Surface tension description

If the surface tension is a fiinction of position, then there is an additional temi, da/dx, to the right-hand side in the last equation. From the above description it can be shown drat the equation of motion for the Fourier component of the broken synnnetry variable is... 

Where surface-active agents are present, the notion of surface tension and the description of the phenomena become more complex. As fluid flows past a circulating drop (bubble), fresh surface is created continuously at the nose of the drop. This fresh surface can have a different concentration of agent, hence a different surface tension, from the surface further downstream that was created earlier. Neither of these values need equal the surface tension developed in a static, equiUbrium situation. A proper description of the flow under these circumstances involves additional dimensionless groups related to the concentrations and diffusivities of the surface-active agents. 

The simplest technique introduced by Young as early as 1805 [18] is the measurement of the contact angle as a measure of surface tension and surface energy [1,19, 20,21], In many cases this gives an indication of surface composition and can be used to observe changes in composition, structure and/or roughness at the surface during a particular surface treatment. A quantitative description or distinction between different parameters is hardly possible in most cases. 

This description of the nonpolar contribution to the free energy has been extensively used in biophysical applications [72-75]. In practice, the surface tension 7V is usually obtained from experimental transfer free energies of small organic molecules... 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

The choice of the size parameter d is somewhat ambiguous since even the relative values of d vary somewhat between solid, liquid, and gaseous salts because of the influence of interactions other than those represented by Eq. (7). For the case of a change of phase or for the description of phenomena where the environment of the ions changes drastically (as in the discussions of vapor pressure and surface tension), the influence of these other interactions is relatively large and other characteristic thermodynamic parameters (such as the melting temperature), which at least partly reflect these other interactions, should lead to more realistic relationships. Where there is no drastic change... 

These ten interfacial parameters give a very complete description of the energetics of a detergency system. Further surface tension variables for a fluid-air or solid-air interface will also be used to evaluate these ten interfacial parameters. The remainder of this section will explore their evaluation. 

Skeggs innovative step, the introduction of air bubbles into the flowing stream, attempted to minimize the time taken for a steady-state condition to be reached in the detector. The definitive description of dispersion in segmented streams (Snyder [37]) showed a complex relationship between internal diameter, liquid flow rate, segmentation frequency, residence time in the flow system, viscosity of the hquid and surface tension. 

The surface entropy of liquids is given by (-d y/dT). This means that the entropy is positive at higher temperatures. The rate of decrease of surface tension with temperature is found to be different for different liquids (Appendix A), which supports the foregoing description of liquids. This observation explains the molecular description of surface tension. 

In the following pages a brief description of the more important methods employed for the accurate determination of the surface tensions of liquids is given. 

The equivalence of the force and energy description of surface tension and surface energy... 

The approximation that limits this analysis of capillary rise originates from neglecting the weight of the liquid in the crown of the curved meniscus. We see in Section 6.8b that the height of capillary rise can be related to surface tension without making this approximation, although the connection is somewhat unwieldy. A more detailed description of the experimental aspects of the capillary rise method can be obtained from advanced textbooks (e.g., Adamson 1990). 

Throughout this chapter we have dealt with surface tension from a phenomenological point of view almost exclusively. From fundamental perspective, however, descriptions from a molecular perspective are often more illuminating than descriptions of phenomena alone. In condensed phases, in which interactions involve many molecules, rigorous derivations based on the cumulative behavior of individual molecules are extremely difficult. We shall not attempt to review any of the efforts directed along these lines for surface tension. Instead, we consider the various types of intermolecular forces that exist and interpret 7 for any interface as the summation of contributions arising from the various types of interactions that operate in the materials forming the interface. 

Beside the theoretically derived Gibbs adsorption isotherm, a large number of models have been developed that empirically describe a relationship between the interfacial coverage, the surface tension, and the surfactant concentration in the bulk phase. These adsorption isotherms are known under the names of the authors that first described them—i.e., the Fangmuir, Frumkin, or Volmer isotherms. A complete mathematical description of these isotherms is beyond the scope of this unit and the reader is encouraged to consult the appropriate literature instead (e.g., Dukhin et al., 1995). 

For pure liquids the description becomes much simpler. We start by asking, how is the surface tension related to the surface excess quantities, in particular to the internal surface energy and the surface entropy ... 

At low surface excess, Gibbs monolayers can often be described as two-dimensional gases. This description is based on the observation that, at low concentration, the surface tension decreases linearly with the concentration of the added amphiphile c ... 

Here, Pc is the capillary pressure which is a function of s, permeability K, and surface tension. Equations (5.33-5.45) along with Navier-Stokes Equations and species equations constitute a fully 3-D description of a PEMFC. When the membrane is replaced by a solid, non porous electrolyte conducting oxide ions instead of protons, the above model essentially becomes a model for SOFCs. In an SOFC, of course, there is no condensation /zphase = 0 and Equations (5.43-5.45) would not be necessary. 

Equations (1.72)—(1.78) provide relationships between characteristic parameters of the interface (qM, qs, Cd, Cu and surface concentrations of ionic species) and macroscopic magnitudes such as the surface tension, the applied potential and the bulk concentration of electrolyte. However, they provide no information about the double-layer structure. Next, some theoretical models about the structural and geometrical description of the electrical double layer are discussed briefly. 

A new method of surface tension determination has been developed which is continuous, automated, compatible with computer data acquisition systems, and capable of monitoring flowing process streams. The method is a variant of the well-known maximum bubble pressure technique. To illustrate the principles, we will describe the simplest initial configuration of the instrument here. Further details and a description of a refined version of the instrument will be reported later. 

Herein, cl and cG are parameters responding to the capillary forces which has an effect between the solid and gas phase and between the liquid and gas phase, respectively. They depend on the form and nature of the pores and of the surface tensions between the phases. This new approach to the interaction forces allows the description of capillary motion in porous solids, see de Boer Didwania [6]. 

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