Structured Surfaces for a Giant Liquid Slip

Superhydrophobic drag reduction in laminar flows: a critical review

“…Despite its relatively low accuracy (>1 µm in measurable slip length), the commercial rheometer has shown to be a convenient tool when measuring a (8) Q = − πr 4 8η dP dx 1 + 4δ r large slip length (e.g., >5 µm), as shown in Fig. 4c (Choi and Kim 2006a;Truesdell et al 2006;Lee et al 2008;Li et al 2010;Ming et al 2011;Lee and Kim 2011a;Srinivasan et al 2013). Not being pressure-driven, the typical surface structures are not intruded by the liquid.…”

“…Following early work (Philip 1972a, b), many analytical models about slip lengths on simple SHPo surfaces have been developed (Lauga and Stone 2003;Ybert et al 2007;Sbragaglia and Prosperetti 2007a, b;Davis and Lauga 2009a, b;Feuillebois et al 2009;Belyaev and Vinogradova 2010a, b;Davis and Lauga 2010;Asmolov and Vinogradova 2012;Cottin-Bizonne et al 2012) and corroborated by numerical simulations (Cottin-Bizonne et al 2003Priezjev et al 2005;Hendy and Lund 2007;Biben and Joly 2008;Hyvalouma and Harting 2008;Teo and Khoo 2008;Cheng et al 2009;Wang 2009, 2010;Teo and Khoo 2010). By fabricating near-perfect microstructures in an extremely clean condition, Lee et al (2008) succeeded to measure the slip length as a function of surface features, finally verifying the early theoretical models (Lauga and Stone 2003;Ybert et al 2007) quantitatively and bringing a conclusion to the issue.…”

“…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.…”

“…Another indirect approach to slip measurement is to measure shear stress or frictional drag on a SHPo surface (Choi and Kim 2006a;Truesdell et al 2006;Steinberger et al 2007;Lee et al 2008;Bhushan et al 2009;Govardhan et al 2009;Wang et al 2009;Li et al 2010;Lee and Kim 2011a;Ming et al 2011;Maali et al 2012;Srinivasan et al 2013). Despite its relatively low accuracy (>1 µm in measurable slip length), the commercial rheometer has shown to be a convenient tool when measuring a (8) Q = − πr 4 8η dP dx 1 + 4δ r large slip length (e.g., >5 µm), as shown in Fig.…”

“…Then, the resultant torque is used to estimate a slip length. In this cone and plate configuration, the relationship between the torque and slip length is given by the following equation (Lee et al 2008). …”