Effective slip and friction reduction in nanograted superhydrophobic microchannels

Abstract

Enabled by a technology to fabricate well-defined nanogrates over a large area ͑2 ϫ 2 cm 2 ͒, we report the effect of such a surface, in both hydrophilic and hydrophobic conditions, on liquid slip and the corresponding friction reduction in microchannels. The grates are designed to be dense ͑ϳ230 nm pitch͒ but deep ͑ϳ500 nm͒ in order to sustain a large amount of air in the troughs when the grates are hydrophobic, even under pressurized liquid flow conditions ͑e.g., more than 1 bar͒. A noticeable slip ͑i.e., slip length of 100-200 nm, corresponding to 20%-30% reduction of pressure drop in a ϳ3 m high channel͒ is observed for water flowing parallel over the hydrophobic nanogrates; this is believed to be an "effective" slip generated by the nanostrips of air in the grate troughs under the liquid. The effective slip is clearer and larger in flows parallel to the nanograting patterns than in transverse, suggesting that the nanograted superhydrophobic surfaces would not only reduce friction in liquid flows under pressure but also enable directional control of the slip. This paper is the first to use nanoscale grating patterns and to measure their effect on liquid flows in microchannels.

Superhydrophobic drag reduction in laminar flows: a critical review

“…1b). Nevertheless, the slip enhancement was found significant compared with smooth surfaces (Watanabe et al 1999;Ou et al 2004;Choi and Kim 2006a;Choi et al 2006), propelling the superhydrophobic (SHPo) 1 surfaces of Fig. 1c as a potential dragreducing surface for fluidic systems above micrometers.…”

“…If the thickness of the gas layer is h and liquid and gas viscosities are given by η liquid and η gas , the effective slip length δ can be calculated by assuming continuity of shear stress at the liquid-gas interface: δ = h(η liquid /η gas − 1). A slip length of 50 µm is expected if the gas layer is 1-µm-thick air in water at room temperature (Choi et al 2006). However, this ideal configuration is only hypothetical, as a uniform gas film is thermodynamically unstable and cannot be sustained.…”

“…176 Page 2 of 20 Choi et al 2006). According to these expressions, as a rule of thumb, a drag reduction of ~10 % is expected when the slip length is 10 % of the characteristic length scale of the flow system, e.g., the channel height for channel flows.…”

“…However, the numerous experimental studies in the literature have reported (many erroneously, as discussed in Sects. 3.2.5 and 3.3.5) a wide range of slip lengths spanning from tens of nanometers to even millimeters on SHPo surfaces consisting of regular (periodic) structures (Ou et al 2004;Ou and Rothstein 2005;Choi et al 2006;Davies et al 2006;Truesdell et al 2006;Maynes et al 2007;Steinberger et al 2007;Byun et al 2008;Lee et al 2008;Tsai et al 2009;Jung and Bhushan 2010;Lee and Kim 2011a;Kashaninejad et al 2012;Kim and Hidrovo 2012;Maali et al 2012;Karatay et al 2013;Bolognesi et al 2014;Lee and Kim 2014) or random structures (Watanabe et al 1999(Watanabe et al , 2003Gogte et al 2005;Choi and Kim 2006a;Joseph et al 2006;Bhushan et al 2009;Govardhan et al 2009;Shirtcliffe et al 2009;Wang et al 2009;Kim and Hwang 2010;Li et al 2010;Wang and Bhushan 2010;Ming et al 2011;Srinivasan et al 2013). Sometimes orders-of-magnitude differences in the measured slip lengths were reported even on structurally similar SHPo surfaces (e.g., Lee et al 2008vs.…”

“…Reynolds number (Cheng et al 2009;Hyvalouma and Harting 2008), a confinement condition (the channel height being much smaller than the free surface distance between structures) (Philip 1972a;Sbragaglia and Prosperetti 2007a), and a slip on solid patches (Choi et al 2006;Cottin-Bizonne et al 2004;Hendy and Lund 2007;Ybert et al 2007) can affect slip lengths under certain conditions.…”