Energy Dissipation of Moving Drops on Superhydrophobic and Superoleophobic Surfaces.

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 WS is derived from the observable apparent receding contact angle Θrapp and 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 Ws that 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 Θr and 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.