Effective velocity boundary condition at a mixed slip surface

M. Sbragaglia, Andrea Prosperetti

Research output: Contribution to journalArticleAcademicpeer-review

62 Citations (Scopus)

Abstract

This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for arbitrary fractional area coverage β. As an example, the general theory is applied to the low-β limit and this result is extended heuristically to finite β with a resulting slip length proportional to aβ/(1 − β), where a is a characteristic size of the islands. A specification of the nature of the free-slip islands is not required in the analysis. They could be nano-bubbles, as suggested by recent experiments, or hydrophobic surface patches. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called ‘lotus effect’
Original languageUndefined
Pages (from-to)435-451
Number of pages17
JournalJournal of fluid mechanics
Volume578
DOIs
Publication statusPublished - 2007

Keywords

  • METIS-240471
  • IR-74879

Cite this

@article{93dad86fdc894e20869621340c977f09,
title = "Effective velocity boundary condition at a mixed slip surface",
abstract = "This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for arbitrary fractional area coverage β. As an example, the general theory is applied to the low-β limit and this result is extended heuristically to finite β with a resulting slip length proportional to aβ/(1 − β), where a is a characteristic size of the islands. A specification of the nature of the free-slip islands is not required in the analysis. They could be nano-bubbles, as suggested by recent experiments, or hydrophobic surface patches. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called ‘lotus effect’",
keywords = "METIS-240471, IR-74879",
author = "M. Sbragaglia and Andrea Prosperetti",
year = "2007",
doi = "10.1017/S0022112007005149",
language = "Undefined",
volume = "578",
pages = "435--451",
journal = "Journal of fluid mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

Effective velocity boundary condition at a mixed slip surface. / Sbragaglia, M.; Prosperetti, Andrea.

In: Journal of fluid mechanics, Vol. 578, 2007, p. 435-451.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Effective velocity boundary condition at a mixed slip surface

AU - Sbragaglia, M.

AU - Prosperetti, Andrea

PY - 2007

Y1 - 2007

N2 - This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for arbitrary fractional area coverage β. As an example, the general theory is applied to the low-β limit and this result is extended heuristically to finite β with a resulting slip length proportional to aβ/(1 − β), where a is a characteristic size of the islands. A specification of the nature of the free-slip islands is not required in the analysis. They could be nano-bubbles, as suggested by recent experiments, or hydrophobic surface patches. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called ‘lotus effect’

AB - This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for arbitrary fractional area coverage β. As an example, the general theory is applied to the low-β limit and this result is extended heuristically to finite β with a resulting slip length proportional to aβ/(1 − β), where a is a characteristic size of the islands. A specification of the nature of the free-slip islands is not required in the analysis. They could be nano-bubbles, as suggested by recent experiments, or hydrophobic surface patches. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called ‘lotus effect’

KW - METIS-240471

KW - IR-74879

U2 - 10.1017/S0022112007005149

DO - 10.1017/S0022112007005149

M3 - Article

VL - 578

SP - 435

EP - 451

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

ER -