Surface dilation

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

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

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. 

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. 

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... 

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). 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

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

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. 

Another indirect method for the estimation of Gibbs elasticity modulus is based on the determination of the surface dilatation modulus E in experiments in which the surfaces of the surfactant solutions undergo small amplitude deformations of oscillatory nature [100-102], It is shown [100, see also Chapter 7] that the concentration dependence of a Gibbs elasticity modulus at constant film thickness should be nearly the same as the concentration dependence of (twice) the surface elastic modulus E when film thickness and frequency are related by... 

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. 

Introducing the modulus (= absolute value in complex number language) of the surface dilational modulus K° as... 

Figure 3.87. Surface dilational data for stearic acid monolayers. Oj = 0.205 nm, pH = 6 1 mM solutions, 25°C. The cation is indicated. (Redrawn from Yazdanian et al., (1992).)...

Figure 4.27. Absolute value of the surface dilational modulus obtained by the wave technique (closed symbols) and from oscillating bubbles (open symbols). Surfactant, tridecyldimethyl phosphine oxide A, A c = 2 xlQ-S M O. c = 5 x lO M. Drawn curves fit to [4.5.431. Temperature 22°C. (Redrawn from Wantke et al. (loc. cit.).)...

The d)mamics of adsorption of emulsifiers at fluid interfaces have been determined by tensiometry and surface rheology (Figure 14.3) that is, from the time dependence of surface pressure and surface dilatational modulus (E). We found that tt and E increase with time (9), which should be associated with emulsifier adsorption (Patino and Nino, 1999 Nino et al., 2003 Carrera et al., 2005). 

In Figure 14.3c a normalization in a single master curve of E vs. tt data reflects the interfacial behavior of emulsifier adsorbed films for different emulsifier concentrations, at different adsorption times, and under different processing conditions (Nino and Patino, 2002 Nino et al., 2003). The plot suggests that interactions between adsorbed emulsifier molecules (residues) increase with tt. In fact, at lower tt values the slope of the -tt plot was close to 1, which corresponds to the behavior of an ideal gas with low emulsifier interactions. However, at higher tt values the slope changes, which implies an important nonideal behavior with higher molecular interactions as the amount of emulsifier at the interface increases. These data indicate that the interfacial activity and the surface dilatational modulus of emulsifier films are mainly a result of the amount of adsorbed emulsifier. 

Surface dilatational rheology is a very sensitive technique to analyze the competitive adsorption/displacement of protein and LMWE emulsifier at the air-water interface (Patino et al., 2003). A common trend is that the surface dilatational modulus increases as the monolayer is compressed and is a maximum at the highest surface pressures, at the collapse point of the mixed film, and as the content of LMWE in the mixture increases. At higher TT, the collapsed protein residues displaced from the interface by LMWE molecules have important influence on the dilatational characteristics of the mixed films. The mechanical properties of the mixed films also demonstrate that, even at the highest tt, the LMWE is unable to displace completely protein molecules from the air-water interface. 

As for pure LMWE films, the surface dilatational modulus is higher for protein-saturated-LMWE than for protein-unsaturated-LMWE mixed films at every surface pressure. The surface dilatational properties of mixed protein-emulsifier films also depend on the presence of some food components (ethanol and sucrose) in the aqueous phase. In general, a decrease in the dilatational rheological properties on the addition of ethanol was found for protein-water-insoluble LMWE. That is, the static and... 

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