Non-equilibrium interfacial tensions

In contrast to the situation for pure liquids, for which data are sccirce, there is an abundance of information about non-equilibrium interfacial tensions for solutions, particularly for solutions of surface-active substances. One reason is that the latter effect is more mundane and therefore easier to observe. Moreover, it also has practical importance in many industrial processes. Explanations are readily offered, although on closer inspection interpretation of the observed relaxation is not always straightforward. 

Methods for measuring non-equilibrium Interfacial tensions of (surfactant) solutions can be divided into two groups. 

Figure 1.32. Non-equilibrium interfacial tension at the oil-water interface system water + hexane, containing palmitic acid, of which the concentration c is indicated. The drawn curves relate to a model interpretation involving diffusion. (Redrawn from J. van Hunsel, G. Bleys and P. Joos, J. Colloid Interface Set 114 (1986) 432.)...

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... 

In this section we address the measurement of interfacial tensions that are time dependent because the interface is not at equilibrium. Sometimes such tensions are called dynamic surface tensions but we prefer non-equilibrium surface tensions. Their measurement will be discussed in this section, particularly against the background of the techniques described so far. Most of the interpretation (in terms of surface rearrangements, transport to and from interfaces, etc.) and additional monolayer techniques (wave damping, for instance) will be deferred to chapters 3 and 4. 

Reactive blends at processing temperatures caimot exhibit an equilibrium interfacial tension in the usual thermodynamic sense. First, as long as some reaction is occuring, no matter how slowly, the system is not at equilibrium. Second, due to the existence of the copolymer it is more proper to envision a broad interphase region across which the composition varies. The rheology of the interphase may indeed be quite different from the rheologies of the individual components. Nevertheless, one can measure the apparent interfacial tension by a number of methods, which are used in non-reactive systems. This text will simply refer to the results of such measurements as the interfacial tension, as is conunon usage in the field. 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

When mixing two surfactants species in a SOW system, an equilibrium takes place between the oil and water phases and the interface for each species. Since the two species do not necessarily exhibit the same affinity for the interface and the oil and water bulk phases, the compositions of the surfactant mixtures at interface and in the phases might be different. For instance if a very hydrophilic species is mixed with a very lipophihc one, as often recommended in the old formulation literature, then the hydrophihc surfactant has a strong tendency to partition in water, whereas the lipophihc one would partition in the oil. In this case the surfactant mixture in water will contain a large majority of hydrophilic species, i.e., it will be very hydrophilic, whereas the oil phase will predominantly contain the hpophihc species, with the remaining adsorbing at interface. This situation in which each species actuates on its own, more or less independently of the other, has been called non-collective behavior. Since the surfactant mixture composition at interface is often the one that commands the actual property of the system, such as the interfacial tension or the stabihty of the emulsion, it is most important to know how to calculate or measure the characteristics of the mixture present at interface. Such methods will be discussed in the next section. 

This chapter describes recent work in our laboratories examining density modification of DNAPLs through a combination of batch non-equilibrium rate measurements and DNAPL displacement experiments in 2D aquifer cells. The objective of this work was to evaluate the applicability of nonionic surfactants as a delivery mechanism for introducing hydrophobic alcohols to convert the DNAPL to an LNAPL prior to mobilizing the NAPL. Three different nonionic surfactants were examined in combination with n-butanol and a range of DNAPLs. Overall, it was found that different surfactants can produce dramatically different rates of alcohol partitioning and density modification. However, for some systems interfacial tension reduction was found to be a problem, leading to unwanted downward... 

The characteristic effect of surfactants is their ability to adsorb onto surfaces and to modify the surface properties. Both at gas/liquid and at liquid/liquid interfaces, this leads to a reduction of the surface tension and the interfacial tension, respectively. Generally, nonionic surfactants have a lower surface tension than ionic surfactants for the same alkyl chain length and concentration. The reason for this is the repulsive interaction of ionic surfactants within the charged adsorption layer which leads to a lower surface coverage than for the non-ionic surfactants. In detergent formulations, this repulsive interaction can be reduced by the presence of electrolytes which compress the electrical double layer and therefore increase the adsorption density of the anionic surfactants. Beyond a certain concentration, termed the critical micelle concentration (cmc), the formation of thermodynamically stable micellar aggregates can be observed in the bulk phase. These micelles are thermodynamically stable and in equilibrium with the monomers in the solution. They are characteristic of the ability of surfactants to solubilise hydrophobic substances. 

Non-equilibrium liquid films formed in the process of spreading have been considered in some early works, especially in the test of the theory of interfacial tension and the rule of Antonov [204], A review on the rule of Antonov and its interpretation on the basis of isotherms of disjoining pressure in wetting films is presented in [532]. However, these works do not deal with precise measurement of film thickness and the studies confined only the kinetics of spreading and lens formation. 

