Stability ratio experimental

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

The experimental stability ratio (W), the potentiometrically-determined surface charge, and the electro-kinetic mobility of 70 nm particles over the pH range from 3 to 11 are shown. The drawn-out line in Fig. c summarizes experiments obtained with I = 0.05 - 0.1. (Modified from Liang and Morgan, 1990.)... 

Summary plot of experimentally derived stability ratios, Wexp, of hematite suspensions, as a function of added electrolyte or adsorbate concentration at pH around 6.5 (pH = 10.5 for Ca2+ and Na+). Hematite concentration is about 10-20 mg/ . The stability ratio, Wexp, was determined from measurements on the coagulation rate it is the reciprocal of the experimentally determined collision efficiency factor, a. 

Experimentally derived stability ratio, Wexp, of hematite suspensions, plotted as a function of fatty acid concentration at pH 5.2. The ionic strength is 50 milimolar NaCI and hematite concentration is 34.0 mg/ . Laurie acid is denoted by C, capric acid by C10, caprylic add by Cs and propionic acid by C3. (From Liang and Morgan, 1990)... 

Experimental measurements in each lake included particle concentration and size measurements in the water column, sedimentation fluxes in sediment traps, and chemical and size characteristics of materials recovered from sediment traps. The colloidal stability of the particles in the lake waters was determined with laboratory coagulation tests. Colloidal stability was described by the stability ratio (a). For a perfectly stable suspension, a = 0 for a complete unstable one, a = 1.)... 

A major outcome of the abovementioned studies is the importance of pH and notably of the salinity of the groundwater controlling colloid concentrations and, consequently, the relevance of colloids for radionuclide transport. The pH-dependent colloid stability varies considerably for different colloid types. Experimental data for the relationship of the stability ratio W... 

Using the approach developed in Example 13.3 and interaction energy expressions for spherical particles, it has been possible to predict how the stability ratio W varies with electrolyte concentration according to the DLVO theory. Since W can be measured by experimental studies of the rate of coagulation, this approach allows an even more stringent test of the DLVO theory than CCC values permit. We shall not bother with algebraic details, but instead go directly to the final result ... 

Discuss the agreements and disagreements between the theoretical predictions for the stability ratio with what is observed experimentally. 

The most common scenario for measuring the experimental stability ratio involves its initial value (t =0). If the initial state of a suspension is arranged to comprise only primary particles, then Eq. 6.58 applies and Eq. 6.70 reduces to the expression ... 

The experimental stability ratio is defined generally as the rate of fast flocculation divided by the rate of slow coagulation (see, e.g., Section 7.8 in R. J. Hunter, op. cit.1). Equation 6.70 is a mathematical interpretation of this definition in terms of experimentally accessible quantities related to floccule size. 

Strong specific anion effects were reported particularly at low electrolyte concentrations (10 4—10 2 M),1 a range in which the DLVO theory is considered accurate. However, as shown later, the present experimental data cannot be reproduced by the traditional theory in this range of electrolyte concentrations. In the past, no agreement could be obtained, on the basis of the traditional theory, because small changes in the values of the parameters, caused by the nonuniformity of the particles, affected strongly the stability ratio.18 The polarization model provides similar results in the above range of electrolyte concentrations, when the dipole densities are sufficiently low and cannot explain the data. 

Figure 2. Experimental values of the stability ratio of protein-covered latex particle as a function of electrolyte concentration, at pH = 10.0, reported by Lopez-Leon et al.,1 compared to those calculated from the polarization-based hydration model, for the following parameter values NA = 1.2 x 1018 sites/m2, NB = 1.62 x 1018 sites/m2, A, = 0.9 x lO 20 J, KH = lCL6 M, Aon = 8.95 x 10 8 M, KNh = 0.021 M, (p/e )Na = 1.8 D (1) Ka = 0.76 M, (p/e)ci = 2.3D (2)Kno = 0.62M,(p/e )no3 = -1.8D stars, NaN03 squares, NaCL...

Figure 3. Stability ratios at low concentrations of NaSCN at pH = 10. The calculations have been carried out for Na = Nb = 0.5 x 1018 sites/m2 and various dissociation constants Ans based on the present model (thick lines) and on the DLVO theory, with different values for Ans (dotted lines), predict almost identical results but varies much more rapidly with electrolyte concentration than the experimental values reported in ref 1 (circles). K = A(>i = 1C1 1 M, (/ /r ), — 1.8 D, n = 0.8 M, (p/e )scn = -0.8 D, Ah = 0.1 x 10 201 J. (1) polarization model, ANa = 12.5 x 10-6M DLVO,ANa = 2.5 x 10-eM. (2)polarization model, AKa = 23.1 x 10 6 M DLVO, ANa = 5.83 x 10-6 M. (3) polarization model, Axa = 54.7 x 10 M DLVO, An, = 12.6 x 10-6 M. (4) polarization model, ANa = 164 x 10-6 M DLVO, Axa = 42 x 10 6 M.

An important issue that has to be emphasized is that the experimentally determined dependence ofthe stability ratio on electrolyte concentration, at low ionic strengths, exhibits (at least for NaSCN) a strongly non-DLVO behavior, in a range in which the DLVO theory is considered fairly accurate. Therefore, we are inclined to believe that the electrolyte (even at low ionic strength) induces indeed structural modifications of the adsorbed protein layer at least near the interface. 

While the above expression is widely used, it is also understood that this does not accurately reflect experimental data. The problem mainly arises due to the relatively discontinuous nature of the stability ratio demonstrated experimentally, a feature the above expression is not capable of predicting accurately (with such a sharply changing function, small discrepancies in terms can result in large differences in the value of the function). 

From experimental values of the stability ratio, the maximum in the interaction eneigy can be determined according to the calculation [59]... 

In a 1980 paper [49], our group discussed several possible competition mechanisms leading to kinetics in which the stabilization ratio decreases with increasing photocurrent density. Four out of the resulting kinetic equations have been found to describe the experimental cases. These s(y, /) relations, the cases in which they were observed, and the corresponding mechanisms are described here (cases (i) to (iv)). 

Fig. 8 Comparison of theoretical and experimental stability ratios for TiO (0.05g/L) and AI2O3 (0.15 g/L) colloids in 10 M KNO3.

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