Vapour pressure Young-Laplace equation

As with all thermodynamic relations, the Kelvin equation may be arrived at along several paths. Since the occurrence of capillary condensation is intimately, bound up with the curvature of a liquid meniscus, it is helpful to start out from the Young-Laplace equation, the relationship between the pressures on opposite sides of a liquid-vapour interface. 

The Young-Laplace equation (3.4/3.5) shows that, pA>pB, the pressure inside a bubble or drop exceeds that outside. For a sphere, Ap=pA - Pb = 2y/R, so that Ap varies with the radius, R. Thus the vapour pressure of a drop should be higher, the smaller the drop. This is shown by a related equation, the Kelvin equation [13,26], which is described here. 

Equation (3.6) is called Young-Laplace equation, in which R is the harmonic mean of the principal radii of curvature. The capillary pressure promotes the release of atoms or molecules from the particle surface. This leads to a decrease of the equilibrium vapour pressure with increasing droplet size Kelvin equation) ... 

The most important application of the Young-Laplace equation is possibly the derivation of the Kelvin equation. The Kelvin equation gives the vapour pressure of a curved surface (droplet, bubble), P, compared to that of a flat surface, P °. The vapour pressure (P) is higher than that of a flat surface for droplets but lower above a liquid in a capillary. The Kelvin equation is discussed next. 

The Kelvin equation is derived from the Young-Laplace equation and the principles of phase equilibria. It gives the vapour pressure, P, of a droplet (curved surface) over the ordinary vapour pressure (P ) for a flat surface (see Appendix 4.2 for the derivation) ... 

Equation [7.15] gives the pressure drop that occurs on crossing the liquid-vapour interface in the positive direction, and is known as the Laplace-Young equation. When ri andr2 are both positive Ap is positive, i.e. pi > p2, and there is a decrease in pressure on... 

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