The Shape of Floating Lenses

These lengths are associated with the A/air, B/air, and A/B interfaces, respectively. 

For very small droplets, gravity is negligible and Laplace s internal pressure is constant. Surfaces have a uniform curvature. A droplet is made of two spherical caps that satisfy Neumann s vector relation all along the triple line  

The sinking depth e is such that Archimedes force offsets the weight of the drop. It is possible to relate e and e by writing that the hydrostatic pressures on either side of the liquid/liquid interface (assumed planar) are equal  

If Pb PAi the lens is immersed much like an iceberg, whereas it protrudes if PA PB- 

Upon minimizing the energy F e) at constant volume, one obtains 

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