Kelvin Equation

Synonyms

Particle size-solubility relation

Definition

The Kelvin equation describes the effect of droplet or particle size on the solubility of the disperse phase. The difference in chemical potential between different-sized droplets was given by Lord Kelvin:

$$ \rm S(r) = S(\infty )\exp \left( {\frac{{2\gamma {{V}_m}}}{{rRT}}} \right), $$

where S(r) is the solubility surrounding a particle or droplet of radius r, S(∞) is the bulk solubility, γ is the interfacial tension (for solid particles γ is replaced by σ, the solid-liquid interfacial tension), V_m is the molar volume of the dispersed phase, R is the gas constant, and T is the absolute temperature. The quantity (2 γ V_m/ RT) is termed the characteristic length. It has an order of ∼ 1 nm or less, indicating that the difference in solubility of a 1-μm droplet is of the order of 0.1 % or less. The Kelvin equation shows that the smaller droplets or particles are more soluble than the larger ones and with time, they tend to dissolve (by...