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.

超疏水纹理表面减少了微通道中压力驱动层流中的流体动力阻力。然而，尽管在微流体装置中广泛使用非牛顿液体，但迄今为止，在纹理超疏水微通道中减少摩擦的背景下，很少研究此类液体的流动行为。因此，我们研究了拓扑不同的粗糙表面对微通道中剪切稀化液体的摩擦减少的影响。首先，在一般表面纹理（例如柱、孔、纵向和横向肋）上的摩擦系数比（纹理表面与平坦表面上的摩擦系数之比）在 Carreau 数范围内进行数值估计，作为微通道收缩率、气体分数和幂律指数。类似于牛顿液体的流动行为，纵向肋条和柱子的流动摩擦明显小于横向肋条和孔，而所有纹理的摩擦因数比都表现出随 Carreau 数的非单调变化。尽管无论微通道收缩率如何，摩擦因数比的最小值都在恒定的 Carreau 数下被注意到，但随着幂律指数和气体分数的增加，最小值已转移到更高的 Carreau 数。还在微通道中用含水黄原胶液体进行了实验。流动增强（相对于光滑表面具有超疏水纹理的流速）表现出非单调行为，并随着幂律指数的增加而衰减，相当于模拟。