Interfacial dilational viscosity

Since there is no change in surface tension with a change in the rate of a pure liquid surface (i.e., d A/d II = infinity), the elasticity is zero. The interfacial dilational viscosity, ks, is defined as... 

By way of introduction, consider the dilational experiment of fig. 3.49. At t = t the monolayer is instantaneously subjected to a stress r° = r = r°, which is kept constant till t = t, after which it is suddenly removed. Panels (b) and (c) refer to the strain response AA/A for a purely elastic and a purely viscous monolayer, respectively, The elastic monolayer directly follows the applied stress after cessation it relaxes instantaneously. The viscous one starts to flow after cessation of the stress the flow stops. The height of the block in panel (b) is equal to r / K (compare [3.6,18]) whereas in panel (c) the interfacial (dilational) viscosity follows from the slope as... 

Dilational interfacial properties can be determined in various ways both at small and at large strains. In the former case results are normally interpreted in terms of interfacial dilational storage moduli, interfacial dilational loss moduli or dynamic interfacial dilational viscosities and the loss tangents as a function of applied deformation frequency, see sec. 3.6f. For large strains one obtains the Interfacial dilational viscosity. Various techniques have been discussed In the reviews by Miller et al. and Prins, mentioned in sec. 3. lOd. For the wave behaviour, see fig. 3.45. 

Many experiments have been proposed for measuring the interfacial shear viscosity and elasticity and interfacial dilatational viscosity and elasticity at gas/liquid and liquid/ liquid interfaces [22]. Interfacial shear viscosities of different oil/aqueous systems have been studied worldwide. Some experimental results indicate that low interfacial shear viscosities do not necessarily imply that an emulsion will be unstable [23]. The dilatational rheology is based on area changes due to an expansion or compression of a fluid surface and stress relaxation experiments. The experiment results show that the interfacial dilatational properties can be much higher than the interfacial shear properties for the same system [15,24-27]. This makes researchers believe that interfacial dilatational viscosity and elasticity may have a better relationship with the stability of the emulsion than with interfacial shear properties. 

Rheology is the study of the deformation and flow of materials under the influence of an applied stress. The interfacial rheology of a surfactant film normally accounts for the interfacial viscosity and elasticity of the film. The interfacial viscosity can be classified with interfacial shear viscosity and interfacial dilational viscosity. Films are elastic if they resist deformation in the plane of the interface and if the surface tends to recover its natural shape when the deforming forces are removed. The interfacial elasticity can also be classified with interfacial shear elasticity and interfacial dilational elasticity (6, 7, 12). Malhotra and... 

Barber and Hartland present results for several assumed boundary conditions at r=R. Although the quantitative results are different in each case, the qualitative results are consistent. The case used here is that where the shear stress is assumed to vanish at r=R. Although Barber and Hartland present their results in integral form, one can integrate their film drainage rate equation to obtain the following relation between the coalescence time t, the applied force F, the effective contact radius R, the bulk phase viscosity of the film y, the critical collapse distance 6, and the combination r) = k + e of the apparent interfacial dilational viscosity and the intrinsic interfacial shear viscosity ... 

The interfacial dilational viscosity ilf can be simply defined if one considers a uniform expansion of the interface at a constant-rate d In A/dt i.e.. 

Prins et al. [19] found that a mixture of sodium dodecyl sulfate (SDS) and dodecyl alcohol gives a more stable 0/W emulsion when compared to emulsions prepared using SDS alone. This enhanced stability is due to the higher interfacial dilational elasticity e for the mixture when compared to that of SDS alone. Interfacial dilational viscosity did not play a major role since the emulsions are stable at high temperature whereby the interfacial viscosity becomes lower. This correlation is not general for all surfactant films since other factors such as thinning of the film between emulsion droplets (which depends on other factors such as repulsive forces) can also play a major role. 

Tirf, ) are normalized by their values at pH = 5. The experimental data show that both the surface elasticity, Ec, and relaxation time, increase with increase of pH. The interfacial dilatational viscosity, y d, exhibits a maximum at pH = 6. A similar peak of the interfacial shear viscosity of BSA at pH = 6 has been observed by Graham and Phillips [188] at petroleum ether—water interface. The results in Fig. 9 demonstrate a marked influence of the ionic strength on the rheological parameters. 

Figure 9 Interfacial elasticity Eq, diffusion relaxation time t and interfacial dilatation viscosity T rf versus pH of solutions of 0.0125 wt% BSA the other phase is decane. pH is maintained by a phosphate buffer the ionic strength, I, is adjusted by NaCl. The droplet expansion method is applied. (After Ref. 84.)...

A study on a commonly used demulsifier, namely, a phenol-formaldehyde resin, elucidated how various parameters such as interfacial tension, interfacial shear viscosity, dynamic interfacial-tension gradient, dilatational elasticity, and demulsifier clustering affect the demulsification effectiveness [1275]. 

