Microstructured superhydrorepellent surfaces: Effect of drop pressure on fakir-state stability and apparent contact angles

TL;DR

This paper develops a generalized model to analyze how drop pressure affects contact angles and impalement transitions on microstructured superhydrophobic surfaces with different pillar shapes, revealing design strategies for optimal repellency.

Contribution

It introduces a generalized Cassi-Baxter equation incorporating drop pressure effects and compares impalement and detachment pressures across pillar geometries.

Findings

Conical pillars are prone to impalement but easily detach due to low pull-off pressure.

Cylindrical pillars with conical tips balance high resistance to impalement and easy detachment.

Drop pressure significantly affects apparent contact angles depending on pillar shape.

Abstract

In this paper we present a generalized Cassi-Baxter equation to take into account the effect of drop pressure on the apparent contact angle theta_{app}. Also we determine the limiting pressure p_{W} which causes the impalement transition to the Wenzel state and the pull-off pressure p_{out} at which the drop detaches from the substrate. The calculations have been carried out for axial-symmetric pillars of three different shapes: conical, hemispherical topped and flat topped cylindrical pillars. Calculations show that, assuming the same pillar spacing, conical pillars may be more incline to undergo an impalement transition to the Wenzel state, but, on the other hand, they are characterized by a vanishing pull-off pressure which causes the drop not to adhere to the substrate and therefore to detach very easily. We infer that this property should strongly reduce the contact angle hysteresis as experimentally osberved in Ref. \cite{Martines-Conical-Shape}. It is possible to combine large resistance to impalement transition (i.e. large value of p_{W}) and small (or even vanishing) detaching pressure p_{out} by employing cylindrical pillars with conical tips. We also show that depending on the particular pillar geometry, the effect of drop pressure on the apparent contact angle theta_{app} may be more or less significant. In particular we show that in case of conical pillars increasing the drop pressure causes a significant decrease of theta_{app} in agreement with some experimental investigations \cite{LafunaTransitio}, whereas theta_{app} slightly increases for hemispherical or flat topped cylindrical pillars.