ON SOME CHARACTERISTICS OF THE STRUCTURE OF CAPILLARY-POROUS COLLOIDAL BODIES

S. I. Smolyaninov, G. G. Krinitsyn

(Presented by the Scientific-Methodological Seminar of the CTF)

In studying structure-forming processes occurring during the drying of capillary-porous colloidal bodies, according to the principles of the physicochemical mechanics of disperse structures developed by Academician P. A. Rehbinder [1], one of the characteristics of peat structures proposed by M. P. Volarovich and N. V. Churaev [2] may be of definite interest—the hydraulic pore radius \((\delta)\), calculated as the ratio of active porosity to the value of the kinetic specific surface and characterizing the average dimensions of water-conducting pores.

In all probability, the hydraulic pore radius as an averaged characteristic of peat capillaries may be used in estimating capillary-pressure forces in the Laplace equation or in the expression for the capillary potential [1, 2].

In a state of equilibrium, the capillary potential of a body at any point is equal to the potential of the force of gravity [3]. Since the latter acts as an external force, it is apparently possible to establish a relationship between the capillary potential and any external force tending to change it.

The validity of such a conclusion can be shown using the experimental data of M. P. Volarovich and N. V. Churaev [2] on determining the change in the structural characteristics of peat during its compression (Table 1).

Under the condition of constancy or an admissible change in surface tension and wettability, which is quite acceptable for various peats, the Laplace formula may be written as

\[ P_{\delta}=\frac{a}{\delta}, \]

where \(a\) is a constant;
\(\delta\) is the hydraulic pore radius.

The values of \(a\) calculated by us are given in Table 1. An attempt was made here to take into account the coefficient of lateral pressure \((\varepsilon)\), which, according to Terzaghi [4], determines the relationship between the capillary pressure \((P_{\delta})\) and the pressure determined from the compression curve \((P_s)\). In one case the coefficient of lateral pressure was taken equal to unity; in the other it was calculated from an empirical equation [5]. As can be seen from Table 1, the correction for the coefficient of lateral pressure does not introduce fundamental changes into the character of the dependence obtained; moreover, the subsequent pro-

Table 1

Changes in the water properties and structure of medium peat.
Calculation of the constant in the Laplace equation.

verification showed that at \(\varepsilon=1\) the results obtained are closer to the data of other authors.

Thus, a satisfactory constancy is observed in the values of the named constant, which on average may be taken as equal to \(0.043\ \text{kg}\cdot\text{cm}\cdot 10^{4}\), provided that \(P_\varepsilon\) is expressed in \(\text{kg}/\text{cm}^{2}\) and \(\delta\) in microns.

Since it may be assumed that the established relationship is valid with sufficient accuracy in most cases, the hydraulic radius of the pores in a peat system can be determined if the capillary pressure is known.

In this respect, the studies of S. S. Korchunov [6] are of great interest. He showed that

\[ \varphi=\varphi_{0}\cdot e^{-\frac{1}{\alpha}W}, \]

or

\[ \lg\varphi=\lg\varphi_{0}-\frac{1}{2.3\alpha}\cdot W, \]

where

\[ \begin{aligned} W &\text{— absolute moisture content of peat, g/g;}\\ \varphi &\text{— energy of binding of water with peat, } \text{g cm}/\text{cm}^{3};\\ \varphi_{0}\ \text{and}\ \alpha &\text{— coefficients constant for a given peat sample.} \end{aligned} \]

It has been shown that the relationship found is universal in character, and the constant \(\varphi_{0}\) does not depend on the type of peat; according to S. S. Korchunov, its logarithm is on average equal to 3.50. As for the other constant \(\alpha\), S. S. Korchunov established its relationship with the full moisture capacity of peat \((W_{\text{п}})\),

\[ \alpha=0.14W_{\text{п}}, \]

and this constant was named the coefficient of moisture capacity.

As S. S. Korchunov indicates, the energy of binding of water with peat, calculated by the formula given, is identical to the capillary pressure.

Many investigators [2, 4, 6] point to an analogy between shrinkage during drying of peat and its mechanical compression. Consequently, the regularities considered make it possible to determine the most important characteristics of structure-forming processes in peat systems (capillary pressure and hydraulic pore radius), on the basis of measuring two comparatively easily found quantities—the moisture content of peat at each given moment of time and its full moisture capacity.

Thus, for calculating the hydraulic pore radius, the following formula may be proposed:

\[ \lg\delta=3.09\frac{W}{W_{\text{п}}}-1.87, \]

where

\[ \begin{aligned} \delta &\text{— hydraulic pore radius, } \mu;\\ W &\text{— absolute moisture content of peat, g/g;}\\ W_{\text{п}} &\text{— full moisture capacity of peat, g/g, determined by a known method [7].} \end{aligned} \]

The value of the hydraulic pore radius calculated by the proposed formula should be regarded as an approximate quantity; moreover, the validity of applying this formula under various conditions requires unconditional verification. However, the present method has the advantage that it makes it possible to determine the change in the sought parameters over a wide range of moisture content, which cannot be done by other methods.

