Laminar flow in a microchannel with hydrophobic surface patterned microribs oriented parallel to the flow direction

Abstract

This paper reports results of an analytical and experimental investigation of the laminar flow in a parallel-plate microchannel with ultrahydrophobic top and bottom walls. The walls are fabricated with microribs and cavities that are oriented parallel to the flow direction. The channel walls are modeled in an idealized fashion, with the shape of the liquid-vapor meniscus approximated as flat. An analytical model of the vapor cavity flow is employed and coupled with a numerical model of the liquid flow by matching the local liquid and vapor phase velocity and shear stress at the interface. The numerical predictions show that the effective slip length and the reduction in the classical friction factor-Reynolds number product increase with increasing relative cavity width, increasing relative cavity depth, and decreasing relative microrib/cavity module length. Comparisons were also made between the zero shear interface model and the liquid-vapor cavity coupled model. The results illustrate that the zero shear interface model underpredicts the overall flow resistance. Further, the deviation between the two models was found to be significantly larger for increasing values of both the relative rib/cavity module width and the cavity fraction. The trends in the frictional pressure drop predictions are in good agreement with experimental measurements made at similar conditions, with greater deviation observed at increasing size of the cavity fraction. Based on the numerical predictions, an expression is proposed in which the friction factor-Reynolds number product may be estimated in terms of the important variables.

Superhydrophobic drag reduction in laminar flows: a critical review

“…This meniscus-induced slip decrease is expected to be more pronounced on microstructures with a larger structural pitch and a higher gas fraction. Also, the confined flow condition (i.e., a small channel height compared with the structural pitch) inside microchannel can contribute to a further decrease in slip length (Maynes et al 2007;Tsai et al 2009) under certain conditions, as predicted by analytical analyses (Sbragaglia and Prosperetti 2007a;Feuillebois et al 2009) and numerical simulation (Cheng et al 2009). Lastly, the circulation of the entrapped gas within the microstructures may have decreased the slip length in some cases significantly, as explained by Busse et al (2013).…”

“…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.…”

“…Well-defined structural features on regular structures make the comparison between experimental data and the theoretical predictions easier, helping to establish the correlation between structural features and slip lengths. The experimentally tested regular structures were of simple patterns such as grates (either parallel or transverse to liquid flow) (Ou et al 2004;Ou and Rothstein 2005;Choi et al 2006;Davies et al 2006;Truesdell et al 2006;Maynes et al 2007;Byun et al 2008;Lee et al 2008;Tsai et al 2009), posts (Ou et al 2004;Ou and Rothstein 2005;Lee et al 2008;Jung and Bhushan 2010;Lee and Kim 2011a;Kim and Hidrovo 2012;Maali et al 2012;Lee and Kim 2014) and holes (Steinberger et al 2007;Kashaninejad et al 2012) as collected in Fig. 5.…”

Development of a Miniature Shear Sensor for Direct Comparison of Skin-Friction Drags

“…However, such a relationship has yet to be established for turbulent flows (Park et al 2013). While the analytical, numerical and experimental results of SHPo drag reduction converged finally for laminar flows (Lauga & Stone 2003;Ou et al 2004;Maynes et al 2007;Woolford et al 2009a), the studies of turbulent flows have mostly been numerical. Assuming ideal circumstances, e.g., no air loss and flat air-water interface, numerical efforts nevertheless have suggested valuable physical insights, such as the possible mechanism of turbulent drag reduction (Min & Kim 2004;Martell et al 2009Martell et al , 2010Busse & Sandham 2012;Park et al 2013), scaling issue (Fukagata et al 2006;Jeffs et al 2010;Busse & Sandham 2012;Park et al 2013), and effects of directional slip (Min & Kim 2004;Fukagata et al 2006;Hasegawa et al 2011;Busse & Sandham 2012).…”

Slip length for transverse shear flow over a periodic array of weakly curved menisci

“…These surfaces reduce friction due to the presence of free surfaces, or menisci, spanning interstitial grooves between protrusions in the substructure of the surface. Much theoretical [3][4][5][6][7][8][9][10][11] , experimental [12][13][14] and numerical work [15][16][17][18] has been done to understand the friction properties of these surfaces. A paper by Philip 3 , which solves a varierty of pertinent mixed boundary value problems, has become a wellknown reference in this area but it only deals with flat menisci and under the assumption that they are shearfree.…”