Calculation of the BET-Compatible Surface Area from Any Type I Isotherms Measured above the Critical Temperature.
In our previous papers [Tóth, J., et al., J. Colloid Interface Sci. 212, 402 (1999); 212, 411 (1999)] it has been proven that a BET-compatible specific surface area, a(s)(c)(N(2), 77), can be calculated from any Type I monolayer isotherms and from the monolayer domain of Type II isotherms, both measured below the critical temperature. In this paper, the calculation of a(s)(c)(N(2), 77) from Type I isotherms at temperatures above the critical temperature is discussed. These calculations are also based on the thermodynamical consistent form of the Tóth (T) equation. This relationship can be derived from the differential equation dn(s)/n(s)=[psi(p)](-1)dp/p, where the function psi(p) is calculable from the measured isotherms and includes the change in the surface free energy. The basic problem of the calculation of a(s)(c)(N(2), 77) is the determination of the upper limit of integration (p(u)) required to solve this differential equation. It is demonstrated that p(u) can be calculated from the equation ln(p(u))=-alphaT(-1)+beta. The constants alpha and beta are independent of the temperature of the isotherms but they are very sensitive to the structure of adsorbents and to the quality of adsorptives. This fact also makes it possible to characterize exactly the nanostructure of solids and the state of adsorptives. Copyright 2000 Academic Press.
Extension of Tóth Psi function from gas-solid to liquid-solid equilibria and application to reversed-phase liquid chromatography systems.
The extension of the Psi function developed by Tóth from equilibria taking place at gas-solid interfaces to those taking place at liquid-solid interfaces was investigated. The results were applied to conventional liquid-solid systems used in reversed-phase liquid chromatography (RPLC). The adsorbents in these systems are made of porous silica having a hydrophobic solid surface obtained by chemically bonding C(18) alkyl chains to a porous silica gel then endcapping the surface with trimethylsilyl groups. The liquid is an aqueous solution of an organic solvent, most often methanol or acetonitrile. The probe compound used here is phenol. Adsorption data of phenol were measured using the dynamic frontal analysis (FA) method. The excess adsorption of the organic solvent was measured using the minor disturbance (MD) method. Activity coefficients in the bulk were estimated through the UNIFAC group contributions. The results show that the Psi function predicts 90% of the total free energy of immersion, DeltaF, of the solid when the concentration of phenol is moderate (typically less than 10 g/L). At higher concentrations, the nonideal behavior of the bulk liquid phase becomes significant and it may contribute up to about 30% of DeltaF. The high concentration of adsorbed molecules of phenol at the interface decreases the interfacial tension, sigma, by about 18 mN/m, independently of the structure of the adsorbed phase and of the nature of the organic solvent.
Analysis of the stress wave effect during coal breakage by a high-pressure abrasive air jet
In view of the defects of borehole collapse, inhibition of gas desorption and migration of gas existing in hydraulic fracturing and other hydraulic permeability–increasing measures for soft coal seams with low-permeability technology is proposed for coal breakage by a high-pressure abrasive gas jet for relieving pressure and increasing permeability. The comparative analysis of gas jet flow field structure between convergent nozzle and Laval nozzle has been given by numerical simulation. For Laval nozzle, the expansion wave and compression wave alternate and move forward steadily in gas jet and vanish when potential core length reaches maximum. So, the Laval nozzle can form more stable flow filed structure of gas jet and avoid shock wave in gas jet. Furthermore, a high-speed camera is adopted to analyze the jet structure and verify the conclusion of numerical simulation. Based on thermodynamic theory, this article calculates and analyzes the critical local sound velocity and pressure generated from the stress wave during the process of coal breakage by the gas jet. Furthermore, experimental coal breakage by a high-pressure abrasive gas jet is carried out. The high-pressure abrasive gas jet impacts the coal body as a quasi-static load and a dynamic load and forms corrosion pits on the surface of the coal body. Penetrating cracks are formed within the coal in the pattern of the loaded stress wave which leads to coal breakage. The effects of porosity and permeability on the propagation of the stress wave in coal are analyzed by establishing the dispersion equation for the spread of the stress wave in coal. The results show that porosity has a significant effect on wave velocity and that the attenuation of the stress wave is intensified with an increase in porosity. Moreover, the stress wave attenuation is more obvious at high frequency. The effect of permeability on the wave velocity is not significant at low frequencies. In contrast, at high frequency and relatively low permeability, the wave velocity increases with the permeability, and the attenuation of the wave velocity initially increases and then decreases. When the permeability is greater than 10−11 m2, the wave velocity is not affected by the permeability. However, the stress wave is not attenuated.