Surface shear elasticity

The prime cause of the surface shear viscosity is friction between surfactant molecules the cause of surface shear elasticity is attractive forces between those molecules, leading to a more or less continuous two-dimensional network. For a closely packed layer, the effects may be substantial. For layers of small-molecule surfactants, however, the values of rif are generally immeasurably small, about 10 5 N s m 1 or less. For adsorbed polymers, values between 10 3 and lN-m-s-1 have been reported. 

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 interfacial rheology of protein adsorption layers has been intensively studied in relation to the properties of foams and emulsions stabilized by proteins and their mixtures with lipids or surfactants. Detailed information on the investigated systems, experimental techniques, and theoretical models can be found in Refs. [762-769]. The shear rheology of the adsorption layers of many proteins follows the viscoelastic thixotropic model [770-772], in which the surface shear elasticity and viscosity depend on the surface shear rate. The surface rheology of saponin adsorption layers has been investigated in Ref. [773]. 

The main classic theory on the oscillatory rheology of dispersions of thin-walled capsules is due to Oldroyd [80]. In a latter paper, apart from the interfacial tension, Oldroyd introduced surface shear viscosity, surface shear elasticity, dilatational viscosity, and dilatational elasticity [33]. 

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). 

In addition to the film elasticity, other factors that may affect foam stability arc surface shear viscosity, bulk viscosity of the foaming liquid, and the presence of particulate matter. 

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).

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. 

QCM-D measurements that include dissipation allow a more accurate estimate of mass changes through application of Voigt model that takes into account the viscoelastic properties of the system. Modeling software QTools supphed by Q-Sense uses the full thick layer expressions to model the response. Here, this program has been used to estimate the mass, thickness, viscosity, and shear elastic modulus of the adsorbed pectin layer on BSA surface, with a best fit between the experimental and model/and D values. 

One unique capability of the QCM-D technique is its successful extraction of quantitative information about a film s viscoelasticity. Figure 8.9 shows the variation of viscosity and shear elastic moduli of a pectin layer during pectin adsorption on the BSA surface from the Voigt model. It is noted that the shear elastic moduli is much... 

In the situation described above, the dynamic experiment was cturied out in dilation the resulting complex modulus was divided into a real ( elastic ) and an imaginary ( viscous ) part. As a counterpart, the experiment can also be carried out in shear, resulting in a complex surface shear viscosity G°, consisting of a real (viscous) part, the surface shear viscosity G° and the surface shear loss viscosity, G"" identical to the elasticity. This inversion of method is formally identical to measuring complex dielectric permittivities instead of complex conductivities, discussed in sec. I1.4.8a. In that case, flg. 3.26 is modified in that panel (b) describes G°, panel (c) G " and jianel (d) the sum, with - tan 0 = G" /G. ... 

Previously introduced, the thermodynamic surface tension 7 represents the elastic resistance to surface dilation. Furthermore, two types of viscosities are defined within the interface, a dilational viscosity and a shear viscosity. For a surfactant monolayer, the surface shear viscosity rjS is analogous to the three-dimensional shear viscosity the rate of yielding of a layer of fluid due to an applied shear stress. The phenomenological coefficient s represents the surface dilational viscosity, and expresses the magnitude of the viscous forces during a rate expansion of a surface element. Figures 10a and 10b illustrate the difference between the two surface viscosities. 

Finally, there has been some evidence that the coefficient for shear elasticity may be a function of the surface extension, increasing with increasing deformation. This was first proposed by Fischer in an effort to resolve discrepancies between theoretical predictions and observed behavior of red cells undergoing dynamic deformations in fluid shear [Fischer et al., 1981 ]. Increasing elastic resistance with extension has also been proposed as an explanation for discrepancies between theoretical predictions based on a constant modulus and measurements of the length of a cell projection into a micropipette [Waugh and Marchesi, 1990]. However, due to the approximate nature of the mechanical analysis of cell deformation in shear flow, and the limits of optical resolution in micropipette experiments, the evidence for a dependence of the modulus on extension is not clear-cut, and this issue remains unresolved. 

The most modern picture of membrane deformation recognizes that the membrane is a composite of two layers with distinct mechanical behavior. The membrane bilayer, composed of phospholipids and integral membrane proteins, exhibits a large elastic resistance to area dilation but is fluid in surface shear. The membrane skeleton, composed of a network of structural proteins at the cytoplasmic surface of the bilayer, is locally compressible and exhibits an elastic resistance to surface shear. The assumption that the membrane skeleton is locally incompressible is no longer applied. This assumption had been challenged over the years on the basis of theoretical considerations, but only very recently has experimental evidence emerged that shows definitively that the membrane skeleton is compressible. This has led to a new constitutive model for membrane behavior [Mohandas and Evans, 1994]. The principal stress resultants in the membrane skeleton are related to the membrane deformation by ... 

Membrane shear modulus A measure of the elastic resistance of the membrane to surface shear deformation that is, changes in the shape of the surface at constant surface area (Equation 60.8). (Units 1 mN/m = 1 dyn/cm)... 

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... 

When the interfacial shear elasticity is moderate, at moderate surface viscosity, the thinning velocity will be greater than the Reynolds velocity. An increased surface viscosity means decreased surface mobility and a longer drainage time. These are all factors to be considered in decisions toward positive steps of destabili-zation. 

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