The Kelvin equation describes the change in vapour pressure due to a curved liquid/vapor interface (meniscus) with radius (for example, in a capillary or over a droplet). The Kelvin equation is used for determination of pore size distribution of a porous medium using adsorption porosimetry. The equation is named in honor of William Thomson, also known as Lord Kelvin.
The Kelvin equation may be written in the form
where is the actual vapour pressure, is the saturated vapour pressure, is the surface tension, is the molar volume, is the universal gas constant, is the radius of the droplet, and is temperature.
Equilibrium vapor pressure depends on droplet size.
- If, then liquid evaporates from the droplets
- If, then the gas condenses on to the droplets increasing their volumes
As increases, decreases and the droplets grow into bulk liquid.
If we now cool the vapour, then decreases, but so does . This means increases as the liquid is cooled. We can treat and as approximately fixed, which means that the critical radius must also decrease. The further a vapour is supercooled, the smaller the critical radius becomes. Ultimately it gets as small as a few molecules and the liquid undergoes homogeneous nucleation and growth.
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