Effective velocity boundary condition at a mixed slip surface

M. Sbragaglia; A. Prosperetti

doi:10.1017/s0022112007005149

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Effective velocity boundary condition at a mixed slip surface

M. Sbragaglia·A. Prosperetti

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

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M. Sbragaglia, A. Prosperetti. 2006-07-01. Effective velocity boundary condition at a mixed slip surface. https://doi.org/10.1017/s0022112007005149

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