Giant superhydrophobic slip of shear-thinning liquids
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914949345837056 |
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| author | Schnitzer, Ory Ray, Prasun K. |
| author_facet | Schnitzer, Ory Ray, Prasun K. |
| contents | We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions ($ε\ll1$) and strong shear thinning ($β\ll1$, $β$ 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 $β$ is decreased, the scaling of the effective slip length at small solid fractions is enhanced from the logarithmic scaling $\ln(1/ε)$ for Newtonian fluids to the algebraic scaling $1/ε^{\frac{1-n}{n}}$, attained for $β=\mathcal{O}(ε^{\frac{1-n}{n}})$, $n\in(0,1)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09374 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Giant superhydrophobic slip of shear-thinning liquids Schnitzer, Ory Ray, Prasun K. Fluid Dynamics We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions ($ε\ll1$) and strong shear thinning ($β\ll1$, $β$ 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 $β$ is decreased, the scaling of the effective slip length at small solid fractions is enhanced from the logarithmic scaling $\ln(1/ε)$ for Newtonian fluids to the algebraic scaling $1/ε^{\frac{1-n}{n}}$, attained for $β=\mathcal{O}(ε^{\frac{1-n}{n}})$, $n\in(0,1)$ 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. |
| title | Giant superhydrophobic slip of shear-thinning liquids |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2409.09374 |