Surface force disjoining pressure

The emulsion drops in floes and creams are separated with thin liquid films, whose rupture leads to eoalescence and phase separation. At equilibrium the area of the films and their contact angle are determined by the surface forces (disjoining pressure) acting across the films (Sec. lll.A.l). Several ways of breakage of these emulsion films have been established capillary-wave meehanism, pore-nucle-ation mechanism, solute-transport meehanism, barrier mechanism, etc. (Sec. 111.A.2). 

As already mentioned in Chapter 1, aU solid surfaces in contact with a volatile or nonvolatile liquid at equilibrium are covered by a thin liquid film. The thickness of this equilibrium film is determined by the action of surface forces (disjoining pressure isotherm). That is, the choice of the reference state is uniquely determined in order to consider the vicinity of the three-phase contact line at the equilibrium state of a bulk liquid in contact with a solid substrate the reference state is the state of solid substrate covered with the equilibrium liquid film That is why a reference state that has a plane parallel film with the lowest possible equilibrium thickness (that is, a-flhns introduced in Section 2.1), which corresponds to the vapor pressure p in the ambient air, is selected. In this section, two-dimensional equilibrium menisci in a flat chamber with a half-width H or two-dimensional equilibrium liquid drops are considered for simplicity. Extension of the derivation, in the following text, to axial symmetry is briefly discussed at the end of this section. 

Each of the constituent terms of Equation 11.1 represents a distinct force field. From left to right the terms represent the contributions of viscous forces, surface tension forces due to the curvature at the free interface (Laplace pressure), and the excess intermolecular forces (disjoining pressure) respectively [37, 38, 65, 67]. The viscous force in no way influences the stability as it merely controls the dynamics of the system. For tangentially immobile films, the prefactor of the viscous term 3 is replaced by 12 [38, 65]. The Laplace pressure arising from surface tension has a stabilizing influence, as already discussed. Thus, the only term that may induce an instability in the system is the one representing the excess intermolecular interactions [37,38,65]. 

In a real liqnid, the nature of the disjoining pressure can be a complicated function of the distance, due to the simultaneous coutributiou of several types of forces [1,4-6], For two bodies with flat surfaces separated by a distance z, the van der Waals interaction, which varies as z (or z, if one considers retardation) for single atoms and molecules, gives rise to a power law of the form ... 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

Capillary phenomena are due to the curvature of liquid surfaces. To maintain a curved surface, a force is needed. In Eq. (8), this force is related to the second term in the integral. The so-called Laplace pressure due to the force to maintain the curved surface can be expressed as, Pl = 2-yIr, where r is the curvature radius. The combination of the capillary effects and disjoining pressure can make a liquid film climb a wall. 

The concept of disjoining pressure is not in contradiction to the formalism of surface forces. It is sometimes more useful to think in terms of disjoining pressure. For example, if... 

All techniques mentioned so far are mainly used to study the force between solid surfaces. In many applications one is interested in the disjoining pressure between liquid-liquid or liquid-gas interfaces, such as those found in foams and emulsions. One such technique is described in Section 12.5.3. 

For systems which spread spontaneously it is well-known that a spreading drop forms a thin (< 0.1 pm) primary or precursor film [279-282], Its thickness and extension are determined by surface forces. In the precursor film, energy is dissipated by viscous friction. The liquid transport in the precursor film is driven by the disjoining pressure in the precursor film which sucks liquid from the wedge of the drop. 

The force between neutral surfaces (with a surface dipole density) depends on the electrolyte concentrations, as shown in Fig. 3b, particularly at large separations. However, at small separations, the interaction appears to be well described by an exponential with a decay length AH. For neutral lipid bilayers, the equilibrium is reached at a distance of about 20 A, at which the attractive van der Waals interaction balances the repulsive hydration and thermal undulation interactions [43], The experiments regarding the forces between neutral lipid bilayers [11] sample the interactions at separations smaller than 20 A, for which the dependence on ionic strength is much weaker. By adding to the total pressure a typical van der Waals disjoining pressure [12] ... 

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 above equations describe a simple mechanical model of the film, its adjacent transition zone and the bulk meniscus. According to this model the force quantities, lAytosd and 2Ayf, are applied only on the basic surface of tension. The disjoining pressure and the capillary pressure act always and everywhere normally to the phase surfaces, identified as surfaces of tension. There are other two A) in0 force components related to the two phase surfaces. These components counterbalance each other at any point of the basic surface of tension. Eq. (3.33) coincides formally with the force balance condition of de Feijter and Vrij [22] if one would write... 

From a practical point of view the dynamic method is fast and relatively simple. It has the intrinsic advantage over any equilibrium technique that disjoining pressure isotherms with dYl/dh > 0 can be monitored. It has been successfully applied to measure van der Waals attraction and retardation effects in foam films [80,235], The dynamic method has been applied to foam films of liposomal suspensions [234] and quite recently surface forces of oscillating nature were monitored in foam [235] and pseudoemulsion [236] films. 

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