Sbragaglia, M.Prosperetti, Andrea2020-03-102020-03-107/1/2006Copyright 2007 Journal of Fluid Mechanics. This is a pre-print version of a published paper that is available at: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/effective-velocity-boundary-condition-at-a-mixed-slip-surface/D4D9D52D85D93B6804F0267201FB894F Recommended citation: Sbragaglia, M., and A. Prosperetti. "Effective velocity boundary condition at a mixed slip surface." arXiv preprint physics/0607003. This item has been deposited in accordance with publisher copyright and licensing terms and with the author’s permission.https://hdl.handle.net/10657/6127This paper studies the nature of the effective velocity boundary conditions for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that, to lowest order in the area fraction ? covered by free-slip regions with characteristic size a, a macroscopic Navier-type slip condition emerges with a slip length of the order of a?. The study is motivated by recent experiments which suggest that gas nano-bubbles may form on solid walls and may be responsible for the appearance of a partial slip boundary conditions for liquid flow. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called “lotus effect”.en-USN/Aarticle