Effective velocity boundary condition at a mixed slip surface

Abstract

This 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 $\beta$ covered by free-slip regions with characteristic size $a$, a macroscopic Navier-type slip condition emerges with a slip length of the order of $a\beta$. 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''.

14 pages, 1 figure

References in corpus (1)

• Slippage of water past superhydrophobic carbon nanotube forests in microchannels

Cited by in corpus (4)

• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
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• Boundary induced non linearities at small Reynolds Numbers
• Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions