Liquid-Fluid Interfaces

As pointed out in Chapter 2, it is common practice to describe a liquid surface as having an elastic skin that causes the liquid to assume a shape of minimum surface area, its final shape being determined by the strength of that skin relative to other external factors such as gravity. In the absence of gravity, or when suspended in another immiscible liquid of equal density, a hquid spontaneously assumes the shape of a sphere. In order to distort the sphere, work must be done on the hquid surface, increasing the total surface area and therefore the free energy of the system. When the external force is removed, the contractile skin then forces the drop to return to its equilibrium shape. 

While the picture of a skin like a baUoon on the surface of a hquid is easy to visualize and serves a useful educational purpose, it can be quite misleading, since there is no skin or tangential force as such at the surface of a pure hquid. It is actually an imbalance of forces on surface molecules puUing into the bulk hquid and out into the adjoining vapor phase that produces the apparent contractile skin effect. The forces involved are, of course, the same van der Waals interactions that account for the hquid state in general and for most physical interactions between atoms and molecules. Because the hquid state is of higher density than the vapor, surface molecules are pulled away from the surface and into the bulk hquid, causing the surface to contract spontane- 

FIGURE 8.1. The unbalanced, inward pull of bulk liquid molecules on those at the surface results in the phenomenon observed as surface tension. The drive to reduce the surface area to a minimum produces the observed tendency of liquids to form spherical drops (in the absence of gravity)—the geometry of minimum surface area for a given volume of material. 

TABLE 8.1. Typical Liquid Surface aud Interfadal Tensions at 20°C (niN m-1) 

Liquid Surface Tension Interfacial Tension versus Water 

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The mapping (7) introduces the unknown interface shape explicitly into the equation set and fixes the boundary shapes. The shape function h(x,t) is viewed as an auxiliary function determined by an added condition at the melt/crystal interface. The Gibbs-Thomson condition is distinguished as this condition. This approach is similar to methods used for liquid/fluid interface problems that include interfacial tension (30) and preserves the inherent accuracy of the finite element approximation to the field equation (27)... 

Third, turbulent transport is represented as a succession of simple laminar flows. If the boundary is a solid wall, then one considers that elements of liquid proceed short distances along the wall in laminar motion, after which they dissolve into the bulk and are replaced by other elements, and so on. The path length and initial velocity in the laminar motion are determined by dimensional scaling. For a liquid-fluid interface, a roll cell model is employed for turbulent motion as well as for interfacial turbulence. 

M. Turbulent Mass Transfer near a Liquid-Fluid Interface Based on the Turbulent Diffusivity Concept Turbulent Flow of a Liquid Film on a Vertical Wall... 

Two approaches can be used for the analysis of turbulent mass transfer near a liquid-fluid interface. One has the time-averaged convective diffusion equation as the starting point. For obtaining in that procedure an equation for... 

In contrast to a solid boundary, the damping of the turbulence at the liquid-fluid interface can also be affected by the surface tension a of the liquid. In other words, the state of turbulence near that interface is dependent not only on a characteristic velocity u0, on the viscosity r of the liquid and its density p, but also on the surface tension reciprocal time constant t which must be included for dimensional reasons in Eq. (350), is therefore expected to be a function of the four physical quantities ... 

Levich (L8), 1948 Considers theoretically mass transfer across liquid/fluid interfaces, with special treatment of gas absorption by turbulent liquid films. 

J. Lyklema, Fundamentals of Interface and Colloid Science III Liquid-Fluid Interfaces, Academic Press, San Diego, 2000. 

Excluded area approach for determination of 6 is based on the simple fact that the area occupied by particles in the monolayer containing more than one kind of species is inaccessible for all other components. For a monolayer at the liquid/fluid interface comprised of partially hydrophobic particles and an... 

Having laid down the physico-chemical basis of interface and colloid science in Volume 1, and then presented a systematic treatment of solid-fluid interfaces in Volume 11, we now conclude the interface science part of FICS with a treatment of liquid-fluid interfaces. Colloids will be discussed in Volumes fV and V. 

Interfacial and surface tensions are the most important chciracteristics of fluid-fluid interfaces and hardly any paper exists in which such tensions do not play a central role. In fact the entire present volume of FICS will be devoted to them. In chapter 2 a molecular Interpretation will be given. Chapters 3 and 4 deal extensively with liquid-fluid interfaces containing spread and adsorbed molecules, respectively and chapter 5 will treat three-phase contacts. For all these applications, measurement is a first and necessary element. Langmuir troughs, to be described in sec. 3.3.1, also involve a kind of interfacial tension determination since... 

