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Slipping free jet flow near channel exit at moderate Reynolds number for large slip length

Published online by Cambridge University Press:  22 March 2016

Roger E. Khayat
Roger E. Khayat*
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9
*
†Email address for correspondence: [email protected]
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Abstract

The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. The ratio of the slip length to the channel width $S$ is assumed to be of order one, one order of magnitude larger than the perturbation parameter ${\it\varepsilon}=Re^{-1/2}$, $Re$ being the Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer of the free surface, with the outer layer extending to the jet centreline. The inner-layer thickness grows like $\sqrt{x/Re\,S}$. A slipping jet is found to contract like $x/Re$ very near and far from the channel exit, but does not have a definite behaviour in between compared to $(x/Re)^{1/3}$ for an adhering jet, $x$ being the distance from the channel exit. Eventually, the jet reaches uniform conditions far downstream. As in the case of entry flow, there is a rapid departure in flow behaviour for a slipping jet from the $S=0$ limit. This rapid change is notably observed in the drop of boundary-layer thickness, increase in exit and relaxation lengths as well as in jet width with slip length. Finally, the connections with microchannel and hydrophobic flows are highlighted.

JFM classification

Boundary Layers: Boundary Layers Interfacial Flows (free surface): Contact lines Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 667 - 708
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Copyright
© 2016 Cambridge University Press 

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