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 ($\epsilon\ll1$) and strong shear thinning ($\beta\ll1$, $\beta$ being the ratio of the viscosity at infinite shear rate to that at z...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
14.09.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2409.09374 |