Super-hydrophobic textured surfaces reduce hydrodynamic drag in pressure-driven laminar flows in micro-channels. However, despite the wide usage of non-Newtonian liquids in microfluidic devices, the flow behaviour of such liquids was rarely examined so far in the context of friction reduction in textured super-hydrophobic micro-channels. Thus, we have investigated the influence of topologically different rough surfaces on friction reduction of shear-thinning liquids in micro-channels. First, the friction factor ratio (a ratio of friction factor on a textured surface to a plain surface) on generic surface textures, such as posts, holes, longitudinal and transverse ribs, was estimated numerically over a range of Carreau number as a function of microchannel constriction ratio, gas fraction and power-law exponent. Resembling the flow behaviour of Newtonian liquids, the longitudinal ribs and posts have exhibited significantly less flow friction than the transverse ribs and holes while the friction factor ratios of all textures has exhibited non-monotonic variation with the Carreau number. While the minima of the friction factor ratio were noticed at a constant Carreau number irrespective of the microchannel constriction ratio, the minima have shifted to a higher Carreau number with an increase in the power-law index and gas fraction. Experiments were also conducted with aqueous Xanthan Gum liquids in micro-channels. The flow enhancement (the flow rate with super-hydrophobic textures with respect to a smooth surface) exhibited a non-monotonic behaviour and attenuated with an increase in power-law index tantamount to simulations. The results will serve as a guide to design frictionless micro-channels when employing non-Newtonian liquids.

Surface texturing at the micro/nanolevel allows air to be trapped in sufficiently small cavities, thereby reducing the flow resistance over the surface in the laminar regime. The nature of the liquid–gas meniscus plays an important role in defining the boundary condition and it depends on the flow conditions and geometrical properties of textures. In the present work, we employ the unsteady volume of fluid model to investigate the behavior of the liquid–gas meniscus for ridges arranged normal to the flow direction to substantiate the frictional resistance of flow in a microchannel. It is found that the assumption of ‘zero shear stress’ at the liquid–gas interface grossly overpredicts the effective slip length with meniscus curvature and local partial slip length playing the dominant role. Numerical simulations performed in the laminar regime (20 < Re < 120) over single layered ridges normal to the flow direction revealed the effect of texture geometry on the reduction in pressure drop. In single layered structures, lotus-like geometries exhibited a greater reduction in drag (more than 30%) when compared to all other texture geometries. It is recognized that the flow experiences expansion and contraction cycles as it flows over the transverse ridges increasing the frictional resistance. Our findings will help to modify the boundary condition at the liquid–gas meniscus for accurate modeling in the laminar regime and to optimize the texture geometry to improve drag reduction.

Despite numerous investigations in the literature on slip flows in textured microchannels, experimental results were seldom in agreement with the theory. It is conjectured that contamination of the liquid-gas interface by impurities might be one of the sources of this discrepancy. However, the effect of impurities on slippage at the liquid-gas interface is neither understood nor previously reported. To this end, this work presents numerical investigation on the flow past a liquid-gas interface embedded with solid particles in textured microchannels. Initially, we present numerical simulations past transverse ribs with cylindrical particles on the liquid-gas interface. A reduction in effective slip length (or slip loss) with respect to the particle-free interface as a function of gas fraction, constriction ratio, and particle position was quantified. A significant slip loss (∼20-80%) was induced, owing to acceleration-deceleration cycles experienced by the liquid advecting across the particle-laden liquid-gas interface. Even a small number of solid particles adsorbed on a liquid-gas interface were shown to reduce the effective slip length considerably. This renders a textured microchannel with the particle-laden interface to be ineffective as compared to a completely wetted textured microchannel under certain conditions. Furthermore, a flow past two bi-dimensional textures, viz. posts and holes, with their interfaces embedded with spherical particles was also simulated. Our results show that texture configurations with an unbounded liquid-gas interface can mitigate the detrimental effects of particles adsorbed at the interface. The results presented here will help guide in designing efficient textured surfaces in future.