Before giving a more systematic treatment we shall review and extend some of the thermodynamic and statistical-thermodynamic foundations laid down in Volume I. This framework serves to find relationships and to determine the limits of application, and can later be extended, for instance to include curvature phenomena. Given the scope of FIGS we shall restrict ourselves to liquid-fluid interfaces (i.e. interfaces for which tensions can be measured), emphasizing ambient conditions (say 0-100°C and atmospheric pressures) and systems of simple, low molecular mass molecules. For the same reason, we shall not consider... 

The answer is yes. In fact, in many colloidal systems containing large liquid-fluid Interfaces, such as foams and emulsions, there is abundemt evidence for the action of surface rheology in addition to the omnipresent rheology of the adjoining bulk phases. Let us give three illustrations. 

Possibly the most typical property of a liquid-fluid interface is that it cannot be autonomous it only exists as the boundary between two adjacent bulk fluids. Any movement or flow in an interface will cause some corresponding motion in the adjacent bulk phases and vice versa. To identify interfacial (excess) rheological properties, measured rheological properties of the system have to be divided into two parts, one attributable to the interface and one to the bulk. Such a division is always somewhat arbitrary and may depend on the experimental method used. 

The importance of SPM for the study of monolayers is that it allows the visualization of the structure and defects of transferred and self-assembled monolayers on solid substrates at length scales from <0.1 nm to > 10 pm. It is not fyet ) possible to image monolayers at liquid/fluid Interfaces with SPM techniques. However, it has already been shown that it is feasible to measure interaction forces between a colloidal particle and such interfaces in the presence and absence of monolayers ). 

This fifth chapter is, in a sense, already an application, because knowledge of liquid-fluid interfaces, the theme of this Volume, has been applied to systems also... 

Bockris Reddy (1970) describes the Butler-Volmer-equation as the "central equation of electrode kinetics . In equilibrium the adsorption and desorption fluxes of charges at the interface are equal. There are common principles for the kinetics of charge exchange at the polarisable mercury/water interface and the adsorption kinetics of charged surfactants at the liquid/fluid interface. Theoretical considerations about the electrostatic retardation for the adsorption kinetics of ions were first introduced by Dukhin et al. (1973). 

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 ... 

A review of various theoretical (molecular-statistical, scaling and thermodynamic) models which describe the adsorption of proteins at liquid/fluid interface was presented in [86]. Here the thermodynamic models derived to describe the protein adsorption are discussed briefly. The adsorption isotherm (2.27), and also the equation of state (2.26) accounting for the... 

A theoretical model is presented which describes the equilibrium behaviour of a surfactant mixture at liquid/fluid interfaces. The theory accounts for the nonideality of the surface layer (with respect to both enthalpy and entropy of mixing), thus comprising mixtures of surfactants with different molar areas. The theoretical results are in a good agreement with experimental data. The parameter describing the interaction between molecules of different species is quite close to the value calculated from additivity. 

During the process of adsorption of surfactant ions at a liquid-fluid interface the surface electric potential and charge density increase with time. This leads to the formation of an electric double layer inside the solution. The charged surface repels the new-coming surfactant molecules (Fig. 4.10), which results in an apparent deceleration of the adsorption process. On the other hand, the existence of the electric double layer (DEL in agreement with the nomination given in [2]) changes the amount of adsorbed surfaetant ions needed to reach equilibrium. This decreases the rate of adsorption so that the total rate is a counterbalance of various influences and it cannot be estimated a priori if a deceleration or an acceleration of the equilibration of an adsorption layer results. The most recent analysis of the different relaxation processes inherent in the adsorption process of ionic surfactants has been performed by Danov et al. [33]. In this work the inclusion of counterions into the Stem layer was performed for the first time. 

Surface-tension-driven flow concerns the actuation and control of fluid dynamic transport through a manipulation of the surface tension forces. The manipulation, in principle, can be hydrodynamic, thermal, chemical, electric, or optical in namre. It is also important to mention here that there must be a free surface or a liquid-fluid interface in order to have a surface-tension-driven flow. 

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