Bulk Dispersions

Electrolytically evolved gas bubbles affect three components of the cell voltage and change the macro- and microscopic current distributions in electrolyzers. Dispersed in the bulk electrolyte, they increase ohmic losses in the cell and, if nonuniformly distributed in the direction parallel to the electrode, they deflect current from regions where they are more concentrated to regions of lower void fraction. Bubbles attached to or located very near the electrodes likewise present ohmic resistance, and also, by making the microscopic current distribution nonuniform, increase the effective current density on the electrode, which adds to the electrode kinetic polarization. Evolution of gas bubbles stirs the electrolyte and thus reduces the supersaturation of product gas at the electrode, thereby lowering the concentration polarization of the electrode. Thus electrolytically evolved gas bubbles affect the electrolyte conductivity, electrode current distribution, and concentration overpotential and the effects depend on the location of the bubbles in the cell. Discussed in this section are the conductivity of bulk dispersions and the electrical effects of bubbles attached to or very near the electrode. Readers interested in the effect of bubbles dispersed in the bulk on the macroscopic current distribution in electrolyzers should see a recent review of Vogt.31 

Gas bubbles dispersed in the bulk electrolyte, common in industrial electrolysis, are essentially randomly distributed spheres having zero conductivity. There are a number of different approaches to describing the effect of such dispersions on the overall conductivity. Simplification of the problem is possible when the dispersed phase is dilute or when a limited range of void fraction is considered. Some writers discuss media in which the dispersed phase occupies well-defined lattice positions while others treat random dispersions. One may also consider spheres of equal size or dispersions containing a distribution of sizes. I classify the approaches by the type of dispersion they aim to describe and compare the theory for these classes to appropriate experimental data. 

O Brien42 also calculated the conductivity function to O(/2) by relating the dipole strength of a sphere to integrals over the sur- 

Chiew and Glandt46 modeled the structure of a dispersion of identical spheres as an equilibrium hard sphere fluid. They used pair correlation functions to compute the contributions of pairs of spheres to the effective thermal conductivity of the dispersions. Their results, derived for arbitrary values of the conductivity of the two phases, reduce to the following equation for the case of gas bubbles in electrolyte  

Meredith and Tobias49 noted that Bruggeman s equation overcorrects in the concentrated ranges and devised another approach called the Distribution Model by considering only two size fractions. As in the Bruggeman equation, the smaller size fraction is added first and then is considered as part of a continuous medium having its own bulk conductivity when the larger size fraction of bubbles is added  

Data for the conductivity of random dispersions of spheres of equal sizes was obtained by DeLaRue and Meredith. DeLaRue experimented with uniform dispersions of glass spheres suspended by gyrating his cell during the measurements until a steady state value for the conductance was obtained. He used alternating current and a nearly saturated solution of aqueous zinc bromide as the continuous phase to match the density of the glass spheres. Tabulations of data and graphs published in 1961 on the conductivities 

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As in previous theoretical studies of the bulk dispersions of hard spheres we observe in Fig. 1(a) that the PMF exhibits oscillations that develop with increasing solvent density. The phase of the oscillations shifts to smaller intercolloidal separations with augmenting solvent density. Depletion-type attraction is observed close to the contact of two colloids. The structural barrier in the PMF for solvent-separated colloids, at the solvent densities in question, is not at cr /2 but at a larger distance between colloids. These general trends are well known in the theory of colloidal systems and do not require additional comments. 

The effects of confinement due to matrix species on the PMF between colloids is very well seen in Fig. 1(c). At a small matrix density, only the solvent effects contribute to the formation of the PMF. At a higher matrix density, the solvent preserves its role in modulating the PMF however, there appears another scale. The PMF also becomes modulated by matrix species additional repulsive maxima and attractive minima develop, reflecting configurations of colloids separated by one or two matrix particles or by a matrix particle covered by the solvent layer. It seems very difficult to simulate models of this sort. However, previous experience accumulated in the studies of bulk dispersions and validity of the PY closure results gives us confidence that the results presented are at least qualitatively correct. 

Accounting for the instantaneous higher moments of the charge distributions of the atoms leads to an inverse eighth-power functional form (dipole-quadrupole interactions). The bulk dispersive potential is represented as shown by Mayer (1933) ... 

Another interesting phenomenon is that of depletion flocculation. This can be observed with dispersions (e.g. lattices) which contain inert additives, such as free polymer, non-ionic surfactant or even small (e.g. silica) particles. As the latex particles approach one another, the gaps between them become too small to accommodate the above additives, but the kinetic energy of the particles may be sufficient to enable them to be expelled from the gap i.e. a de-mix occurs, for which AG is positive. When this de-mix has been achieved, an osmotic situation exists in which the remaining pure dispersion medium will tend to flow out from the gap between the particles in order to dilute the bulk dispersion medium, thus causing the particles to flocculate. 

