Viscosity Surface dilatational

Another important property is the surface dilational viscosity, k... 

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. 

Hsu and Berger [43] used the maximum bubble pressure method (MBP) to study the dynamic surface tension and surface dilational viscosity of various surfactants including AOS and have correlated their findings to time-related applications such as penetration and wetting. A recent discussion of the MBP method is given by Henderson et al. [44 and references cited therein]. 

Figure 12a gives the surface dilatational viscosities for a nonionic surfactant, namely, nonylphenol 10 EO, and for C12-C14 AOS. Both products were ad-... 

There is good correlation between the concentration giving the maximum surface dilatational viscosity and that giving the best foam performance. The nonylphenol 10 EO is a low-foaming nonionic surfactant with a maximum foam height of 150 ml in this test, whereas AOS produced 670 ml of foam. Figure 12 clearly shows that there is an optimum surfactant concentration for a dynamic process such as foam generation. 

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... 

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). 

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. 

The theoretical analysis indicated that asymmetric drainage was caused by the hydrodynamic instability being a result of surface tension driven flow. A criterion giving the conditions of the onset of instability that causes asymmetric drainage in foam films was proposed. This analysis showed as well that surface-tension-driven flow was stabilised by surface dilational viscosity, surface diffusivity and especially surface shear viscosity. 

Lucassen J and Hansen RS (1966) Damping of waves on monolayer-covered surfaces. I. Systems with negligible surface dilational viscosity. J Colloid Interface Sci 22 32-44... 

If it concerns a monolayer of an amphiphile that is insoluble in the bordering phases, the modulus is purely elastic (although at strong compression, i.e., large AA/A, the surface layer may collapse), and SD is constant in time and independent of the dilatation rate. If the surfactant is soluble, exchange of surfactant between interface and bulk occurs, and Esr> will be time dependent. This means that also an apparent surface dilatational viscosity can be measured ... 

Here, are the surface shear viscosity, the surface dilational viscosity and the... 

Using the classical equation of Boussinesq (1913) for the surface dilational viscosity, a relationship between surface tension change, surface elasticity and surface dilatation viscosity is obtained. 

The theory of pulsating bubbles is also a well developed one (Wantke et al. 1980, 1993). Recently, it was generalised by Johnson Stebe (1994). According to their results, the determination of the frequency dependence of the phase lag between oscillation generation and pressure response should allow the exchange of surfactant and the surface dilational viscosity to be differentiated. There are no experiments available so far to check this hypothesis. 

The Marangoni elasticity can be determined experimentally from dynamic surface tension measurements that involve known surface area changes. One such technique is the maximum bubble-pressure method (MBPM), which has been used to determine elasticities in this manner (24, 26). In the MBPM, the rates of bubble formation at submerged capillaries are varied. This amounts to changing A/A because approximately equal bubble areas are produced at the maximum bubble pressure condition at all rates. Although such measurements include some contribution from surface dilational viscosity (23, 27), the result will be referred to simply as surface elasticity in this work. 

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. 

Figure 10. The concepts of surface shear and surface dilational viscosities (a) deformation of a soap film and (b) dilation of a soap film.

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... 

In some cases the dynamic surface tension may exceed the equilibrium value. Scriven (S4) shows that for a Newtonian surface viscosity model an extra term equal to AKjftjR should be added to the right-hand side of Eq. (5), where k is the effective surface-dilational viscosity. 

K Effective surface dilational viscosity fi Viscosity V Kinematic viscosity p Density... 

The viscosity emphasized in this chapter, called elongational or extensional viscosity, was originally designated (34) tensile viscosity. When this bulk-phase parameter is near the interface, its two-dimensional equivalent is called the surface dilational viscosity. The importance of this parameter in the foaming of coatings, which arises from differences in surfactant structures, has been discussed (35). In cosmetic applications, foam and gel structures are important and probably reflect the reason the hydrophobically modified acrylic acid polymers were emphasized in the last section of Ghapter 7. 

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]. 

To understand the main difficulty in the definition of the surface dilatational viscosity, 7]dih let us consider a simple case of uniform expansion of an airlwater adsorption layer (see Fig. 2). The surface element with an area A is extended to a new area A + for a time interval from t to t St (see Fig. 2). The total deformation, a, and the rate of deformation, d, are defined as ... 

The subscript m denotes the reference values of o and T these reference values are chosen for convenience in matching up with experiments. The additional parameters that show up in the boundary conditions on the free surface are the surface shear viscosity and surface dilatational viscosity, represented hy jt and K, respectively, and the surface diffusivity of the surfactant denoted by D. ... 

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