Surface dilational elasticity

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

Ed is the dilatational elasticity, and rid is the dilatational viscosity. It is characteristic for a stable foam to exhibit a high surface dilatational elasticity and a high dilatational viscosity. Therefore effective defoamers should reduce these properties of the foam. 

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

At equilibrium, the surface elasticity, or surface dilational elasticity, EG, is defined [15,25] by ... 

The earliest available hydrodynamic theory of water wave damping by elastic surface films was published by Lamb (1895). He refers to Reynolds (1880) and the experiments by Aitken (see Scott 1979, Giles and Forrester 1970), but prior publication of the detailed theory is not indicated. All but the outline of the theory was omitted from later editions of this book, and it is likely that Lamb assumed that damping was greatest with an inextensible film, and that intermediate elasticities, therefore, had less effect (cited after Scott 1979). This conclusion was shown by Dorrestein (1951) to be incorrect. The paper by Levich (1940) was the first to present in detail the linearised hydrodynamics of waves on a water surface with surface dilational elasticity. The only cases considered in detail concern insoluble films, and represent the clean and incompressible-film-covered surface. A detailed treatment of the hydrodynamic theory of surface waves, including the effect of an elastic surface film, was published by Levich in 1962. In addition, the damping caused by dissolved surface-active material was considered. Further laboratory experiments performed until 1978 were briefly reviewed by Scott (1979). 

The effect of surface dilational elasticity was first formulated by Gibbs (1957) as... 

The surface dilational elasticity was firstly defined by Gibbs (1906)... 

The rheology of wet foams was analysed by Wasan et al. (1992) and a relation was derived (Edwards et al. 1991) connecting the foam dilational viscosity Kp to the surface dilational elasticity E ... 

Beside the capillary wave techniques, the oscillating bubble method belongs to the first experiments for measuring the surface dilational elasticity (Lunkenheimer Kretzschmar 1975, Wantke et al. 1980, 1993). For soluble adsorption layers it allows of the exchange of matter at a harmonically deformed bubble surface to be determined. 

Fig. 6.10 Comparison of surface dilation elasticities determined from two different wave damping experiments with Triton X-100 solutions at 150 Hz plane waves ( ), cylindrical waves ( ) according to Jiang et al. (1992)...

If the areal change remains small, then the difference in thermodynamic tension can be approximated by using the surface dilational elasticity m. 

We have confined ourselves to a description of the dynamics of surface roughness and the influence of the interaction forces on these dynamics. In reality, however, there are many more dynamic processes in the film and especially in the adsorbed monolayers that should be considered to describe in full detail the film dynamics. Apart from dynamics of the film surfaces parallel to the normal of the interfaces, motions of the adsorbed surface molecules in the interface must be considered. According to Lucas-sen-Reynders and Lucassen, the actual stresses in an interface are described by four rheological coefficients, reflecting the viscoelastic properties of the interface. Two of these, the surface dilatational elasticity and the surface dilatational viscosity, measure the surface s resistance against changes in area. The dilatational module e, considered before, expresses the dilatational elasticity. In our description of the film system, we neglected the viscous behavior of the interface, which implies that no diffusion of surface active molecules between bulk and interface was considered. If, however, surface-to-bulk diffusion is taken into account, the expression... 

The components of the surface stress tensor depend upon the extent and the rate of surface deformation, in a relationship involving the resistance of the surface to both changes in area and shape. Either of these two types of resistance can be expressed in a modulus which combines an elastic with a viscous term. This leaves us with four formal rheological coefficients which suffice for a description of the surface stress. Two of these, viz., the surface dilatational elasticity, and viscosity, measure the surface resistance to changes in area, the other two, viz., the surface shear elasticity, e, and viscosity, r describe the... 

The experimental results shown in Figure 12.10 demonstrate the capacity of the drop and bubble shape technique. After the adsorption process has reached an equilibrium state, over a period of time of about 6 h, some square pulses of the drop area are subsequently, produced. Such area perturbations are suitable for determining the surface dilational elasticity of the interfacial layer. Efficient dosing systems even allow a sinusoidal area change, again providing information... 

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