Effectiveness of a crude oil demulsifier is correlated with the lowering of shear viscosity and dynamic tension gradient of the oil-water interface. Using the pulsed drop technique, the interfacial dilational modulii with different demulsifiers have been measured. The interfacial tension relaxation occurs faster with an effective demulsifier. Electron spin resonance with labeled demulsifiers indicate that the demulsifiers form reverse micelle like clusters in bulk oil. The slow unclustering of the demulsifier at the interface appears to be the rate determining step in the tension relaxation process. 

For effective demulsification of a water-in-oil emulsion, both shear viscosity as well as dynamic tension gradient of the water-oil interface have to be lowered. The interfacial dilational modulus data indicate that the interfacial relaxation process occurs faster with an effective demulsifier. The electron spin resonance with labeled demulsifiers suggests that demulsifiers form clusters in the bulk oil. The unclustering and rearrangement of the demulsifier at the interface may affect the interfacial relaxation process. 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Boussinesq (B4) proposed that the lack of internal circulation in bubbles and drops is due to an interfacial monolayer which acts as a viscous membrane. A constitutive equation involving two parameters, surface shear viscosity and surface dilational viscosity, in addition to surface tension, was proposed for the interface. This model, commonly called the Newtonian surface fluid model (W2), has been extended by Scriven (S3). Boussinesq obtained an exact solution to the creeping flow equations, analogous to the Hadamard-Rybczinski result but with surface viscosity included. The resulting terminal velocity is... 

We can distinguish between two types of stresses on an interface a shear stress and a dilatational stress. In a shear stress experiment, the interfacial area is kept constant and a shear is imposed on the interface. The resistance is characterized by a shear viscosity, similar to the Newtonian viscosity of fluids. In a dilatational stress experiment, an interface is expanded (dilated) without shear. This resistance is characterized by a dilatational viscosity. In an actual dynamic situation, the total stress is a sum of these stresses, and both these viscosities represent the total flow resistance afforded by the interface to an applied stress. There are a number of instruments to study interfacial rheology and most of them are described in Ref. [1]. The most recent instrumentation is the controlled drop tensiometer. 

Unlike in three dimensions, where liquids are often considered incompressible, a surfactant monolayer can be expanded or compressed over a wide area range. Thus, the dynamic surface tension experienced during a rate-dependent surface expansion, is the result of the surface dilational viscosity, the surface shear viscosity, and elastic forces. Often, the contributions of shear and/or the dilational viscosities are neglected during stress measurements of surface expansions. Isolating interfacial viscosity effects is difficult because, since the interface is connected to the substrate on either side of it, the interfacial viscosity is coupled to the two bulk viscosities. 

Unlike the wet foam calculation where primary viscous stresses are localized within Plateau border regions and derived from interfacial viscous properties, the total viscous stress for a dry foam (i.e., dispersed-phase volume fraction approaching 1) is distributed throughout the thin liquid films. The leading-order dilatational viscosity of a dry foam composed of a spatially periodic array of tetrakaidecahedron (39) bubbles was given by Edwards and Wasan (40) as follows ... 

The foam-dilatational viscosity, K, arises because of two primary mechanisms (37) (1) viscous flow within the thin films, and (2) interfacial tension gradients acting along the foam bubble surfaces. The effect of interfacial tension gradients is to increase the foam viscosity as they impede flow near the surfaces of the thin foam films by contributing to a larger film stress. As in the wet foam (eq 6), the foam dilatational viscosity for a dry foam, K, is inversely proportional to film thickness as well (eq 9). 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

Yq surface tension of the pure solvent r = r F2 total adsorption 5 relative oscillation amplitude AHj molar standard enthalpy of transfer Anp density difference Sjj dilational elasticity dilational viscosity rig shear viscosity relative area change X=k/xn dimensionless rate constant interfacial chemical potential n = Yq-y surface tension co, co2 partial molar areas in - 27if circular frequency... 

Figure 12 shows that when the temperature is lower than 30°C, the interfacial shear viscosity increases as the shear rate increases. This phenomenon shows a dilatant behavior (shear thickening) as in a three-dimension system (12). These results fiirther prove that wax particles can contribute to the rheological properties of the interfacial film between... 

There are four rheologieal parameters which describe the response to imposed interfaeial stresses or deformation. For a Newtonian interfaee, the signifieant rheological properties that determine interfaeial motion are the interfacial shear viscosity, the interfaeial dilational viscosity, and the interfaeial tension gradient. The interfaeial shear elasticity, e and viscosity, describe the resistance of the... 

Neustadter et al. (166) earlier measured interfacial dilation elasticities, e j, and viscosity, qj, for Iranian crude oil/water and deduced that the extent of the relaxation process was not a function of time due to the lack of change in viscosity, q j, at fixed frequency. However, as frequency changed, q j decreased, indicating that the relaxation involved the interchange of bulk material to and from the interface. The increased elas-ticy, ej, with time suggested that there was irreversible adsorption of high-molecular-weight species. 

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