It follows from the dependence presented that the hydraulic radius of pores, determined by capillary pressure, at the moisture content of peat corresponding to full moisture capacity, will be about 16 microns, regardless of the type of peat, provided that the value of \(a\) is constant. Taking into account the method for determining \(W_{\text{p}}\), this value is in full agreement with A. V. Lykov’s [3] definition of capillary pores from the ratio of the capillary potential to the potential of the gravitational field.

S. S. Korchunov [6] indicates that the extrapolated value is much lower than the actual binding energy of the last traces of water in peat, and therefore the formula he proposes is valid only for comparatively high moisture-content values. Apparently, this lower moisture limit should be such a water content in peat as corresponds to 10–30 molecular layers adsorbed on the inner surface of the capillaries, i.e., to an absolute moisture content of 0.5 g/g [2]. This moisture content, according to the formula cited above, corresponds to a capillary radius on the order of \(3 \cdot 10^{-7}\) mm and a capillary pressure of \(14.3\ \text{kg}/\text{cm}^2\). It is interesting to note that precisely such a pressure is required, according to A. V. Dumanskii [6], to squeeze out capillary moisture.

In the process of natural drying of samples of formed peat passed three times through a meat grinder and of its mixture (fuel-smelting material) with iron ore (magnetite concentrate) in a ratio of 100:6, the change in moisture content was determined. The full moisture content of peat was 12.50 g/g, and that of the peat–ore mixture (TPM) was 10.8 g/g.

Figure 1 presents the values of capillary pressure calculated by us using the equation of S. S. Korchunov. As can be seen, the curves of change in this index over time have a characteristic S-shaped form, which fully corresponds to previously established regularities [8].

The hydraulic pore radii calculated by the above-proposed equation change during drying for peat from 0.362 to 0.015 microns when the moisture content changes from 5.80 to 0.20 g/g and for (TPM)

Fig. 1. Change in capillary pressure in samples of peat (curve 1) and fuel-smelting materials (curve 2) during natural drying in open air.

from 0.240 to 0.014 microns as the moisture content decreases from 4.38 to 0.15 g/g.

The values obtained are in good agreement with the values of this parameter obtained earlier by another method [2], and with the general regularities of drying capillary-porous colloidal bodies [3], which testifies in favor of the applicability of the indicated equation.

It is of interest to note that throughout the entire drying period the capillary pressure in the TFM samples is greater, and the hydraulic radius of the pores correspondingly smaller, than in the peat samples. Thus, the addition of finely ground iron ore to the raw peat mass leads to the formation of more compact coagulation structures, and this influence is noticeable at all stages of the structure-forming processes occurring during drying.

Conclusions

1. The possibility has been demonstrated of using the averaged characteristic of the structure of capillary-porous colloidal bodies proposed by M. P. Volarovich and N. V. Churaev—the hydraulic radius of the pores—to characterize the forces of capillary contraction.

2. To determine the capillary pressure over a wide range of changes in moisture content, the equation of S. S. Korchunov was used.

3. A semiempirical equation has been proposed for determining the hydraulic radius of the pores.

4. It has been shown that the introduction of finely ground iron oxides into the raw peat mass leads to a decrease in the hydraulic radius of the pores and to a corresponding increase in capillary pressure.

Literature

1. P. A. Rebinder. Problems of the Physicochemical Mechanics of Fibrous and Porous Disperse Structures and Materials. “Zinatne” Publishing House, Riga, 1967.

2. M. P. Volarovich, N. V. Churaev. Investigation of Peat with the Aid of Radioactive Isotopes. Publishing House of the Academy of Sciences of the USSR, Moscow, 1960.

3. A. V. Lykov. Transfer Phenomena in Capillary-Porous Bodies. Gostekh­teorizdat, Moscow–Leningrad, 1954.

4. N. N. Kulakov. Introduction to the Physics of Peat. Gosenergoizdat, Moscow–Leningrad, 1947.

5. Handbook on Peat. Gosenergoizdat, Moscow–Leningrad, 1954.

6. S. S. Korchunov. Investigation of the Physicomechanical Properties of Peat. Gosenergoizdat, Moscow–Leningrad, 1953.

7. E. P. Sementskii. Technical Analysis of Peat. “Nedra,” Moscow, 1966.

8. A. I. Fedotov, N. V. Churaev, N. S. Shaban. In: Problems of the Physicochemical Mechanics of Fibrous and Porous Disperse Structures and Materials. “Zinatne” Publishing House, p. 398, Riga, 1967.