At about the same time as the papers by Speerschneider and Li, Symons [4,9] described the growth of lamellar single crystals from dispersed PTFE dispersion particles (Fig. 4) and we described thin lamellae on the free surfaces of bulk dispersion PTFE samples (Fig. 5) [4], both prepared by slow cooling fol-... 

Since a sequence of dispersion structures in bulk dispersions has been correlated with flooding results, the dependence of dispersion structure on phase behavior is also briefly reviewed. This leads to a discussion of phase behavior and its dependence on surfactant structure and other thermodynamic parameters. 

That a steady state occurred for the distribution of primary particles between the bulk dispersion and the surface, and this distribution could be described by a Langmuir adsorption isotherm. 

Simultaneous Flow of Emulsified and Bulk Dispersed Phase... 

The ratio of the relative diffusion constants of brine and oil in the microemulsion phase was found to be very important. Figure 19 shows the effect of varying this ratio. When oil diffusion is less than that of brine, as would be expected in an oil-in-water microemulsion, the fraction of liquid crystal at the dispersion front Increases over that in the bulk dispersion. This situation corresponds to diffusion path 1 in Figure 19. Essentially, brine diffuses out of the dispersion faster than oil can diffuse in, causing a decrease in overall brine concentration at the interface and hence the formation of additional liquid crystal, the phase having the lower brine content. As mentioned previously, this buildup of liquid crystal was observed experimentally. 

All the consideration up to now implies that the dielectric permittivity and the viscosity in the EDL (at least for x > x see Figure 5.67) are equal to those of the bulk disperse medium. A more refined approach shows that for thin double layers the formulaes, stemming from the von Smoluchowski theory, may remain unaltered if the real potential ( = /(Xj)) is replaced by the quantity ... 

C = continuous phase concentration in equilibrium with bulk dispersed phase, i.e., C =... 

The potential drop between the working and reference electrodes is thus entirely ohmic. As in bulk dispersions, bubbles on the electrode force the current to take longer paths and flow through constricted areas. Calculation of the potential drop requires knowledge of the electrical conductivity of the bubble layer either from theory or experiment. Theoretical treatments of the bubble layer are few because solving Laplace s equation in the complicated asymmetric environment is difficult nevertheless, solution of the... 

Specific interactions between the water molecules and the stabilizing moieties imply that when interpenetration occurs, water molecules are released into the bulk dispersion medium. The energy required for the new degrees of freedom (principally translational and rotational) in the bulk... 

Hesselink etal. 91 ) have preferred the designation osmotic for the major free energy change in the interpenetrational domain. This terminology accurately portrays the consequences of the steric interaction. The interaction of the steric layers generates a difference in the chemical potential between molecules of the dispersion medium in the interactional zone and those in the bulk dispersion medium. This chemical potential difference could, of course, be related to an excess osmotic pressure. 

That the contribution of aggregates to the rate could be neglected, and since they returned to the bulk dispersion they had an insignificant effect on the interfacial area available for occupation by unreacted primary particles ... 

Similarly, the vapor pressure of the dispersed phase, p y, in a concentrated emulsion ean be related to that of the bulk dispersed phase, (p v)o... 

Referring to emulsions for which the test is particularly appropriate, as was mentioned in Sec. I, it is obvious that pure compounds are not found either in the con tinuous phase or in the dispersed phase. Nevertheless, it is necessary to know the behavior of pure compounds as references. Therefore, the thermograms dealing with pine compounds will be described first and their possible distribution in an emulsion, in the bulk, dispersed, or bound phase, will be considered. Afterwards, the example of solutions will be examined and finally the response of emulsions to the DSC test will be analyzed. All the thermograms are depicted in Fig. 3 for direct comparison. 

The bulk dispersion medium i.e. water in the aqueous micellar system or heptane in the inverse-micellar system. 

A differential separation of pigments in a dispersed pigment mixture. Floating is a differential separation of pigments (a) by gravity separation in the bulk dispersion and (b) where the flooding results in a nonuniform or mottled surface coloration. While the terms... 

The process of deposition of particles at interfaces which occurs in many industrial processes, such as surface coating, is described at a fundamental level. Particle deposition can be conveniently split into three major steps (i) transfer of particles from the bulk dispersion over macroscopic distances to the surface (ii) transfer of the particles through the boundary layer adjacent to the interface (hi) formation of a permement adhesive contact with the surface or previously deposited particles leading to particle immobilization (attachment). The role of interparticle interactions on deposition is described in terms of double layer repulsion and van der Waals attraction. Particular attention is given to the effect of addition of electrolytes on particle deposition. The measurement of particle deposition using rotating disc and cyhnder techniques is described. The effect of nonionic polymers and polyelectrolytes (both anionic and cationic) on particle deposition at interlaces is described. The most universal and convenient methods for measuring particle deposition are the indirect methods. 

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