Profile of a large drop
From Soft-Matter
In class we derived the profile <math>z(x)</math> of a large drop as being:
where we had defined <math>e</math> as being the maximum height of the drop:
and <math>\kappa=\sqrt{\frac{\rho g}{\sigma_{lv}}}</math> was the inverse capillary length.
To visualize what the edge of a large drop then looks like, you can use the following two MATLAB programs, which will solve and plot the above differential equation. Figure 1 also shows what some of these plots look like.
In class we had a brief discussion as to the nature of the drop's periphery on superhydrophobic surfaces. In the superhydrophobic limit (i.e., as <math>\theta_e</math> approaches <math>180^{\circ}</math>