Kelvin Equation and Capillary Condensation

The subject of the Kelvin equation is the vapor pressure of a liquid. Tables of vapor pressures for various liquids and different temperatures can be found in common 

3) WiUiam Thomson, later Lord Kelvin, 1824-1907. Physics professor at the University of Glasgow. 

The cause for this change in vapor pressure is the Laplace pressure. The raised Laplace pressure in a drop causes the molecules to evaporate more easily. In the liquid, which surrounds a bubble, the pressure with respect to the inner part of the bubble is reduced. This makes it more difficult for molecules to evaporate. Quantitatively, the change of vapor pressure for curved liquid surfaces is described by the Kelvin equation  

The Kelvin equation is derived by equating the chemical potential of the liquid molecules in the meniscus, Po + = p.Q + YLVm(l/ti + l/r2), with that of 

When applying the Kelvin equation, it is instructive to distinguish two cases a drop in its vapor (or more generally, a positively curved liquid surface) and a bubble in liquid (a negatively curved liquid surface). 

Though not a general adsorption equilibrium model the Kelvin equation does provide the relationship between the depression of the vapor pressure of a condensable sorbate and the radius (r) of the pores into which it is condensing. This equation is useful for characterization of pore size distribution by N2 adsorption at or near its dew point. The same equation can also describe the onset of capillary condensation the enhancement of sorption capacity in meso- and macro-pores of formed zeolite adsorbents. 

Nearly any of the useful theories can be modified to allow for the computation of mulh-component adsorption equilibrium. In addihon to the LRC there are other specialized forms that may be employed. 

The interested reader is referred to Ruthven [2], Yon and Tumock [4], Young and Crowell [5] and Yang [6] for a more comprehensive discussion of the various adsorphon equibbrium theories that are available. 

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