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Removal of Organics and Inorganics by Activated Carbon
Published in Samuel D. Faust, Osman M. Aly, Chemistry of Water Treatment, 2018
The pore size and pore size distribution of activated carbon are determined by an analysis of gas adsorption isotherms in the range where capillary condensation accompanies physical adsorption. The Kelvin equation7 generally is applied to the desorption portion of the adsorption isotherm. The Kelvin equation relates the equilibrium vapor pressure of a curved surface, such as that of a liquid in a capillary or pore, to the equilibrium pressure of the same liquid on a plane surface. Equation 5 is a convenient form of the Kelvin equation: () lnPPo=2γV¯rRTcosθ
Surface thermodynamics
Published in Nils O. Petersen, Foundations for Nanoscience and Nanotechnology, 2017
The Kelvin equation demonstrates how the vapor pressure of the liquid in a drop depends on the surface tension of the material and on the radius of the drop. The vapor pressure of the liquid in a drop will always be greater than that of the liquid in the bulk with a flat surface. Moreover, as the radius of the drop decreases, the vapor pressure of the liquid in the drop increases.
Aerosols
Published in Efstathios E. Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Multiphase Flow Handbook, 2016
Yannis Drossinos, Christos Housiadas
Equation 20.89, known as the Kelvin equation, is a fundamental equation in the thermodynamics of aerosols, because it relates the vapor pressure of a droplet to the (saturation) vapor pressure above a planar interface of the bulk material psat. It shows that the vapor pressure above a droplet is higher than the vapor pressure above a at surface, an Effect that becomes signi cant for dp 0.1 m. e nucleation current is obtained from Equation 20.84 by approximating it according to the previously summarized CNT assumptions. e equilibrium cluster distribution of Equation 20.86 is used. e current, then, is related to the sum of cluster equilibrium distributions times their respective surface areas, summed up to an arbitrarily large cluster size (see, e.g., Debenedetti, 1996). e discrete sum may be replaced by an integral and the clusters free energy of formation is expanded to second-order (an excellent approximation because the integrand is sharply peaked about the critical cluster) to give J = ji * Zni * where the rst term ji * is the rate of arrival of single molecules to the critical droplet the second factor Z is the so-called Zeldovich nonequilibrium factor the last term n i * is the equilibrium number concentration of critical nuclei e rate of arrival of monomers is the product of the forward ux constant (also known as the impingement rate per unit area), which is the single-molecule growth rate calculated from the kinetic theory of gases (with a unity accommodation coe cient), and the critical droplet surface area: ji * = 4 p a * b = 4 p a * p p (20.90)
Porosimetric features of calcium sulfoaluminate and Portland cement pastes: testing protocols and data analysis
Published in Journal of Structural Integrity and Maintenance, 2018
Seongwon Hong, Kyle de Bruyn, Eric Bescher, Chris Ramseyer, Thomas H.-K. Kang
The Kelvin equation relates the size of a pore to the relative pressure of the gas at which capillary condensation occurs inside the pore (Thompson, 1871). Based on this equation, the porosimetric characteristics of cement paste can be examined through nitrogen sorption. According to Aligizaki (2006), the nitrogen sorption method cannot measure macropores, which are too big for capillary condensation, works well for mesopores, and is inapplicable for micropores approximately the same size as the gas molecules. To properly understand the method, the Kelvin equation for cylindrical pores is first discussed and expressed in Equation (6).