Superhydrophobicity on hairy surfaces

Abstract: We investigate the wetting properties of surfaces patterned with fine elastic hairs, with an emphasis on identifying superhydrophobic states on hydrophilic hairs. We formulate a two dimensional model of a large drop in contact with a row of equispaced elastic hairs and, by minimising the free energy of the model, identify the stable and metastable states. In particular we concentrate on "partially suspended" states, where the hairs bend to support the drop -- singlet states where all hairs bend in the same direction, and doublet states where neighbouring hairs bend in opposite directions -- and find the limits of stability of these configurations in terms of material contact angle, hair flexibility, and system geometry. The drop can remain suspended in a singlet state at hydrophilic contact angles, but doublets exist only when the hairs are hydrophobic. The system is more likely to evolve into a singlet state if the hairs are inclined at the root. We discuss how, under limited circumstances, the results can be modified to describe an array of hairs in three dimensions. We find that now both singlets and doublets can exhibit superhydrophobic behaviour on hydrophilic hairs. We discuss the limitations of our approach and the directions for future work.