Surface dilatational modulus

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). 

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... 

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

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... 

The results revealed a significant effect of surface-active and nonsurface active polysaccharides on the properties of adsorbed protein films at the air-water interface. To explain the observed effects on the dynamics of adsorption, the rates of diffusion and rearrangement and the surface dilatational modulus were taken into accoimt (i) the competitive adsorption, (ii) the complexation, and (iii) the existence of a limited thermodynamic compatibility between protein and polysaccharide at the air-water interface and in the aqueous bulk phase. 

The film elasticity was derived from tt-A isotherms as E = — A (d7r/dA). The surface dilatational modulus (E) of films with its elastic and viscous components (Ed and Ev) and loss angle tangent (tan 8) were obtained by sinusoidal periodic compressions and expansions. 

Elastic component of the surface dilatational modulus as a function of surface pressure for E4M, E50LV and E4M at a frequency of 20 mHz. 20°C, pH 7 and 1 = 0.05M. iTa indicates pressure corresponding to the transition from Structure I to Structure II. 

Interfacial tension gradients are very important in stabilising the thin liquid film that is located between the droplets and which is very important at the start of emulsification (films of the continuous phase may be drawn through the disperse phase and collision is very large). The magnitude of the y-gradients and of the Marangoni effect depends on the surface dilational modulus s, which for a plane... 

Erik s research focused on the interfacial properties of the ocean surface, and, in particular, how the chemistry of the air-sea interface affects the dynamics of short waves, nearsurface flows and interfacial fluxes of heat, mass and momentum. During his short career, he contributed to over 30 scientific publications in this area. His doctoral research, carried out under the tutelage of well-known colloid and surface chemist, Sydney Ross, concerned the propagating characteristics of surface waves in the presence of adsorbed films. That work was eventually published as a series of seminal papers on capillary ripples, and his theoretical treatment of ripple propagation and a corrected dispersion relation for surface waves in the presence of a surface dilational modulus (with J. Adin Mann, Jr.) still stand as the definitive word on the subject. 

In this paper we propose a dynamic method for tackling the problem of interactions in soluble monolayers. The surface dilational modulus, e, is a dynamic surface quantity very sensitive to interactions. It is defined as the decrease in local surface pressure per unit relative increase in surface area A in an oscillatory experiment ... 

Figure 2. Example of surface dilational modulus vs. frequency curves. Dode-cyl triethylene glycol (C12E3) solutions. A = 10 9 mole/cm3 0 = 5 X I O 9 mole/cm3 X = 2 X 10 8 mole/cm3. Abscissa log to (a> is angular frequency in...

FIGURE 10.34 Values of the surface dilatational modulus ESD of solutions of decanoic acid at two concentrations (indicated) as a function of time scale t. (Adapted from E. H. Lucassen-Reynders. Anionic Surfactants. Surfactant Series Vol. 11. Marcel Dekker, New York, 1981, p. 201.)... 

FIGURE 10.37 Effect of surface dilatational modulus (ESu) on the motion of an AW surface the aqueous phase flows over a solid support, v = linear velocity t — time scale subscript S means at the surface. Highly schematic. It is assumed that the distance over which the surface can move is small enough to allow Eq. (10.17) to be valid. 

Presence of surfactant at the interface will also directly affect deformation. The surfactant allows formation of a /-gradient. This would affect the deformation mode of a drop, which has indeed been observed. Moreover, enlarging the interfacial area causes y to increase, as mentioned. This implies that the interfacial free energy increase includes two terms y dA + A dy. The first term is due to the deformation of the drop being counteracted by its Laplace pressure the second is due to surface enlargement being counteracted by the surface dilational modulus ESD. Making use of Eq. (10.20) for we obtain... 

Consider a shrinking bubble with a surfactant layer. The decrease in radius means a decrease in surface area, hence an increase in surface load, hence a decrease in surface tension (cf. Section 10.2.3). This implies a mechanism that counteracts the increase in Laplace pressure. The decrease in y is expressed in the surface dilational modulus ESD =dy/d In A [Eq. (10.20)]. According to Gibbs, the following condition now determines whether the bubble will be prevented from shrinking ... 

Symbols for (physical) quantities, be they variables or constants, are given by a single character (generally Latin or Greek letters) and are printed in italics, e.g., F (force), p (pressure), p (chemical potential), k (Boltzmann constant). Further differentiation is achieved by the use of subscripts and/or superscripts these are printed in italics if it concerns the symbol of a quantity, otherwise in roman type, e.g., cp (specific heat at constant pressure), hp (Planck s constant), Ffu (surface dilational modulus). For clarity, symbols are generally separated by a (thin) space, e.g., F=ma, not ma. Some generally accepted exceptions occur, such as pH, as well as symbols (or two letter abbreviations, rather) for the dimensionless ratios frequently used in process engineering, like Re for Reynolds number and Tr for Trouton ratio (in roman type). 

For the first measurements we followed the evolution of y(t) during the adsorption process. After having reached equilibrium, the complex surface dilatational modulus e is obtained from the response of the surface to a sinusoidal dilatation/compression deformation. As usual, the real part corresponds to the elastic properties and the imaginary part to the dissipative properties ... 

Table 2 Ratio of surface dilation modulus E over surface tension for glycinin solution of 0.1 g I1 for pH and ageing time indicated...

The surface dilational modulus E defined by Eq. (6.10), is related to the surface coverage by the equation... 

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