than for a suspension with Cherkasy bentonite of the same concentration. The contact time of the bentonite with the filtrate has a large effect on the detachment force. When the contact time was changed from 30 minutes to one hour, the detachment force for 10% suspensions with Dash-Salakhlinsky and Cherkasy bentonites increased on average by a factor of 2.

The introduction into the suspension or filtrate of the structure-forming agent K-4 (gipan), calculated as 500 g/t of concentrate, increases the detachment force from 100 N/m² to 160 N/m². This corresponds to the adhesive strength of a suspension with Dash-Salakhlinsky bentonite at a concentration of 13%. In all experiments for determining the detachment force, rupture occurred through the layer of the pore suspension, i.e., the cohesion of the suspension, determined by van der Waals forces, was less than the adhesion of the clay-bentonite suspension to magnetite. Thus, the principal component of the cohesion of the system in this case is the capillary (meniscus) force at the boundary between the magnetite plates and the coagulation-structured suspension. The results obtained explain the absence of a significant increase in the strength of green pellets when bentonite is added to the charge, and show that the weak link of the structure is the pore suspension and that, evidently, destruction of the forming granules occurs in the zone of action of molecular forces.

References

1. Igershhöld M., Htoni P. A., Amer. Inst. Min. Eng. Proceeding of the Blast Furnace and Coke Oven, Raw Materials Conference, V. 9, 1950, p. 18.

2. Y. Tayian, “Kohászati lapok,” 1963, köt 96, No. 12, pp. 529–533.

3. V. I. Korotich. Theoretical Foundations of the Pelletizing of Iron-Ore Materials. Metallurgiya, 1966.

4. Masayoshi Wada, Osami Tsuchiya, Proceedings IX International Mineral Processing Congress, 1970, Prague, ČSSR.

APPLICATION OF EXPERIMENTAL DESIGN AND OPTIMIZATION METHODS TO ESTIMATING THE RESOLUTION OF THE APN METHOD

A. A. Zheltonozhko, A. F. Fedorov, A. A. Kaplin, A. G. Stromberg

When several elements with close potentials of the anodic peaks are simultaneously present in a solution, analysis by the amal—

square-wave polarography with accumulation (APN) is complicated by the mutual overlap of peaks. Earlier /1/, it was proposed to take, as the limiting resolution ($j$) of the APN method, the ratio of the peak heights of the interfering and the determined elements at which, on the polarogram, a horizontal plateau appears at the peak potential of the determined element. In accordance with this, the value of the limiting resolution is determined as a function of the kinetic ($\delta'$) and diffusion ($\delta''$) half-widths and of the potentials of the anodic peaks ($\varphi_n$). It follows from the theory of the APN method that these peak characteristics, in turn, depend in a complex way on a large number of diffusion and kinetic parameters ($K_s$, $D$, $B$), on the sizes and shapes of the electrodes, etc. Derivation of theoretical relations for the dependence of $j$ on various parameters and $\varphi_n$ is, as a rule, difficult and is possible only for certain special cases. For example, /2/ established the dependence of the peak potential ($\varphi_n$) on a number of parameters for irreversible processes on a mercury film electrode at small film thicknesses. Estimation of $j$ from the experimental values $\delta'_1$, $\delta''_2$, $\varphi_n$ of individual elements requires a large body of experimental material. Moreover, such an approach does not make it possible to predict theoretically the values of the resolution and to compare them over a wide range of variation of the parameters determining $\delta'$, $\delta''_2$, $\varphi_n$. One approach that, in our opinion, substantially expands the possibilities for estimating resolution on the basis of experimental data is the use of experimental-design methods. On the basis of this approach, it is possible not only to describe the dependence of $j$ on a number of factors within a specified interval of their variation, but also subsequently to analyze the regression equations in order to choose the optimal conditions for attaining a specified or maximum resolution.

The aim of the present work was to choose conditions corresponding to the maximum resolution on the basis of a preliminary mathematical description of the analyzed region of parameter study using experimental-design methods.

As the analyzed response function ($y$), the limiting resolution was chosen. From theoretical premises, the following were chosen as the variable parameters:

1. \(x_1\) — concentration of the indifferent electrolyte, M/l;
2. \(x_2\) — rate of change of potential, V/min;
3. \(x_3\) — thickness of the mercury film, \(\mu\)m.

Selection of the ranges of parameter variation

1. Electrolyte concentration. Varied within the range \(0.05\text{–}1.05\) M/l. The use of higher solution concentrations increases the voltage drop in the cell and makes purification of the solution more difficult. At electrolyte concentrations below \(0.05\) M/l, the migration component of the current may have an effect and the influence of the background concentration on the peak characteristics may decrease.

2. Rate of change of potential. The upper limit (\(3.0\) V/min) is determined by the design features of the OH-102 polarograph. The lower limit (\(0.25\) V/min) was chosen from the condition of limited analysis time: at a rate of change of potential \(w < 0.25\) V/min, the analysis time increases significantly.

