A Volume-Corrected Wenzel Model

The
Wenzel model, commonly used for predicting the equilibrium
contact angle (CA) of drops which penetrate the asperities of a rough
surface, does not account for the liquid volume stored in the asperities.
Interestingly, many previous experimental and molecular dynamics studies
have noted discrepancies between observed CAs and those predicted
by the Wenzel model because of this neglected liquid volume. Here,
we apply a thermodynamic model to wetting of periodically patterned
surfaces to derive a volume-corrected Wenzel equation in the limit
of small pattern wavelength (compared to drop size). We show that
the corrected equilibrium CA is smaller than that predicted by the
Wenzel equation and that the reduction in CA can be significant when
the liquid volume within the asperities becomes non-negligible compared
to the total droplet volume. In such cases, the corrected CAs agree
reasonably well with experimental observations and results of molecular
dynamics simulations reported in previous studies.