Dilational surface

Dilatational surface rheology is a less discriminating experimental technique. At air-water and sunflower oil-water interfaces, it is found (Lucassen-Reynders and Benjamins, 1999) that both disordered p-casein... 

Numerous investigators have elaborated the theory by including bulk transport and surface diffusion of the surfactant molecules [45], or the effect of shear and dilatation surface viscosity [49], The general conclusion is that the rate of thinning predicted by Reynolds equation is too low (the reader may find the details in ref. [237]). Hopefully our case is different and we do not have to enter into these considerations (see Section 3.2). 

Monomolecular surface films change the structure of the uppermost water layer within a thickness of around some micrometers to possibly some hundred micrometers (Huhnerfuss and Alpers 1983, Huhnerfuss 1986). For example, ice-like clathrate structures are induced by OLA films in a water layer of d < 190 pm. Furthermore, the surface potential of pure water of about - 180 mV becomes positive and may approach values of > 400 mV (Gericke and Huhnerfuss 1989), and the dilational surface viscosity is drastically increased (Huhnerfuss 1985). The relaxation time for disturbances of the surface film order TCOmp attains values of around 10 to 20 min, which are about 1013 times larger than the relaxation time xs of the water molecules (Huhnerfuss and Alpers 1983). 

The techniques used to measure dilational surface properties have been described in detail (4, 6). Surfaces of surfactant solutions are subjected to small amplitude, sinusoidal area variations, and the dilational modulus is given by the ratio between surface tension change measured and fractional area change applied. The modulus generally depends on the frequency at which the experiment is carried out, and this frequency... 

A final substitution of Eq. (5.271) into relation (5.267) and taking into account Eq. (5.266) we find the dynamic dilational surface elasticity of micellar solutions... 

The isotropic term Vs (Odiils) takes into account the role of the disjoining pressure, II, if the second interface is situated close to the given one (at distance smaller than 200 nm). Other contribution in Vs ((JdiiIs) is the dilatational surface viscous stress, T [ n. 

The Boussinesq-Scriven constitutive law postulates that = rj id. The surface viscosity, however, being a property of the adsorption layer itself, should be related to the relative displacement of the adsorbed molecules. As a result the dilatational surface viscous stress should be proportional to the rate of local deformation, i.e.. For insoluble... 

Three techniques may be applied for measurement of the dilational surface elasticity and viscosity (25). The first method applies surface waves to the interface (with frequency co). The dilational elasticity, e, is given by the expression... 

Drop and bubble methods have been developed significantly during the last years. These techniques provide access to dynamic properties of liquid interfaces. The drop and bubble shape technique as well as the fast oscillating drops and bubbles are described essentially as tools for dilational surface rheology. 

Callaghan and Neustadter [31] have made a study of the foam stabilities of air-crude oil and natural gas-crude oil systems using a variety of light crude oils of viscosities 14 mPa s. This study, at ambient temperature using a sparging method, concerned so-called dead oils from which natural gas had been separated. It also involved a comparison of the foam behavior with critical film rupture thicknesses, bulk phase, and surface shear viscosities together with dilatational surface properties. 

Equations (87)-(89) can be used to interpret data from expansion-relaxation experiments see, for example. Refs. 39, 83, and 84. Fitting the experimental data for the interfacial dilatation, one can in principle determine the Gibbs elasticity, Eq, the diffusion relaxation time, t and the dilatational surface viscosity, (or The latter is accessible to the accuracy of the aforementioned experimental techniques for high-molecular-weight surfactants and proteins sometimes, (or -qd,) can be determined also for low-molecular-weight anionic surfactants, but in the presence of multivalent counterions (like... 

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