DLVO theory

Nowadays, it is rather common to extend the DLVO theory with the Bom repulsion or hardcore interaction, which is a short-ranging repulsion that excludes the interpenetration of approaching surfaces (Ruckenstein and Prieve 1976 Lyklema 1991, p. 4.5). The calculation is usually based on a power-law approach for the Bom repulsion of atoms and molecules as used in the Lennard-Jones (12,6) potential (e.g. Feke et al. 1984). 

The shape of the function Vi h) for the total interaction energy depends on the Hamaker function the difluse layer potentials t/ j (approximated with the 

In the 1940s, a scientific theory describing the delicate balance of colloidal dispersion and aggregation was developed by Derjaguin and Landau and by Verwey and Overbeek. The theory is usually called the DLVO theory for short. In this theoretical description, a potential V is used to describe the different interactions between colloidal particles in solution and we can simply write 

The predictions of DLVO theory describe the behavior of a simplified colloidal solution and should predict if a colloid will aggregate or remain suspended in a given solvent however, in real systems this simplified model is not often accurate. For example, these models do account for the effects of steric interactions between particles or excluded volume effects. These effects are discussed in the following sections. Other factors not considered include the effects of water structure, particle hydrophobicity, and any specific ionic arrangements around the particles. DLVO theory is a good starting point to think about the behavior of colloidal solutions. 

FIGURE 5.4 An example of a DLVO curve is shown in green as the sum of van der Waals attraction and the electrostatic repulsive forces. In some cases, the green curve can dip below the zero potential line, resulting in a second stable minimum at which particles can be weakly bound to each other. 

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Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Fig. XrV-6. (a) The total interaction energy determined from DLVO theory for n-hexadecane drops for a constant ionic strength - 5.0 nm) at various emulsion pH (b) enlargement of the secondary minimum region of (a). (From Ref. 39.)...

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

The inset in Figure XIV-6 shows the coalescence time tc for the droplets for the pH corresponding to each DLVO curve. Does DLVO theory adequately explain the variation of tc with pH What additional factors may play a role ... 

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

DLVO Theory. The overall stabiUty of a particle dispersion depends on the sum of the attractive and repulsive forces as a function of the distance separating the particles. DLVO theory, named for Derjaguin and Landau (11) and Verwey and Overbeek (12), encompasses van der Waals attraction and electrostatic repulsion between particles, but does not consider steric stabilization. The net energy, AGp between two particles at a given distance is the sum of the repulsive and attractive forces ... 

A summary of the effects of basic coUoid variables predicted by DLVO theory is presented in Table 3. 

The theory has certain practical limitations. It is useful for o/w (od-in-water) emulsions but for w/o (water-in-oil) systems DLVO theory must be appHed with extreme caution (16). The essential use of the DLVO theory for emulsion technology Hes in its abdity to relate the stabdity of an o/w emulsion to the salt content of the continuous phase. In brief, the theory says that electric double-layer repulsion will stabdize an emulsion, when the electrolyte concentration in the continuous phase is less than a certain value. 

The Yukawa potential is of interest in another connection. According to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, colloidal... 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

The DLVO theory [88,89], a landmark in the study of colloids, interprets stability as dependent on the competition between the long-range repulsion forces of similarly charged... 

At short interparticle distances, the van der Walls forces show that two metallic particles will be mutually attracted. In the absence of repulsive forces opposed to the van der Walls forces the colloidal metal particles will aggregate. Consequently, the use of a protective agent able to induce a repulsive force opposed to the van der Walls forces is necessary to provide stable nanoparticles in solution. The general stabihzation mechanisms of colloidal materials have been described in Derjaguin-Landau-Verway-Overbeck (DLVO) theory. [40,41] Stabilization of colloids is usually discussed... 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

Fig. 1 Illustration of the DLVO theory interaction of two charged particles as a function of the interparticle distance (attractive energy curve, VA, repulsive energy curve, VR and net or total potential energy curve, Vj).

Comparison of the proposed dynamic stability theory for the critical capillary pressure shows acceptable agreement to experimental data on 100-/im permeability sandpacks at reservoir rates and with a commercial a-olefin sulfonate surfactant. The importance of the conjoining/disjoining pressure isotherm and its implications on surfactant formulation (i.e., chemical structure, concentration, and physical properties) is discussed in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of classic colloid science. 

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

The DLVO theory provides a qualitative explanation of the ionic strength and solution pH effects on particle release. 

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