Giant superhydrophobic slip of shear-thinning liquids

TL;DR

This paper demonstrates that shear-thinning complex fluids flowing over superhydrophobic surfaces can exhibit significantly enhanced slip lengths, especially at small solid fractions, due to combined geometric and rheological effects.

Contribution

It introduces a theoretical framework showing how shear-thinning behavior amplifies slip length scaling over superhydrophobic surfaces, extending previous Newtonian models.

Findings

Effective slip length scales algebraically with solid fraction for shear-thinning fluids.

Scaling enhancement occurs as shear-thinning becomes more pronounced.

Numerical simulations confirm the asymptotic analysis.

Abstract

We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions ($\epsilon\ll1$) and strong shear thinning ($\beta\ll1$, $\beta$ 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 $\ln(1/\epsilon)$ for Newtonian fluids to the algebraic scaling $1/\epsilon^{\frac{1-n}{n}}$, attained for $\beta=\mathcal{O}(\epsilon^{\frac{1-n}{n}})$, $n\in(0,1)$ 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.