Dispersion plateau concentration

Assuming that the contributions of axial dispersion and mass transfer resistances are additive, the breakthrough profile of the first component is given by the same equation as in the single-component case, but with a higher plateau concentration, Cf (Eq. 8.12a). Accordingly, the shock layer thickness for this... 

Thus, the SLT between two successive zones in the isotachic train depends on the axial dispersion coefficient and the mass transfer coefficient of the two components (the theory is valid only if = D /+i and = fcy i+i), on their separation factor, and on the concentration and retention factor of the displacer [11], The SLT does not depend on the retention factor or the feed concentration of the components. Obviously, when the isotachic train is formed, the concentration of each band reaches a plateau concentration which is determined by the concentration of the displacer. 

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

Critical Flocculation Electrolyte Concentration The critical flocculation electrolyte (Na2S0.) concentration was determined by following the average particle size of the dilute dispersion (where the particles were coated with PVA corresponding to the plateau adsorption) as a function of Na2S0 concentration, using a Coulters Nanosizer (Coulters Electronics Ltd) as described before (20). 

On further Increasing the MEGA-n concentration, there appears a sudden kink indicative of some drastic change in the dispersion state. The III/I ratio steeply increases and eventually attains a plateau which corresponds to the polarity found in the MEGA-n micelles. 

The concentrations of contaminants in the atmosphere and their dispersion in the air can be influenced by topography, i.e., whether the location of the polluting source is in a valley, plateau or mountain, or near a lake or the sea. For example, mountains can act as barriers to air flow while valleys will cause persistence in wind direction. 

When a wide rectangular injection pulse is injected in a column and the width is such that the plateau is not completely eroded when it is eluted, the solution of the system of equations of the ideal model (Eqs. 8.1a and 8.1b) includes a constant state, followed by a simple wave, as shown by the theory of partial differential equations [12,13]. The importance of this result is due to the existence of a relationship between the concentrations of the two components of the binary mixture in the simple wave region. This relationship is independent of the position of the band along the column. We have discussed the properties of the hodograph transform in the case of the ideal model (Oiapter 8, Sections 8.1.2 and 8.8). In the case of the equilibrium-dispersive model (Eqs. 11.1 and 11.2), this result is no longer valid. However, the plots of Ci versus C2 are often close to the simple wave solu-... 

This value is in agreement with the one derived from band profiles calculated with the equilibrium-dispersive model [9]. The time given by Eq. 16.20 provides useful information regarding the specifications for the experimental conditions under which staircase binary frontal analysis must be carried out to give correct results in the determination of competitive isotherms. The concentration of the intermediate plateau is needed to calculate the integral mass balances of the two components, a critical step in the application of the method (Chapter 4). This does not apply to single-pulse frontal analysis in which series of wide rectangular pulses are injected into the column which is washed of solute between successive pulses. 

A carbon black addition above a percolation threshold of 5 vol% increases the conductivity until a plateau is reached at 20 vol%. " As the level increases above 10 vol%, the viscosity of the filled polypropylene increases rapidly (see Figure 9.9). As with polyethylene, carbon black is preferentially contained in one phase of a two phase blend."" This phenomenon is used in practice to lower the concentration of carbon black required for a certain level of conductivity. Here, again, carbon black is concentrated in the preferred location. Carbon black and copper powder were used to improve connectivity of YBaCuO in ceramic superconductors. "" Dispersion of copper particles and the related changes in conductivity were enhanced by the presence of acrylic acid modifier. ... 

The method termed mass titration was originally described by Noh and Schwarz [59]. Dispersions containing 0.01, 0.1, 1,5, 10 and 20% of solid in deionized and outgased water are equilibrated for one day under nitrogen atmosphere. The pH is measured and plotted versus log (mass% of solid) and the plateau in the curve indicates the PZC. Addition of inert electrolyte was recommended (but not applied) in the original paper and the problem of optimum concentration of inert electrolyte was not addressed. The agreement between results obtained by mass titration and the CIP was good for alumina but problematic for titania. 

We have compared these theoretical predictions of the low-frequency modulus to experimental measurements on compressed emulsions and concentrated dispersions of microgels [121]. The emulsions were dispersions of silicone oil (viscosity 0.5 Pas) in water stabilized by the nonionic surfactant Triton X-100 [102, 121]. The excess surfactant was carefully eliminated by successive washing operations to avoid attractive depletion interactions. The size distribution of the droplets was moderately polydisperse with a mean droplet diameter of 2pin. The interfacial energy F between oil and water was 4mJ/m. The contact modulus for these emulsions was thus F 35 kPa. The volume fraction of the dispersed phase was easily obtained from weight measurements before and after water evaporation. Concentrated emulsions have a plateau modulus that extends to the lowest accessible frequencies, from which the low-frequency modulus Gq was obtained. Figure 11 shows the variations of Gq/E"" with 0 measured for the emulsions against the values calculated in the... 

In the mass titration method, the PZC is determined as the natnral pH of a concentrated dispersion. A detailed description of the experimental procedure can be found in [667], Mass titration become popular in the late 1980s [668,669], but the same method was already known in the 1960s as the pH drift method [183], Usually, a series of natural pH values of dispersions with increasing solid loads is reported, but only the natural pH of the most concentrated dispersion is actually used. The only role of the data points obtained at lower solid loads is to confirm that a plateau was reached in pH as a function of solid load that is, a further increase in the solid load is unlikely to bring about a change in pH. The mass titration method is based on the assumption that the solid does not contain acid, base, or other surface-active impurities. This is seldom the case, thus mass titration often produces erroneous PZCs. In this respect mass titration is similar to the potentiometric titration without correction illustrated in Figure 2.7, only the solid-to-liquid ratio is different. The experimental conditions in mass titration (solid-to-liquid ratio, time of equilibration, nature and concentration of electrolyte, and initial pH) can vary, but little attention has been paid to the possible effects of experimental conditions on the apparent PZC. The effect of an acid or base associated with solid particles on the course of mass titration was studied in [670], To this end, a series of artificially contaminated samples was prepared by the addition of an acid or base to a commercial powder. The apparent PZC of silicon nitride obtained in [671] by mass titration varied from 4.2 (extrapolated to zero time of equilibration) to 8.2 for time of equilibration longer than 20 days. The method termed mass titration was used in [672], but it was different from the method discussed above. 

Because the surfactant concentration in the oil phase (the disperse phase) is higher than the equilibrium concentration, surfactant molecules cross the oil-water interface toward the aqueous phase. Thus, surfactant accumulates within the flhn, because the bulk diffusion throughout the film is not fast enough to transport promptly the excess surfactant into the Plateau border. As the background surfactant concentration in the aqueous phase is not less than CMC, the excess surfactant present in the film is packed in the form of micelles (denoted by black dots in Figure 5.48a). This decreases the chemical potential of the surfactant inside the flhn. Nevertheless,... 

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