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

Abstract

In this paper we present a generalized Cassie–Baxter equation to takeinto account the effect of drop pressure on the apparent contact angleθapp. Also we determinethe limiting pressure pW which causes the impalement transition to the Wenzel state and the pull-off pressurepout at which the drop detaches from the substrate. The calculations have been carried out foraxial-symmetric pillars of three different shapes: conical, hemispherical-topped andflat-topped cylindrical pillars. Calculations show that, assuming the same pillar spacing,conical pillars may be more inclined to undergo an impalement transition to the Wenzelstate, but, on the other hand, they are characterized by a vanishing pull-off pressure whichcauses the drop not to adhere to the substrate and therefore to detach very easily. Weinfer that this property should strongly reduce the contact angle hysteresis asexperimentally observed in Martines et al (2005 Nano Lett. 5 2097–103). It ispossible to combine large resistance to impalement transition (i.e. large value ofpW) and small (or even vanishing) detaching pressurepout by employing cylindrical pillars with conical tips. We also show that, depending on theparticular pillar geometry, the effect of drop pressure on the apparent contact angleθapp may be more or less significant. In particular we show that in the case ofconical pillars increasing the drop pressure causes a significant decrease ofθapp inagreement with some experimental investigations (Lafuma and Quéré 2003 Nat. Mater. 2 457), whereasθapp slightly increases for hemispherical or flat-topped cylindrical pillars.