Giant superhydrophobic slip of shear-thinning liquids

We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions (& varepsilon;<< 1) and strong shear thinning (beta << 1, beta being the ratio of the viscosity at infinite shear rate to that at zero shear rate). Considering a Carreau liquid within the canonical scenario of longitudinal shear-driven flow over a grooved superhydrophobic surface, we show that, as beta is decreased, the scaling of the effective slip length at small solid fractions is enhanced from the logarithmic scaling ln(1/& varepsilon;) for Newtonian fluids to the algebraic scaling 1/& varepsilon;(1-n)/(n), attained for beta=O(& varepsilon;(1-n)/(n)), n is an element of(0,1) being the exponent in the Carreau model. We illuminate this scaling enhancement and the geometric-rheological mechanism underlying it through asymptotic arguments and numerical simulations.