Dynamic surface elasticity

It can be considered from the scheme that one has to distinguish between the foam kinetics, i.e. the rate of generation of foam under well defined conditions (air input and mechanical treatment) and the stability and lifetime of a foam once generated. The foam kinetics is also sometimes termed foamability in the literature. These quantities can be related to interfacial parameters such as dynamic surface tension, i.e. the non-equilibrium surface tension of a newly generated surface, interfacial rheology, dynamic surface elasticity and interfacial potential. In the case of the presence of oily droplets (e.g. an antifoam, a... 

Miller R, Fainerman VB, Aksenenko EV, Makievski AV, Kraegel J, Liggieri L, Ravera F, Wuestneck R, and Loglio G (2000) "Surfactant Adsorption Kinetics and Exchange of Matter for Surfactant Molecules with Changing Orientation within the Adsorption Layer" in Emulsion, Foams, and Thin Films, Mittal and Kumar Editors, Ch. 18, Marcel Dekker, pp. 313-327 Miller R, Fainerman VB, Makievski AV, Leser M, Michel M and Aksenenko EV (2004) Determination of Protein Adsorption by Comparative Drop and Bubble Profile Analysis Tensiometry. Colloids Surfaces B 36 123-126 Neumann AW and Spelt JK Eds., Applied Surface Thermodynamics, Surfactant Science Series, Vol. 63, Marcel Dekker Inc., New York, 1996 Noskov B and Logho G (1998) Dynamic surface elasticity of surfactant solutions. Colloids Surfaces A 143 167-183... 

For transverse waves the amplitudes of potential flow exceed by a few orders of magnitude the amplitudes of the vortical flow A20 Bo2 and A21 B12. This means that the inhomogeneities of surface tension mainly scatter the capillary waves, and the inhomogeneities of the dynamic surface elasticity play a minor role. 

Noskov BA, Alexandrov DA, Gumennik EV, Krotov W, Miller R (1998) Dynamic surface elasticity of solutions of dodecylsulphate Na in the frequency range 0.8Hz-5Hz. Colloid Z 60 227-234... 

Numerous data on dynamic surface tension [77-93] and dynamic surface elasticity [94-103] of aqueous micellar solutions have been published until now. These data evidence the influence of micelles on the adsorption kinetics, although they are present only in the bulk phase. This effect can surprise on a first glance because it is well-known that the surface activity of micelles is negligible and hence their adsorption is almost zero. However, the influence of micelles can be easily explained if one takes into account that the adsorption kinetics of surfactants at fluid -fluid interface is determined by the diffusional exchange between the subsurface and the bulk phase [104, 105]. It is exactly the diffusion of monomers that changes in the presence of micelles. This point of view is widely accepted and difficulties arise only if one tries to obtain quantitative estimates of the observed effects. 

The dynamic surface elasticity s detennines the response of the system (the perturbation of surface tension 5y) to a small change of the area of a surface element 5 S... 

The measurement of the wave characteristics and application of Eq. (5.256) to experimental results allow to determine the surface parameters y and e. The dynamic surface elasticity is the most interesting property because it is connected with the kinetic coefficients of the relaxation processes in the system. The observed correlations between i2 and the efficiency of numerous processes of technological implication (foam formation [122], solubilisation of impurities [163], bubble formation [1], liquid spreading [163], emulsification [165]) are determined first... 

The main relations between the complex dynamic surface elasticity and the kinetic characteristics of micellisation are presented below [103, 133, 134]. Let a small surface element of the area S be subjected to a small periodic surface dilation 5 S... 

For small harmonic deformations the dynamic surface elasticity has the form... 

This relation describes not only periodic deformations of a liquid surface. Using methods of integral transformations it is possible to show that the dynamic surface elasticity is a fundamental surface property and its value determines the system response to a small arbitrary surface dilation [161]. With this method it is also possible to determine the dynamic elasticity of liquid-liquid interfaces where the surfactant is soluble in both adjacent phases [133]. Moreover, similar transformations lead to an expression for the dynamic surface elasticity for the case when the mechanism of the slow step of micellisation is determined by scheme (5.185) or for frequencies corresponding to the fast step of micellisation [133,134]. However, as stated above, it is the slow process which mainly influences the adsorption kinetics from micellar solutions. 

