Equilibrium with surface tension

EQUILIBRIUM WITH GRAVITY OR CENTRIFUGAL FORCE, OSMOTIC EQUILIBRIUM, EQUILIBRIUM WITH SURFACE TENSION... 

SMALL IS INTERESTING EQUILIBRIUM WITH SURFACE TENSION 271... 

In the absence of polarization effects, if the material can flow, as in a drop, and if the stress is applied slowly enough, an equilibrium is established with surface tension. When any perturbation is applied to this system, vibrations are set up with frequencies given by... 

Assessment of wettability from the contact angle. A favourable case is when a contact angle 6 can be measured between the liquid and solid in equilibrium with the vapour, so that the Young-Duprd equation can be applied. As early as 1805, Young considered the possibility of such an equilibrium between surface tensions, but it was only in 1869 that Duprd put it in the well-known form of equation ... 

Similarly, for the case of a circular foam film of radius r formed in a capillary tube of radius R at equilibrium with a biconcave liquid meniscus with surface tension cr, contact angle dh and wetting angle [Pg.99]

Mercury porosimetry is governed in each pore by an equilibrium force/surface tension balance (the Washburn equation) that relates the diameter of a cylindrical pore to the pressure needed to force mercury into it. The pressured step-by-step invasion of a pore network is then controlled by a pattern of pone accessibly at each given pressure. Systematic penetration, starting from an empty network surrounded by mercury, can be readily performed. Results for the network in Fig. 5 are given in Fig. 6, showing both the penetration curve and the retraction curve. Stochastic pore networks implicitly predict hysteresis between penetration and retraction as well as a residual final entrapment of mercury. In Fig. 6, the final entrapment is about 45%, with much of the retained mercury entrapped in the larger pores [11]. More details of the pore-by-pore calculation have been published [4]. 

It was established that the surface was in local equilibrium the surface tension calculated for the system with a gradient was indeed the same as for the system in global equilibrium at a given temperature see Figure 2. The fluxes for heat and mass across the surface can be written as... 

This book is the first volume of a Treatise on Thermodynamics based on the methods of Gibbs and De Donder. It deals with the following topics fundamental theorems, homogeneous systems, heterogeneous systems, stability and moderation, equilibrium displacements and equilibrium transformations, solutions, azeotropy, and indifferent states. The second volume deals with surface tension and adsorption while the third and last will be concerned with irreversible phenomena. 

In the study of the structure, i.e. the ionic composition of the investigated molten electrolyte, the physico-chemical analysis, based on the results of measurements of phase equilibrium, density, surface tension, viscosity, and electric conductivity of melts, combined with X-ray phase analysis and IR, respectively, Raman spectroscopy of quenched melts, is used. In the last two measurements, it may be assumed that the high temperature composition is at least qualitatively conserved after quenching. In the investigation of the structure of the electrolytes, the so-called chemical approach is used. 

For a grain structure to be in metastable equilibrium the surface tensions must balance at every junction between the GBs. It is theoretically possible to construct a three-dimensional polycrystal in which the boundary tension forces balance at all faces and junctions, but in a real random polycrystalline aggregate there are always going to be boundaries with a net curvature in one direction and thus curved triple junctions. Consequently, a random grain structure is inherently unstable and, on heating at high temperatures, the unbalanced forces will cause the boundaries to migrate toward their center of curvature. 

Gas adsorption can also be used in systems with mesopores to measure pore size distributions. In this range of pore sizes, the surface energy of the pore walls causes a condensation of the gas (usually N2 in practice) at pressures where it would remain in the gas state if not confined an interface forms with surface tension y and the reduced vapour pressure on the convex side of the meniscus, as expected from the Laplace equation, explains the condensation at equilibrium. Equating the... 

For a pure liquid in eqmlibrium with its vapor, the number density and orientation of molecules at the surface will be different from that of bulk molecules (Fig. 8.2). When new surface is created, it is reasonable to assume that a finite amount of time will be required for new molecules to diffuse to the surface and to return the system to equilibrium. In that interim, as short as it may be, the measured surface tension of the system will be different from that of the system in equilibrium. The surface tension of such new surface is referred to as the dynamic surface tension. 

As Of — 2a, this result is in agreement with the result (1.15). For a spherical liquid drop, having only one surface, with surface tension a, the analysis using the equilibrium of a hemispherical section, or that using the Laplace-Young equation, gives an excess pressure inside the drop of... 

For the complete wetting case (S > 0), a thin film of dynamical origin (off-equilibrium) forms ahead of the apparent contact line of the drop. The formation of a precursor film avoids that viscous dissipation diverges near the (geometrically apparent) contact Une. Thus, macroscopic spreading of a droplet of a nonvolatile liquid (with surface tension yLv)> which wets the substrate, proceeds via the formation of such a thin precursor film ahead of the visible (apparent) contact line (Checco 2009). The thickness of this precursor film is truncated at a value given by ... 

Gibbs adsorption isotherm is valid in thermodynamic equilibrium. In equilibrium, the surface tension should not depend on the total surface area if new surface is produced, surfactant from the bulk diffuses to the surface and the same surface tension is estabhshed as before. If, however, the system is not given enough time to equilibrate, the local surface tension changes with an expansion or shrinkage of the geometric surface area A This is characterized with the surface elasticity E, also called surface dilatational modulus [684]. The surface elasticity is defined as... 

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

It is not uncommon for this situation to apply, that is, for a Gibbs mono-layer to be in only slow equilibrium with bulk liquid—see, for example. Figs. 11-15 and 11-21. This situation also holds, of course, for spread monolayers of insoluble substances, discussed in Chapter IV. The experimental procedure is illustrated in Fig. Ill-19, which shows that a portion of the surface is bounded by bars or floats, an opposing pair of which can be moved in and out in an oscillatory manner. The concomitant change in surface tension is followed by means of a Wilhelmy slide. Thus for dilute aqueous solutions of a methylcellu-... 

Since an actual crystal will be polyhedral in shape and may well expose faces of different surface tension, the question is what value of y and of r should be used. As noted in connection with Fig. VII-2, the Wulff theorem states that 7,/r,- is invariant for all faces of an equilibrium crystal. In Fig. VII-2, rio is the... 

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