Pressure and partial wetting effects on superhydrophobic friction reduction in microchannel flow

Abstract

Friction reduction in microchannel flows can help alleviate the inherently taxing pumping power requirements associated with the dimensions involved. One possible way of achieving friction reduction is through the introduction of surface microtexturing that can lead to a superhydrophobic Cassie-Baxter state. The Cassie-Baxter state is characterized by the presence of air pockets within the surface microtexturing believed to act as an effective "shear free" (or at least shear reduced) layer, decreasing the overall friction characteristics of the surface. Most work in this area has concentrated on optimizing the surface microtexturing geometry to maximize the friction reduction effects and overall stability of the Cassie-Baxter state. However, less attention has been paid to the effects of partially wetted conditions induced by pressure and the correlation between the liquid-gas interface location within the surface microtexturing and the microchannel flow characteristics. This is mainly attributed to the difficulty in tracking the interface shape and location within the microtexturing in the typical top-down view arrangements used in most studies. In this paper, a rectangular microchannel with regular microtexturing on the sidewalls is used to visualize and track the location of the air-water interface within the roughness elements. While visually tracking the wetting conditions in the microtextures, pressure drops versus flow rates for each microchannel are measured and analyzed in terms of the non-dimensional friction coefficient. The frictional behavior of the Poiseuille flow suggests that (1) the air-water interface more closely resembles a no-slip boundary rather than a shearfree one, (2) the friction is rather insensitive to the degree of microtexturing wetting, and (3) the fully wetted (Wenzel state) microtexturing provides lower friction than the non-wetted one (Cassie state), in corroboration with observations (1) and (2).

Superhydrophobic drag reduction in laminar flows: a critical review

“…Although the liquid intrusion into the surface structures reduces the slip length as reported in Sect. 2.2, additional liquid passage created by the intruded liquid might increase the flow rate through microchannel, leading to the overestimation of the slippage effect (Kim and Hidrovo 2012;Lee and Kim 2014). Also, the effective liquid viscosity might undergo a slight change during measurement depending on the solubility of gas in water .…”

“…4a. The slip length can be deduced from the flow rate increase or pressure drop decrease by the slip (Watanabe et al 1999;Ou et al 2004;Choi et al 2006;Jung and Bhushan 2010;Shirtcliffe et al 2009;Kim and Hwang 2010;Kashaninejad et al 2012;Kim and Hidrovo 2012;Lee and Kim 2014). For example, in a microchannel with a circular cross section, the volume flow rate Q driven by the pressure gradient dP/dx can be expressed as a function of slip length δ as shown in the following equation.…”

“…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.…”

Effective slip lengths for immobilized superhydrophobic surfaces

“…Indeed, by changing the normalized groove width 2c/L in the interval [0, 0.47] (where Teo & Khoo (2016) have shown the formula of Davis & Lauga (2009) to be 10 % accurate), we find that for downward protrusion angles around 80 • , the surface can be almost twice as slippery if immobilized as if it is free of shear (cf. Kim & Hidrovo 2012). In confined longitudinal microchannel flows with a lower superhydrophobic wall, say, the effective slip length is usually defined by equating the pressure-driven flux through the channel with that in a channel having a Navier slip condition, λ NS dw/dy = w, imposed on the lower wall; the value of λ NS for which these fluxes are equal 825 R2-10 (for the same driving pressure gradient) is the effective slip length.…”

“…Kim & Hidrovo (2012) performed experiments in a rectangular microchannel with regular sidewall patterning to visualize the location of the air-water interface within the roughness elements. One of their principal conclusions from this study of Poiseuille flow through the microchannel was that the air-water interface more closely resembles a no-slip boundary than a shear-free one, and that a Wenzel state can have better friction reducing properties than the Cassie state.…”