Appendix: Liquid Solder Hydrostatic Pressure

For a small droplet, the surface curvature is high enough that the hydrostatic pressure is significantly higher in the liquid than in the surrounding vapor. The Surface Evolver calculates this pressure as the Lagrange multiplier of the volume constraint, and the components of force exerted on the fiber by this pressure are found by multiplying the pressure by the area bounded by the projection of the triple line in each dimension. For example, the force in the y-direction is given by

$$\vec{F}=P\oint_{TL}z\hat{x}\cdot\vec{d\ell}$$ (8)

where $\hat{x}$ is the unit vector in the x-direction.