At equilibrium the thermodynamical and mechanical interpretations should be equivalent. In sec. 1.2.3, in connection with fig. 1.2.1, this equivalence was addressed and found to be achieved provided the extension of the area is done reversibly, that is, at low Deborcih number (De 1). Only under this condition has the interface enough time to come to equilibrium, that is, to achieve full relaxation of all adsorption equilibria. The values of y obtained in this way are the equilibrium values y (eq.), i.e. those tabulated in reference books. When we want to distinguish these from the non-equilibrium, or dynamic, interfacial tensions, we call them the static Interfaclal tension. Under non-equilibrium conditions the mechanical interpretation remains valid, but the thermodynamical one becomes ill-defined. 

In water solution containing small particles (i.e., suspended solids or turbidity) and non-surface-active solutes, when air is bubbled through it, little or no particles will be removed by any adsorptive bubble separation process. This is because the particles have virtually no natural affinity for air bubbles and hence there is no adhesion when contact is made. This particular phenomena may be explained by the contact angle between a particle and an air bubble. Consider the case of the three-phase fine of contact between a smooth, rigid, solid phase, a liquid phase and a gas phase. The equilibrium contact angle can be expressed in terms of the average surface tensions (i.e., interfacial tensions, dyne/cm) of the liquid-gas solid-liquid (r j ), and solid-gas (r ) interfaces, by the well-known Young s equation ... 

Adamson (51) proposed a model for W/0 microemulsion formation in terms of a balance between Laplace pressure associated with the interfacial tension at the oil/water interface and the Donnan Osmotic pressure due to the total higher ionic concentration in the interior of aqueous droplets in oil phase. The microemulsion phase can exist in equilibrium with an essentially non-colloidal aqueous second phase provided there is an added electrolyte distributed between droplet s aqueous interior and the external aqueous medium. Both aqueous media contain some alcohol and the total ionic concentration inside the aqueous droplet exceeds that in the external aqueous phase. This model was further modified (52) for W/0 microemulsions to allow for the diffuse double layer in the interior of aqueous droplets. Levine and Robinson (52) proposed a relation governing the equilibrium of the droplet for 1-1 electrolyte, which was based on a balance between the surface tension of the film at the boundary in its charged state and the Maxwell electrostatic stress associated with the electric field in the internal diffuse double layer. 

Dynamic Methods In dynamic methods, determination of is based on the time evolution of a fluid element shape, from a non-equilibrium to an equilibrium state. The evolution is driven by the interfacial tension and, depending on the initial shape of the element, it can follow different dependencies. 

The thermodynamics and dynamics of interfacial layers have gained large interest in interfacial research. An accurate description of the thermodynamics of adsorption layers at liquid interfaces is the vital prerequisite for a quantitative understandings of the equilibrium or any non-equilibrium processes going on at the surface of liquids or at the interface between two liquids. The thermodynamic analysis of adsorption layers at liquid/fluid interfaces can provide the equation of state which expresses the surface pressure as the function of surface layer composition, and the adsorption isotherm, which determines the dependence of the adsorption of each dissolved component on their bulk concentrations. From these equations, the surface tension (pressure) isotherm can also be calculated and compared with experimental data. The description of experimental data by the Langmuir adsorption isotherm or the corresponding von Szyszkowski surface tension equation often shows significant deviations. These equations can be derived for a surface layer model where the molecules of the surfactant and the solvent from which the molecules adsorb obey two conditions ... 

In this chapter, we present systematised experimental results for equilibrium surface (in some cases interfacial) tensions for several homologous series of non-ionic and ionic surfactants. In contrast to what is generally believed to be trivial, we paid large attention to the selection of reliable experimental equilibrium data. Two main principles were employed here ... 

In these two equations r/ad, is the viscosity of the adsorbed polymer, >i2e the (non-equilibrium) excess interfacial tension and y,2 the (equilibrium) interfacia] tension, so that the quotient yi2j i2 describes the distance of the thermodynamic system from the equilibrium state. It is ea.sy to see that such behaviour is not at all in accordance with the idea of statistically distributed dispersed phases and non-interacting interfaces. 

Several mechanisms may be proposed to explain the process of spontaneous emulsification, all of which are related to the properties of the interfacial film. The first mechanism is due to interfacial turbulence that may occur as a result of mass transfer or by non-uniform adsorption of the surfactant molecules at the OAV interface. The interface shows unsteady motions - streams of one phase are ejected and penetrate into the second phase. This is illustrated in Figure 4.1(a) which shows the localized reduction in interfacial tension caused by non-uniform adsorption of surfactants or mass transfer of surfactants across the interface (5-7). When the two phases are not in chemical equilibrium, convection currents may be formed which transfers the liquid rich in surfactants towards the areas deficient in surfactants. These convection currents may give rise to... 

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