3. Thickness of the mercury film. Varied within the range \(5\text{–}35\ \mu\)m. With a film thickness below \(5\ \mu\)m, the peak characteristics do not depend on thickness as a parameter. In addition, very thin mercury films practically constitute a silver amalgam. At thicknesses greater than \(35\ \mu\)m, the mercury film acquires elements of sphericity, which changes the nature of diffusion in the electrode volume. The intervals and levels of factor variation are given in Table I.

Table I

The thallium–lead system was investigated; as the indifferent electrolyte, a solution of ammonium fluoride of various concentrations was used. The cathode was a mercury film electrode on a silver substrate with various mercury-film thicknesses; the anode was a saturated calomel electrode; instrument sensitivity, \(i_k = 1.6 \cdot 10^{-8}\) A/mm; electrolysis time, \(\tau = 3\) min; electrolysis potential, \(\varphi_e = 1.0\) V; solution volume—

buffer, \(V = 10\) ml.

To obtain a nonlinear model, one may use a full factorial experiment of the \(2^3\) type. The design matrix of the full factorial experiment includes three two-factor interactions and one three-factor interaction. The results of the experiments are presented in Table 2.

Table 2

On the basis of the experimental data, the coefficients of the regression equation were determined by the method of least squares. The equation has the form:

\[ y = 0{,}485 - 0{,}172 x_1 - 0{,}288 x_2 - 0{,}236 x_3 + 0{,}169 x_1x_2 + 0{,}157 x_1x_3 + 0{,}166 x_2x_3 - 0{,}159 x_1x_2x_3 . \tag{I} \]

The reproducibility variance was assessed by Cochran’s criterion \((G_T = 0{,}478,\; G_p = 0{,}16)\). It was established that all coefficients are significant. To assess the adequacy of the model, experiments were carried out at the center; the results are given in Table 3.

Table 3

The adequacy of the model was confirmed by verification according to Fisher’s criterion \((F_T = 19{,}4\) with \(f_1 = 2;\; f_2 = 2;\; F_p = 6)\).

Thus, regression equation (I) adequately describes the process being analyzed in the specified range of variation of the parameters. In dimensional variables, equation (I) has the form

\[ j = 0.737 - 0.172c - 0.105w - 0.008h + 0.054cw + 0.004ch + \]
\[ +\,0.0016wh - 0.0014cwh . \]

The next step after the mathematical description of the process problem is to find the parameter values corresponding to the maximum resolution. For this purpose we used the scanning method. From the calculations carried out by the scanning method it follows that the maximum value of the function \(y\) (\(j\)) is found on the boundary of the region and corresponds to the following parameter values: \(c = 0.05\) M/l; \(W = 0.25\) V/min; \(h = 5\) μ. Thus the optimal values of the parameters correspond to the quantity \(j = 1.83\), which is the maximum value of the resolution as a function of the parameters \(c, w, h\) in the intervals of their variation specified in the work.

References

1. A. G. Stromberg, A. A. Zheltonozhko, A. A. Kaplin. ZhAKh, 28, 1045, 1973.

2. V. A. Igolinskii. Izvestiya TPI, 148, 14, 1967.

STUDY ON THE ANALYSIS OF WATER-SOLUBLE SALTS AND CRYSTALS OF COMPLEX COMPOSITION BY THE AMALGAM-POLAROGRAPHIC METHOD

N. V. Podkorytova, A. A. Kaplin, N. T. Rud, V. I. Kuleshov

In this work the amalgam-polarographic method is applied to the analysis of water-soluble salts and ferroelectric crystals of complex composition \((\mathrm{CsH_2AsO_4}, \mathrm{KH_2PO_4}, \mathrm{LiIO_3})\). In contrast to the chemical-spectral analytical procedure for rubidium and cesium arsenates / 1 /, solutions of the salts being analyzed can in most cases be used as polarographic backgrounds for determining impurities, which eliminates the stage of decomposition of the sample. For the determination of \(\mathrm{Cd}\), \(\mathrm{Cu}\), \(\mathrm{Bi}\), \(\mathrm{Pb}\), a mercury film electrode on a silver substrate and a cell with insert cups were used. Nickel was determined by the method of anodic-cathodic polarography with accumulation (ACPN) / 2 / in a circulating electrolyzer / 3 /; the reference electrode was a saturated calomel electrode. The impurity content in the reagents and solutions used was monitored by the APN and ACPN methods.

The polarographic behavior of \(10^{-6}\)–\(10^{-9}\) g/ml of \(\mathrm{Cd}\), \(\mathrm{Pb}\), \(\mathrm{Cu}\), \(\mathrm{Bi}\), \(\mathrm{Ni}\) in \((0.05 \div 0.[[unclear: digit]])\) M solutions of \(\mathrm{CsH_2AsO_4}\) and \(\mathrm{KH_2PO_4}\), [[unclear: text continues]]