On the degree of boundary slip over nonplanar surfaces
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RESEARCH PAPER
On the degree of boundary slip over nonplanar surfaces Ali Dinler • Robert W. Barber • David R. Emerson Stefan K. Stefanov • Kamil Orucoglu
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Received: 25 December 2012 / Accepted: 28 March 2013 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract The breakdown of the no-slip boundary condition at a fluid–solid interface has been recognized in micro/ nanofluidics for many years. However, the relationship between the curvature of the surface and the degree of boundary slip has not been understood sufficiently well. The present study reveals that the degree of slip depends effectively on the surface curvature, which is having an opposing effect over rotating concave and convex surfaces. The results show that as surface curvature increases, the boundary slip becomes negligible over a concave surface, while it becomes increasingly important over a convex surface. In addition, boundary slip formulae are proposed that can accurately predict the boundary slips over convex and concave surfaces. These formulae are found to be in very good agreement with DSMC data for a range of accommodation coefficients and boundary curvatures. The present study then explains the mechanism of the intriguing phenomenon of velocity inversion which has, until the present study, often been mistakenly attributed solely to the effects of boundary curvature.
A. Dinler (&) Department of Mathematics, Istanbul Medeniyet University, 34700 Istanbul, Turkey e-mail: [email protected] R. W. Barber D. R. Emerson STFC Daresbury Laboratory, Centre for Microfluidics and Microsystems Modelling, Warrington WA4 4AD, UK S. K. Stefanov Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Sofia 1113, Bulgaria K. Orucoglu Department of Mathematics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
Keywords Boundary slip Curvature effects Velocity inversion Gas microflows
1 Introduction The breakdown of the no-slip boundary condition at a solid–fluid interface has been reported in many studies (Vinogradova 1999; Zhu and Granick 2002; Majumder et al. 2005; Holt et al. 2006; Whitby and Quirke 2007) with the phenomenon being observed in micro-scale flows in both Newtonian and non-Newtonian liquids, and in gaseous flows. A theoretical understanding of boundary slip is clearly of great importance in the design of microfluidic devices. However, accounting for the complex interactions between the factors that affect the boundary slip (such as surface roughness, the wettability of the surface, the presence of nanobubbles/gaseous layers and the surface curvature) remains a formidable challenge, as reviewed by Neto et al. (2005) and Lauga et al. (2007). The phenomenon of boundary slip is frequently encountered in micro/nanofluidic gas-phase flows (Zhang et al. 2012; Duan 2012; Kandemir and Kaya 2012; Prabha and Sathian 2012; Darbandi and Roohi 2011; Li et al. 2011). As the length scales of microfluidic devices are decreased towards the micro/nanoscale, the degree of slip can substantially alter the flow behavi
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