8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

Thu 811:10-14:00P7.75Drag reduction on a perfectly superhydrophobic sphereGlen McHale 1 and Michael Newton 11 Nottingham Trent University, School of Science and Technology, Clifton Lane NG11 8NS,Nottingham, United KingdomDroplets ball-up and roll-off superhydrophobic surfaces due to the reduced contact with the solid.This concept of a ”slippy” surface is not obviously related to the ability of an immersed surfaceto reduce drag. Nonetheless, experiments suggest that drag reduction may occur for flow of waterthrough millimetric diameter superhydrophobic copper tubes [1]. Experiments on the terminal velocityof macroscopic spheres also suggest that surfaces able to retain a layer of air when immersedcan reduce drag compared to those that do not [2, 3]. However, not all immersed superhydrophobicsurfaces resulted in a drag reduction and at small surface structure length scales drag reductionvanished. It appears experimentally that a plastron (i. e. surface retained layer of air [4, 5]) controlsdrag reduction and that the length scale of the topography is fundamental to the effectivenessof the plastron. Here, we consider an analytical model for low Reynold’s number flow around acompound spherical fluid object [6]. We match boundary conditions across a plastron and showthe resulting flow patterns, which result in apparent slip. When a plastron-retaining sphere witha superhydrophobic surface is considered as a compound object with a solid core surrounded bya thin shell of air, drag reduction can occur compared to the solid core without a plastron. Thebalance between the thickness of plastron providing an effective lubricating circulation and an increasedcross-section for drag is described.[1] N. J. Shirtcliffe et al. , ACS Appl. Mater. Interf. 1, 1316 (2009).[2] G. McHale et al. , Appl. Phys. Lett. 94, art. 064104 (2009).[3] G. McHale et al. , Soft Matter 6, 714 (2010).[4] N. J. Shirtcliffe et al. , Appl. Phys. Lett. 89, art 104600 (2006).[5] M. R. Flynn and J. W. M. Bush, J. Fluid Mech. 608, 275 (2008).[6] E. Rushton and G. A. Davies, Int. J. Multiph. Flow 9, 337 (1983).75