At low electrolyte concentration

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

Density gradients to stabilize flow have been employed by Philpot IT> Yin.s. Faraday Soc., 36, 38 (1940)] and Mel [ j. Phys. Chem., 31,559 (1959)]. Mel s Staflo apparatus [J. Phys. Chem., 31, 559 (1959)] has liquid flow in the horizontal direction, with layers of increasing density downward produced by sucrose concentrations increasing to 7.5 percent. The solute mixture to be separated is introduced in one such layer. Operation at low electrolyte concentrations, low voltage gradients, and low flow rates presents no cooling problem. 

The zero-charge potential is determined by a number of methods (see Section 4.4). A general procedure is the determination of the differential capacity minimum which, at low electrolyte concentration, coincides with Epzc (Section 4.3.1). With liquid metals (Hg, Ga, amalgams, metals in melts) Epzc is directly found from the electrocapillary curve. 

According to Eq. (4.3.13) the differential capacity of the diffuse layer Cd has a minimum at 2 = 0, i.e. at E = Epzc. It follows from Eq. (4.3.1) and Fig. 4.5 that the differential capacity of the diffuse layer Cd has a significant effect on the value of the total differential capacity C at low electrolyte concentrations. Under these conditions, a capacity minimum appears on the experimentally measured C-E curve at E — Epzc. The value of Epzc can thus be determined from the minimum of C at low electrolyte concentrations (millimolar or lower). 

This paper discusses the use of specific ion electrodes for determining the anion-free water. This method is simpler and more accurate at low electrolyte concentration than ordinary chemical methods. It is potentially useful for oilfield application and laboratory automation. The mobility of this water is also examined under forced conditions with pressure gradients. It is expected that by using the methods developed in this paper, one may obtain a better understanding of the clay properties. 

Mobility of The Anion-Free Water. It is well known that water in the electrical double layer is under a field strength of 10 -10 V/cm and that the water has low dielectric constants (36). Since anion-free water is thought to be the water in the electrical double layer between the clay and the bulk solution, at high electrolyte concentrations, the double layer is compressed therefore, the water inside is likely quite immobile. At low electrolyte concentrations, the electrical double layer is more diffuse, the anion-free water is expected to be less immobile. Since the evaluation of the shaly formation properties requires the knowledge of the immobile water, experiments were conducted to find out the conditions for the anion-free water to become mobile. 

At high electrolyte concentrations of the soil solution, the double layer is compressed so that clay remains flocculated. A decrease in ion concentration, e.g. as a result of dilution by percolating rain water, can result in dispersion of clay and collapse of aggregates. If the exchange complex is dominated by polyvalent ions, the double layer may remain narrow even at low electrolyte concentrations and consequently aggregates remain intact (FAO, 2001). 

At low electrolyte concentrations, up to about a 10 3 M solution, the Gouy-Chapman theory agrees quite well with experimental values of... 

Of particular interest for chemical transport into a predominantly smectite medium is the shrink-swell property of the clay material. The swelling properties of smectites are explained by two concepts. The first one, developed by Sposito (1973), shows that smectite swelling is caused by the hydration and mobility of the cations, which in turn balance the negative charge of the layer silicates. The second concept, presented by Low (1981), emphasizes the direct interaction of water molecules with the silicate surface. Both viewpoints fit the common observation that smectite swells in a high-hydration environment and at low electrolyte concentrations and shrinks when water is lost and salt is added to the bulk solution. 

An experimental study was performed to determine the applicability of the theory. Oil-in-water (o/w) emulsions, stabilised with anionic surfactants, were prepared, with known quantities of added electrolyte, and were creamed by either gravitation or centrifugation. The results can be summarised as follows at low electrolyte concentrations, where h would have a finite value, <(> was less than 0.74. Over a range of concentrations, where it was assumed that both 0 and h were negligible, = 0.74 ( 0.02). The emulsions were found to be polydis-perse, so this did not appear to affect the volume fraction to a great extent. In addition, < > was found to be independent of the method of cream formation. 

Equation (6) is valid only if it is justly assumed that the equilibrium values of qM and E are established infinitely quickly. This is not the case at low electrolyte concentrations since then the diffusion of the ions composing the double-layer becomes a rate-determining factor. In other words, mass transport complicates the charging process. For practical reasons, studies of electrode kinetics are usually made in well-conducting solutions, so that this effect can be ignored. 

The net result is shown schematically in Figure 16. Instead of the array of surface charges leading to a well defined surface charge density and surface potential there is now a distribution of charges in space which contribute to the electrical double layer surrounding the particle. At low electrolyte concentrations the latter will extend into the space beyond the polyelectrolyte... 

The interpretation of the behaviour of PBT is more subtle. Overall mass changes upon total PBT oxidation / reduction are similar to the counter ion ("dopant") molar mass, for example FAM/Q = 93 g mol"1 in 0.01-0.1 mol dm 3 Et4N+BF47CH3CN compared to mgp — = 87 g mol"1. These results apparently imply permselectivity with little or fto solvent transfer at low electrolyte concentration, and permselectivity failure at high electrolyte concentration. As we show in the next section, this apparent permselectivity is entirely fortuitous, and results from a compensating combination of mobile species transfers. The message here is that a combination of thermodynamic and kinetic data is required to unequivocally attribute the mass change to the relevant species transfers. 

The change in decomposition mechanism, i.e. the nature of the mobile species, on passing from one solvent to another solvent can be interpreted on the basis of reaction (1) which we proposed to explain the pH-dependence of the results in aqueous medium at low electrolyte concentration (Lingier, 1987). 

The last approximate expression shows that, at low electrolyte concentrations (X - °° ), the total adsorption is positive when the potential well is sufficiently deep (A=exp( W, /kT) >2). In this case, the surface tension decreases almost linearly with increasing electrolyte concentration. However, the slope does not remain constant, its magnitude decreasing with increasing electrolyte concentration, because of the surface potential generated by the asymmetric distribution of electrolyte ions. The slope dy/dc becomes positive at concentrations higher than a critical electrolyte concentration, obtained from ... 

Karraker and Radke [18] proposed another explanation of this minimum. At low electrolyte concentrations, the positive adsorption of OH leads to a decrease of surface tension, while at sufficiently high ionic strengths, the depletion of Cl", repelled by the negative surface charge as well as by the van der Waals and image forces, becomes dominant and the surface tension increases. 

Fig. 8. The change in surface tension at low electrolyte concentrations (the Jones-Ray effect). Circles Experimental data from Ref. [33]. Curve (1) predicted surface tension for the simple model which accounts for OH adsorption and only ion hydration effects for electrolyte ions, within the Poisson-Boltzmann approach. Curve (2) predicted surface tension when image forces are also included in the model. As noted in Section 3, the image forces cannot be neglected at concentration lower than 0.01 M.

The same simple model can also explain the Jones-Ray effect (a minimum of the surface tension at a concentration of approximately 1.0X10 3 KC1 [33]). At low electrolyte concentrations, the accumulation of the electrolyte ions due to the surface charge (as predicted by the Poisson-Boltzmann equation) overwhelms all the other contribution to the surface adsorptions. Consequently, the interfacial tension first decreases with increasing electrolyte concentration. However, the Poisson-Boltzmann adsorption thickness decays strongly with increasing electrolyte concentration, and the repulsion of ions by the interface (due to image forces, change in ion hydration and van der Waals interactions) becomes dominant, and the slope of the interfacial tension becomes positive. 

---