0.13)2/3 10-10 = 160 s. For a still lower concentration, adsorption would also occur, but Too would then be smaller, and the calculated adsorption times are of comparable magnitude. In other words, for small-molecule surfactants, diffusion times are always short, from milliseconds to a few minutes. 

Thiessen (1963) presents results of a similar nature. The effect of surfactant diffusion on droplet coalescence confirms the results of MacKay Mason (1963). In addition, the influence of surface inactive materials such as inorganic salts was investigated. As expected, the sign of the effect is reversed when a surface inactive substance is substituted for a surface active one. Thiessen (1963) points out the relevance of studies of this type to the extraction of salts from aqueous solutions using organic solvents. The isolation of metals by this technique is currently a popular problem. 

The striking peculiarity in the boundary condition (7A.1) for ion adsorption is the substitution of the surfactant diffusion coefficient D by an effective one defined in Eq. (7.18). This is... 

The adsorption kinetics at liquid/liquid interfaces is a more complicated problem, as the transfer of surfactant from one phase to the other has to be taken into account. In the experiments performed by Liggieri and Ravera [197] using the expanded drop method, no preliminary saturation of the oil phase with CjoEOg was made. For this case, instead of Eq. (4.1), the expression (4.94) should be used, where K is the equilibrium distribution coefficient of surfactant between the oil and water phases, and D2 is the surfactant diffusion coefficient in the oil phase. The reduced distribution coefficient defined by = K(D2/Di) is a parameter that reflects quantitatively the adsorption dynamics at such a liquid/liquid interface. 

The results of the preceding section allow us now to move on to describe the surfactant transport from the depth of the bulk phase to the interface or in the opposite direction. If any adsorption barriers are absent, this process determines the adsorption and desorption rates. The main step in the solution of this problem consists in the formulation of the surfactant diffusion equations for micellar solutions. The problem of surfactant diffusion to the interface was considered and solved for the first time by Lucassen for small perturbations [94]. He used the simplified model (5.146) where micelles were assumed to be monodisperse and the micellisation process was regarded as consisting of one step. Later Miller solved numerically the problem of adsorption on a fresh liquid surface using the same assumptions [146], Joos and van Hunsel applied also the same model to the interpretation of dynamic surface tension of... 

A more rigorous approach to the description of the colloid surfactant diffusion to the interfaee was proposed by Noskov [133]. The reduced diffusion equations for micelles and monomers, which take into account the multistep nature of micellisation and the polydispersity of micelles, were derived for time intervals corresponding to the fast and slow processes using the method applied initially by Aniansson and Wall to uniform systems. Analogous equations have been derived later by Johner and Joanny [135] and also by Dushkin et al. [137]. Recently Dushkin has studied also the adsorption kinetics in the framework of a simplified model of quasi-monodisperse micelles. In this case the assumption of the existence of two kinds of micelles permits to study the main features of the surface tension relaxation in real micellar solution [138]. The main steps of the derivation of surfactant diffusion equations in micellar solutions are presented below [133, 134]. 

It is possible, for example, to use the method of Fourier transformations to solve the boundary problems for the system of differential equations (5.198), (5.199). In this case we have jmax linear differential equations of the second order. Because jmax is usually of the order of hundred, a further analytical investigation of Eqs. (5.198), (5.199) is senseless. However, the problem can be essentially simplified if the surfactant diffusion is treated separately for time scales comparable with the relaxation times of the fast and slow steps of micellisation, respectively. 

In conclusion of this section let us consider the surfactant diffusion in a concentrated solution, where the micellisation kinetics is described by the model of Kahlweit et al. (5.185). If we neglect all other routes of the micellisation process, the following diffusion equation corresponds to the mechanism (5.185) ... 

The diffusion equations of micelles and monomers obtained in the preceding sections allow us to formulate a mathematical problem of surfactant diffusion to the interface. Investigation of the adsorption kinetics is reduced then to the solution of this problem. It is noteworthy that the diffusion equations (5.210) - (5.211), (5.223), (5.224), (5.226), (5.228) and the results given in the preceding sections on the relaxation kinetics of the concentration perturbations in the... 

If the PFOR model is used, an analytical solution of the surfactant diffusion problem in a micellar solution can be obtained. For this model only the monomer diffusion has to be considered, which is described by the equation [78, 83, 85, 87-89,93,137,138,147]... 

With the characteristic time of surfactant diffusion and of the relaxation time t of the adsorption process itself [165],... 

Denote through F the molar concentration (mole/m ) of surfactant at the interface. Then the equation describing the change of F, looks like a convective diffusion equation that takes into account the delivery of matter from the liquids which are divided by the interface. Making the assumption that each liquid is a binary solution, the diffusion equation can be derived in the same manner as in Section 4.4. Suppose that chemical reactions are absent, the diffusion is governed by Pick s law, and the diffusion coefficients are constant. Then the equation of surfactant diffusion at the interface has the form [2]... 

The surfactant diffusion coefficient is maximum for the balanced state, and the corresponding expansion gives to leading order... 

Finally, for a structureless or molecularly dispersed (i.e., simple solution) case we would also have high values of > and D . It is normally trivial to distinguish between simple solutions and bicontinuous microemulsions (phase behavior, scattering, etc.), and a diffusion experiment will immediately tell, since for a simple solution the surfactant will show molecular, and thus fast, diffusion. For a bicontinuous microemulsion, surfactant diffusion is typically an order of magnitude lower. 

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