Young-Laplace equation for the pressure difference across a curved surface

3 Young-Laplace equation for the pressure difference across a curved surface 

The Young-Laplace equation gives the pressure difference (inside-outside) across a curved surface. For spherical droplets, the equation is written as (see Appendix 4.1 for the derivation)  

The curvature is very important. Water droplets with radius of 10 pm show a pressure difference of 0.15 bar, which is greatly increased to 15 bar for a radius of 100 nm and 1500 bar if the radius is at the lower limit of coUoids (1 nm). 

There are other forms for other curved surfaces, e.g. for air bubbles the 2-factor in Equation 4.4 should 

Note also the convention that the radius of curvature is measured in the liquid phase and is thus positive for a liquid drop but negative for a gas bubble. This means - see also later the Kelvin equation - that the vapour pressure of a liquid in a small drop is higher than for a flat surface but is lower in a bubble compared to a flat surface. 

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