Effect of gravity in the Cassie-to-Wenzel transition on a micropatterned surface
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Research Letter
Effect of gravity in the Cassie-to-Wenzel transition on a micropatterned surface Arash Azimi and Ping He
, Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA
Address all correspondence to Ping He at [email protected] (Received 3 October 2019; accepted 5 December 2019)
Abstract When the Cassie–Baxter and Wenzel states coexist for a liquid droplet on a micropatterned surface, the Cassie-to-Wenzel transition takes place if the energy barrier is overcome. Although multiple metastable states coexist due to the micropattern, this paper presents a simple Cassie-toWenzel transition of a 2 µL water droplet on a particular micropillared surface: When the droplet is gently deposited above the surface, it equalizes to the Cassie state at zero gravity; however, it transitions to the Wenzel state at the terrestrial gravity, in which the gravitational potential energy overcomes the energy barrier between the Cassie and Wenzel states.
Introduction Wetting of a liquid droplet on rough surfaces has two main states: the Wenzel state and the Cassie–Baxter state (or the Cassie state for short), whose apparent contact angle can be predicted by the Wenzel[1] or Cassie–Baxter[2] equations, respectively. In the Wenzel state, a liquid droplet fully wets the roughness structures, while in the Cassie state, the droplet sits on top of the roughness structures. The Wenzel equation is cos uap = r cos uY
(1)
where θap is the apparent contact angle, r is the roughness ratio, and θY is the Young’s angle. The Cassie–Baxter equation is cos uap = f cos uY + f − 1
(2)
where f is the area fraction of the liquid–gas interface occluded by the porous structures. As a specific type of rough surfaces, wetting on micropatterned surfaces has been studied since the 1990s.[3,4] The results of the Wenzel and Cassie–Baxter equations were found to be the stable states for a liquid droplet on micropatterned surfaces.[5] The Wenzel and Cassie states could coexist on the same micropatterned surface in certain conditions.[6] While the two states are coexisting, there are two energy barriers between the two states, the Cassie-to-Wenzel barrier and the Wenzel-to-Cassie barrier. A theoretical study revealed that the gravitational potential energy could help overcome the energy barrier of the Cassie-to-Wenzel transition.[7] Note that the Cassie-to-Wenzel transition is irreversible because the Wenzel-to-Cassie barrier is much larger than the Cassieto-Wenzel barrier.[8]
A Gibbs energy analysis revealed that either the depinning transition or the sag transition could overcome the Cassieto-Wenzel energy barrier.[9] Multiple metastable Wenzel states were studied on grooved surfaces.[10] 2D/3D micropillared configurations were modeled to study the Cassie state’s stability.[11] Circular micropillared surfaces were studied for the Cassie-to-Wenzel transition.[12,13] We have recently studied the Gibbs energy distributions in the droplet wetting on micropatterned surfaces indicating that the Cassie-to-Wenzel transition is strongly rela
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