Predicting contact-angle hysteresis from measured surface defect statistics

For a liquid on a solid with chemical or topographic defects of density $n_d$, size $d$ and wettability contrast $f_d$, all measured independently, predict the hysteresis $\cos\theta_r-\cos\theta_a$, including the crossover between dilute defects that each pin the line independently and dense defects that pin it collectively. An answer is a formula or simulation protocol that predicts hysteresis within experimental error for surfaces with designed disorder, with no fitted parameters.

Hysteresis measurements on lithographically patterned surfaces with controlled $n_{d}, d\ \text{and}\ f_{d}$, compared with blind predictions from the elastic-line model.