Electrostatic disjoining pressure

FIGURE 4.6. The interface profile (relative to the interface position at r = 0) for an alkane drop in water with a silica probe at an axial separation distance Do of 6.5 and 4.5 nm. The dots denote the coiresponding disjoining pressure value at the marked radial distance. The inset is the disjoining pressure (electrostatic and van der Waals) for a water/aUtane/silica system with a univalent (non-surface-active) electrolyte ( " = 30 nm ijfo = 50 mV). Reprinted from Ref. [67], with permission from Elsevier. 

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] ... 

Disjoining pressure was attributed in Ref 54 to the combined effect of van der Waals attraction and long-range electrostatic repulsion between similarly charged membrane surfaces. 

Figure 4. A conjoining/disjoining pressure isotherm for the constant- potential and weak overlap electrostatic model.

ENORDET AOS 1618) in an 81- fjtm permeability sandpack. Using the parameters listed and the constant- charge electrostatic model for the conjoining/disjoining pressure isotherm, the data are rescaled A ... 

The disjoining pressure vs. thickness isotherms of thin liquid films (TFB) were measured between hexadecane droplets stabilized by 0.1 wt% of -casein. The profiles obey classical electrostatic behavior. Figure 2.20a shows the experimentally obtained rt(/i) isotherm (dots) and the best fit using electrostatic standard equations. The Debye length was calculated from the electrolyte concentration using Eq. (2.11). The only free parameter was the surface potential, which was found to be —30 mV. It agrees fairly well with the surface potential deduced from electrophoretic measurements for jS-casein-covered particles (—30 to —36 mV). 

As pointed out earlier, the disjoining pressure is the sum of interdroplet forces due to van der Waals, electrostatic and steric interactions. Detailed discussion of the nature of these interactions and their effect on the disjoining pressure can be found elsewhere (3,8). Only the final expressions for the contributions of different interactions to the disjoining pressure are given below. 

Interfacial Forces. Neighboring bubbles in a foam interact through a variely of forces which depend on the composition and thickness of liquid between them, and on the physical chemistry of their liquid—vapor interfaces. For a foam to be relatively stable, Ihe net interaction must be sufficiently repulsive at short distances to maintain a significant layer of liquid in between neighboring bubbles, Interfacial forces include ihe van der Waals inieracliun. the electrostatic double layer imeruclion. and disjoining pressure. 

Figure 5.15 shows an example of a disjoining pressure isotherm in which the steric force contributions have been superimposed on the classical DLVO force contributions. It can be seen that this creates two regions for meta-stable foam films. One region is the thick, common black film region, with film thicknesses of approximately 50 nm or so. The other region is the thin, Newton black film region, with film thicknesses of approximately 4 nm. While the common black films are mostly stabilized by electrostatic forces, the Newton black films are at least partly stabilized by the steric forces. 

Figure 5.15 Illustration of a disjoining pressure isotherm (17T) that includes contributions from electrostatic (17E), dispersion (77d), and steric (77s) forces.

The thin liquid films bounded by gas on one side and by oil on the other, denoted air/water/oil are referred to as pseudoemulsion films [301], They are important because the pseudoemulsion film can be metastable in a dynamic system even when the thermodynamic entering coefficient is greater than zero. Several groups [301,331,342] have interpreted foam destabilization by oils in terms of pseudoemulsion film stabilities [114]. This is done based on disjoining pressures in the films, which may be measured experimentally [330] or calculated from electrostatic and dispersion forces [331], The pseudoemulsion model has been applied to both bulk foams and to foams flowing in porous media. 

In the aqueous washing liquor the fabric surface and the pigment soil are charged negatively due to the adsorption of OH- ions and anionic surfactants and this leads to an electrostatic repulsion. In addition to this effect, a disjoining pressure occurs in the adsorbed... 

On the basis of the disjoining pressure (44), an electrostatic part of the pair interaction between colloidal particles can be computed as... 

Equations (70)-(73) define the unary and binary electrostatic potentials, that allows to determine the disjoining pressure given by Eq. (44). In the approximation chosen this latter reads as... 

