Disjoining pressure definition

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The quantity 11/ is a measure of the so-called disjoining action , introduced by Derjaguin in 1936 [12]. The disjoining pressure n [8] is determined by the long-range interaction forces between the surfaces of the film (normal to the both surfaces of tension there) and tends to zero when the film thickness is sufficiently large [5]. Eq. (3.15) proposes a more general definition of IT than that for the equilibrium case (Eq. (3.10))... 

The experimentally observed fact that a definite surfactant concentration is needed to overcome the barrier nmax of disjoining pressure deserves attention [323,332], This is one of the main conditions in the CBF/NBF transition which is not considered by the DLVO-theory (see Section 3.4.3). 

In the original definition of disjoining pressure by Deryaguin [11, 12], only the first two terms on the right-hand side of Equation (16.6) were considered. At low electrolyte concentrations, double layer repulsion predominates and can compensate the capillary pressure that is = P. This results in the formation of an equilibrium-free film which is usually referred to as the thick common film CF ( 50nm thickness). This equihbrium-metastable film persists until thermal or mechanical fluctuations cause mpture. The stability of the CF can be described in... 

The final group of equations focuses on the latter stages of adsorption, where the mesopores (ca. 2 nm to 50 nm in width according the lUPAC definition [9,10]) are filled. This is the region where capillary condensation occurs and the Kelvin equation is the simplest of these interpretations. There are numerous variations on the Kelvin equation that account for effects like multilayer adsorption prior to crqrillary condensation (i.e., BJH method [18]), disjoining pressure effects in die condensed liquid (i.e., DBdB method [19]), etc. 

Compared with the fundamental equation of a simple surface phase [5], Equation 4.148 contains an additional term, YVAdh, which takes into account the dependence of the film surface energy on the film thickness. Equation 4.148 provides an alternative thermodynamic definition of disjoining pressure ... 

In the original definition of disjoining pressure, Deryaguin [11, 12] only considered the first two terms on the right-hand side of Eq. (8.9). At low electrolyte... 

FIGURE 4.3 To the definition of the disjoining pressure, H(h), in a thin flat-parallel plate according to Derjaguin. 

The derivative -dAa h)/dh = is the force per unit cross-sectional area, also known as Derjaguin s disjoining pressure [4,5], Within the context of this definition, both Ao(/t) and W(fi) are positive in the case of a repulsion and negative in the case of an attraction. Molecular attraction forces prevail at long distances, while repulsive forces prevail at very short distances (the so-called Born repulsion). The principal theory that describes the interactions in a thin film is the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which focuses on the analysis of the competitive contribution of molecular (dispersion) attractive forces and electrostatic repulsion to the interaction between surfaces separated by a liquid film. 

FIGURE 2.9 Measurement of disjoining pressure isotherms of air-liquid-air foam films, (a) Porous frit film holder located inside hermetically sealed cell subject to applied gas pressure, Pg. Bulk liquid pressure is Pl (= Pi + PhS hyd text for definition of terms)... 

The disjoining pressure theory by Churaev et al. [6] begins with the definition of the disjoining pressure, n. There is a quantity that is a function of the coverage, F, or adsorbed film thickness , t, defined by the equation (for the theory t and F can be used interchangeably)... 

As noted earlier in this chapter, there is definite relationship between the disjoining pressure theory of adsorption and the x theory. In this section, some thermodynamic relationships for the spreading pressure are derived. It is questionable at this point how useful these relationships will be. They may be useful in extending the theory into the solution chemistry since these relationships are important in that area of research. 

We refer to such capillaries as thick capillaries. In the case of aqueous solutions, Y 70 dyn/cm, 10 erg> d hence, 1 lO cm 10 cm. Otherwise, the capillary is referred to as a thin capillary, that is, the capillary is thin if its thickness H is in the range t H < // , where t is the radius of the disjoining pressure action. According to the definition of thin capillaries, these capillaries are still big enough when compared with the radius of the action of surface forces, tj. If the capillary radius is compared with the radius of action of surface forces, t ... 

FIGURE 2.15 Determining the droplet height, H. Upper part disjoining pressure isotherm lower part shape of function L h) (see definition given by Equation 2.58). 

The latter equation can be rewritten using the definition of the effective disjoining pressure given by Eqnation 2.245 as... 

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