Modeling the behavior of a drop on a superhydrophobic sheet

The interaction between thin sheets and fluid droplets has recently attracted attention due to its frequent occurrence in natural systems and extensive use in technological applications. Motivated by these applications, this paper focuses on the interaction resulting from a drop that rests at the center of a circular superhydrophobic thin sheet. We investigate how the size and surface tension of the drop, together with the elastic and geometric parameters of the sheet, determine the overall deformation of the system. To this end, we formulate an analytical model based on energetic considerations that can predict the mutual interaction between the drop and the sheet. We show that the deformation of the sheet outside the contact region is almost unaffected by the exact shape of the drop, and thus mimics the problem of a rigid indentation. However, inside the contact region, there is a strong coupling between the drop's shape and the sheet's deformation. We derive analytical predictions for the size of the contact region and show that its shape comprises a constant curvature. These findings are in good quantitative agreement with the numerical minimization of the energy.