DLVO Theory and Practice

The theory has been developed for two special cases, the interaction between parallel plates of infinite area and thickness, and the interaction between two spheres. The original calculations of dispersion forces employed a model due to Hamaker although more precise treatments now exist [7]. 

London-van der Waals dispersion forces V ) and the total interaction (Vf). (Adapted from Schramm [15]. Copyright (2003), reproduced with permission of John Wiley Sons, Inc) 

The same principle applies to emulsion droplets. Isaacs and Chow [19] illustrate the destabilization of a W/O emulsion by reducing the potential energy maximum 

In the case of a liquid film separating two bubbles in a foam, and where only the electrical and van der Waals forces are considered. 

For foams, decreases exponentially with increasing separation distance, and has a range about equal to k, while decreases inversely with the square of increasing separation distance. 

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In fact, the SFA was initially developed for practically probing the DLVO theory, and DLVO forces were successfully measured in electrolyte solutions and colloidal systems [4,22]. However, the applications of the apparatus were not restricted to this. Detailed and accurate information was obtained on thickness and refractive index profiles of thin films [6], simple liquid molecular structuring... 

The strong adverse influence of calcium ions on the stability of lyophobic suspensions is predicted by DLVO theory, and has been demonstrated with many types of simple soils. That calcium ions have an overwhelming effect on the redeposition of carbon soil onto cotton tends to support the idea that DLVO theory is a principal key in explaining detersive action. The redeposition of carbon onto cotton has been correlated quantitatively with the calcium ion content of the system, both in the presence and absence of surfactant (95). The adverse effect of calcium ions on wet soil removal in practical washing has also been well established (96). The effect of calcium in detergency cannot be explained solely, however, by its shrinking of... 

Application. To apply the DLVO theory in practice, several pieces of information have to be collected. Particle size (distribution) and shape can generally be experimentally determined. Hamaker constants often are to be found in the literature or can be calculated from Lifshits theory. The surface potential can be approximated by the zeta potential obtained in electrophoretic experiments. The ionic strength is generally known (or can be calculated) from the composition of the salt solution. All the other variables needed are generally tabulated in handbooks. This then allows calculation of V(h). To arrive at an aggregation rate, more information is needed this is discussed in Section 13.2. 

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... 

In a number of recent publications (1, 2) microcrystailine cellulose dispersions (MCC) have been used as models to study different aspects of the papermaking process, especially with regard to its stability. One of the central points in the well established DLVO theory of colloidal stability is the critical coagulation concentration (CCC). In practice, it represents the minimum salt concentration that causes rapid coagulation of a dispersion and is an intimate part of the theoretical framework of the DLVO theory (3). Kratohvil et al (A) have studied this aspect of the DLVO theory with MCC and given values for the CCC for many salts, cationic... 

Both secondary and primary minimum coagulation are observed in practice and the rate of coagulation is dependent on the height of the barrier. In general, coagulation into a primary minimum is difficult to reverse, whereas coagulation into a secondary minimum is often easily reversed, for example, by diluting the electrolyte. DLVO theory tells us... 

From the brief sketch of the Deijaguin, Landau, Verwey, Overbeek (DLVO)-theory the following three important practical conclusions, suitable for foams and emulsions, can be drawn ... 

The interaction forces and potentials between two charged surfaces in an electrolyte are fundamental to the analysis of colloidal systems and are associated with the formation of electrical double layers (EDLs) in vicinity of the solid surfaces. The charged surfaces typically interact across a solution that contains a reservoir of ions, as a consequence of the dissociation of the electrolyte that is already present. In colloid and interfacial sciences, the EDL interaction potential, coupled with the van der Waals interaction potential, leads to the fimdamental understanding of inter-siuface interaction mechanisms, based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1]. In practice, the considerable variations in the EDL interaction, brought about by the variations in electrolytic concentration of the dispersing medium, pH of the medium, and the siuface chemistry, lead to a diverse natiue of the colloidal behavior. A fundamental understanding of the physics of EDL interactions, therefore, is of prime importance in... 

An additional important prediction of the DLVO theory is that under certain conditions, a coUoid may undergo a form of reversible flocculation brought about by the existence of a so-called secondary minimum in the potential-energy curve. The existence of the secondary minimum has been confirmed experimentally and since it represents a potentially important theoretical and practical aspect of the DLVO theory, it will be discussed briefly below. 

The great value of the DLVO theory for the practicing colloid chemist, regardless of the exact nature of the work involved, is that it illustrates dramatically the importance of understanding the electrical properties of a colloid of potential interest, and the importance of understanding the effect of the ionic environment to which that colloid may be exposed. 

In contrast to microemulsions, ordinary emulsions are thermodynamieally unstable, but they can be stable in a practical sense if the energy barrier to flocculation is snfficiently high. As with other colloidal dispersions, this energy barrier may be electrical in nature if the drops are charged, if water is the continuous phase, and if the ionic strength is not too high (cf. the discussion of DLVO theory in Chapter 3). Typically, stabihty is provided by adsorbed surfactants and polymers. However, it can also stem from small solid particles that are not completely wet by either phase and thus accumulate at the drop surfaces (Aveyard et al., 2003). 

At Cei>Cei cr the double layer repulsion is practically suppressed and this is manifested by the fact that the film thickness no longer changes with increasing Cel above Cei.cr (Figure 6.7). Under these conditions, flei = 0, and the experimental results cannot be explained in the framework of DLVO theory only. If one assumes that the only contribution to n is there are very large deviations from the experimental data. This directly implies that there is an additional repulsive contribution to the disjoining pressure, namely flsf... 

Several models that depart partially or totally from DLVO have been proposed. One such model is the Spitzer dissociative electrical double layer theory (Spitzer 1984, 2003 and references therein). It essentially uses the linearized PB equation (which is consistent with Maxwellian electromagnetism) along with a coion exclusion boundary, which prevents ions of the same charge as the surface becomes too close in practice, this avoids negative concentrations, which will be predicted by the linear PB theory. It also includes a double layer association parameter a, which gives the fractions of counterions that are associated to the surface forming the Stern layer (Spitzer 1992). This theory, however, has not been further developed. 

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