Note that the (diffusion of micelles does not influence the dynamic surface elasticity. This fact can be easily explained if we take into account that any increase of the total micellar concentration is accompanied by a decrease of the relative changes of Cm. Hence, changes of the local monomer concentration are partly compensated at the expense of micelles, when the adsorption and desorption processes are determined by diffusion of monomers normal to the interface. However, the corresponding local relative changes of the micellar concentrations are negligible when Cm is sufficiently large. 

The calculations of the real and imaginary parts of the complex dynamic surface elasticity via Eqs. (5.275) and (5.276) (at x = 0) illustrate these conclusions. Figure 15 shows the dependencies of the non-dimensional quantities e =- ,(9y/91nr) (1) and... 

Fig. 5.15. Real and imaginary parts of the dynamic surface elasticity as a function of frequency further explanations are given in the text.

The region of the CMC (n (c +o c ) c l) requires special consideration. Substitution of of t2 and ti from Eq. (5.264) into (5.272), and the transition to the limit c -> 0 leads to the dynamic surface elasticity of sub-micellar solutions [165] and thus to a rather obvious conclusion if a solution contains mainly monomers, micelles do not influence the dynamic surface properties. Therefore, even for low frequencies (diffusion controlled adsorption kinetics) there is a concentration range close to the CMC where the surface elasticity is almost constant and begins to increase gradually only at further increasing concentration. Finally the surface elasticity takes values given by relations (5.275) - (5.278). This concentration dependence was observed in experiments with nonionic surfactants [95]. The oscillating barrier... 

New experimental methods created during the last two decades allow to investigate the concentration and frequency dependence of the dynamic surface elasticity more systematically. That is why the dynamic surface elasticity behaviour in the region of the CMC deserves special attention. Relations (5.264) in the first approximation take the form... 

If only frequencies < Tj are considered, the approximation for the dynamic surface elasticity is... 

Note that relation (5.281) does not contain any kinetic characteristics of micellisation. If the micellar concentration is low and the formation (disintegration) of micelles is sufficiently fast (tj o), the adsorption rate and, consequently, the dynamic surface elasticity depend only on the efficiency of the surfactant transfer by micelles from the bulk to the surface, and, therefore, on the diffusion coefficient of micelles and the mean aggregation number. This means that the micellar size can be determined from dynamic surface properties. Really, if approximation (5.231) for the diffusion coefficient of micelles is used, it follows from Eq. (5.281)... 

The constancy of the damping coefficient beyond the CMC in the systems under consideration corresponds to the approximate constancy of the dynamic surface elasticity. This means that micelles do not take part in the exchange of surfactant molecules between the surface layer and the bulk phase. According to the results of the preceding section this situation is possible when... 

The influence of micellisation on the propagation of capillary waves has been discovered only for solutions of the nonionic surfactant - DePO. The determined values of Z2 are comparable with the results for solutions of DePB but they decrease monotonously with concentration. Therefore, the obtained results evidence that relations (5.284) and (5.285) describe the concentration dependence of the dynamic surface elasticity well. Hence, the method of transverse capillary waves can be used for studies of micellisation kinetics of surfactants with relatively low surface activity. For surfactants with higher surface activity where the formation and disintegration of micelles proceed slower the method of longitudinal surface waves can be used [102, 103]. The characteristics of longitudinal waves are more sensitive to the dynamic surface elasticity, and this allows one to study the micellisation kinetics under the condition... 

Interfacial rheology - Dynamic surface elasticity Interfacial potential/ Intermolecular cohesion Oil particle size... 

Noskov BA, Loglio G, Lin S Y, MillCT R (2006) Dynamic surface elasticity of polyelectrolyte/ surfactant adscaption layers at the air/water inlraface dodecyltrimethylanunonium bromide and copolymer of sodium 2-acrylamido-2-methyl-l-propansutf(Hiate with N-isopropyl-aCTylamide. J Colloid Interface Sci 301 386... 

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