Kelvin equation
The Kelvin equation describes the change in vapour pressure due to a curved liquid/vapor interface (meniscus
The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension. It can be either convex or concave. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the material of the...

) with radius (for example, in a capillary
Capillaries are the smallest of a body's blood vessels and are parts of the microcirculation. They are only 1 cell thick. These microvessels, measuring 5-10 μm in diameter, connect arterioles and venules, and enable the exchange of water, oxygen, carbon dioxide, and many other nutrient and waste...

 or over a droplet). The Kelvin equation is used for determination of pore size distribution of a porous medium
Porous medium
A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

 using adsorption porosimetry
BET theory
BET theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of a material...

. The equation is named in honor of William Thomson
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

, commonly 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
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

, is the molar volume
Molar volume
The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...

, is the universal gas constant, is the radius of the droplet, and is temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...


Equilibrium vapor pressure depends on droplet size.
If , then liquid evaporates from the droplets.

If , then the gas condenses onto 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
Nucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form by way of nucleation in liquids are gaseous bubbles, crystals or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by nucleation...

and growth.
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