title: Energy Dissipation of Moving Drops on Superhydrophobic and Superoleophobic Surfaces.
abstract: A water drop moving on a superhydrophobic surface or an oil drop moving on a superoleophobic surface dissipates energy by pinning/depinning at nano- and microprotrusions. Here, we calculate the work required to form, extend, and rupture capillary bridges between the protrusions and the drop. The energy dissipated at one protrusion WSis derived from the observable apparent receding contact angle Θrappand the density of protrusions n by Ws= γ(cos Θrapp+ 1)/n, where γ is the surface tension of the liquid. To derive an expression for Wsthat links the microscopic structure of the surface to apparent contact angles, two models are considered: A superhydrophobic array of cylindrical micropillars and a superoleophobic array of stacks of microspheres. For a radius of a protrusion R and a receding materials contact angle Θr, we calculate the energy dissipated per protrusion as Ws= πγR2[A - ln(R/κ)]f(Θr). Here, A = 0.60 for cylindrical micropillars and 2.9 for stacks of spheres. κ is the capillary length. f(Θr) is a function which depends on Θrand the specific geometry, f ranges from ≈0.25 to 0.96. Combining both equations above, we can correlate the macroscopically observed apparent receding contact angle with the microscopic structure of the surface and its material properties.
authors.affiliation: Max Planck Institute for Polymer Research , Ackermannweg 10, 55128 Mainz, Germany.
authors.forename: Hans-Jürgen
authors.identifier: 0000-0001-5391-2618
authors.initials: HJ
authors.lastname: Butt
authors.affiliation: Max Planck Institute for Polymer Research , Ackermannweg 10, 55128 Mainz, Germany.
authors.forename: Nan
authors.initials: N
authors.lastname: Gao
authors.affiliation: Department of Physics, University of Ioannina , P.O. Box 1186, GR-45110 Ioannina, Greece.
authors.forename: Periklis
authors.initials: P
authors.lastname: Papadopoulos
authors.affiliation: Max Planck Institute for Polymer Research , Ackermannweg 10, 55128 Mainz, Germany.
authors.forename: Werner
authors.initials: W
authors.lastname: Steffen
authors.affiliation: Max Planck Institute for Polymer Research , Ackermannweg 10, 55128 Mainz, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Kappl
authors.affiliation: Max Planck Institute for Polymer Research , Ackermannweg 10, 55128 Mainz, Germany.
authors.forename: Rüdiger
authors.initials: R
authors.lastname: Berger