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

In this paper we present a generalized Cassie-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 inclined 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 observed in Martines et al (2005 Nano Lett. 5 2097-103). 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 the case of conical pillars increasing the drop pressure causes a significant decrease of theta(app) in agreement with some experimental investigations (Lafuma and Quere 2003 Nat. Mater. 2 457), whereas theta(app) slightly increases for hemispherical or flat-topped cylindrical pillars.