Films of a relatively smaller initial thickness ( 500 nm) can be formed from aqueous electrolyte solutions at low concentrations. They can be also produced either in the absence of a surfactant or in its presence at low concentrations, as long as there acts the electrostatic component of disjoining pressure [53,73],... 

The simplest explanation of film rupture involves reaching a thermodynamically unstable state [20]. A typical example of thermodynamically unstable systems are foam films in which the disjoining pressure obeys Hamaker s relation. Such are films from some aqueous surfactant solutions containing sufficient amount of an electrolyte to suppress the electrostatic component of disjoining pressure as well as films from non-aqueous solutions (aniline, chlorobenzene) [e.g. 80],... 

The DLVO-theory considers only the molecular van der Waals and electrostatic interactions. A complete analysis of the theory can be found in several monographs [e.g. 3-6] where original and summarised data about the different components of disjoining pressure in thin liquid films, including in foam films are compiled. 

According to DLVO-theory the disjoining pressure in thick films is considered as a sum of the electrostatic and van der Waals component... 

An approximated expression of the electrostatic component of disjoining pressure can be derived from Eq. (3.71) at small values of [Pg.126]

The relation between film thickness h and electrolyte concentration Cei obeys the DLVO-theory of electrostatic disjoining pressure (see Eqs. (3.71) and (3.72)). At film equilibrium and known h and Cei it is possible to calculate at the solution/air interface [95,155-157,169,170-173], Hence, a new area in the study of electrosurface forces at this interface has been developed on the basis of determining potential. 

For the study of surface forces acting in foam films, including in black films, another type of isotherm proves to be most informative, i.e. the dependence of film thickness h on electrolyte concentration Cei at Cs = const, pa = const and f = const. This h(Cei) dependence allows to distinguish clearly the action of electrostatic disjoining pressure and to find the electrolyte concentration at which the CBF/NBF transition occurs. 

The results obtained indicate that at (po]Cr only NBF form. These studies prove that the barrier in the TT(/i) isotherm, impeding the transition of one film type to another, is mainly determined by the electrostatic component of disjoining pressure, Tlf(. It should not be forgotten that if there exist other components of disjoining pressure, this estimation is no more valid. A CBF/NBF transition could not even be realised if there is another positive component, such as steric one in polymer films. 

The analysis of the above techniques (Section 3.4.2.2) developed to estimate the conditions under which stable CBF and NBF exist, and reveals the equilibrium character of the transition between them and the particular features of the two types of black films. Furthermore the difference between the techniques of investigation as well as the difference between their intrinsic characteristics proves to be a valuable source of information of these thinnest liquid formations. The transition theory of microscopic films evidences the existence of metastable black films. Due to the deformation of the diffuse electric layer of the CBF, the electrostatic component of disjoining pressure 1 L( appears and when it becomes equal to the capillary pressure plus Ylvw, the film is in equilibrium (in the case of DLVO-forces). As it is shown in Section 3.4.2.3, CBF exhibit several deviations from the DLVO-theory. The experimentally obtained value of ntheoretically calculated. This is valid also for the experimental dependence CeiiCr(r). Systematic divergences from the DLVO-theory are found also for the h(CeiXr) dependence of NaDoS microscopic films at thickness less than 20 nm. 

The fact that the disjoining pressure in NBF does not contain an electrostatic component as well as the lack of a free aqueous core in the film structure allows to use the bilayer lattice model to explain the stability of NBF. This model accounts for the interaction between first neighbour molecules (see Section 3.4.4). 

At higher electrolyte concentrations in the NaDoS solution, e.g. 0.35 mol dm-3 (curve 2, Fig. 3.77), formation of black spots is observed at higher surfactant concentrations which correspond to closer packing of the adsorption layer. Probably with the increase in electrolyte concentration the stabilizing ability of the electrostatic component of disjoining pressure decreases. 

The rupture of NBF (bilayers) in which there is no electrostatic disjoining pressure cannot occur by the wave mechanism. 

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