Absolute and convective instabilities in a liquid film over a substrate moving against gravity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909285515001856 |
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| author | Pino, Fabio Mendez, Miguel Alfonso Scheid, Benoit |
| author_facet | Pino, Fabio Mendez, Miguel Alfonso Scheid, Benoit |
| contents | The drag-out problem for small Reynolds numbers ($\rm Re$) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers ($\rm Ca$), and Derjaguin's solution for large $\rm Ca$. We investigate whether these solutions are absolutely or convectively unstable, solving the Orr-Sommerfeld eigenvalue problem. For Derjaguin's solution, we show that the LLD solution is convectively unstable for $\text{Ka}<17$ and absolutely unstable for $\text{Ka} \gtrsim 0.15 \,\text{Re}^{1.7}$ for $\text{Re} > 10$. For water ($\text{Ka}=3400$), the LLD solution is always convectively unstable. The absolute instability is observed only when the dip-coated film is additionally fed from above. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_14613 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Absolute and convective instabilities in a liquid film over a substrate moving against gravity Pino, Fabio Mendez, Miguel Alfonso Scheid, Benoit Fluid Dynamics The drag-out problem for small Reynolds numbers ($\rm Re$) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers ($\rm Ca$), and Derjaguin's solution for large $\rm Ca$. We investigate whether these solutions are absolutely or convectively unstable, solving the Orr-Sommerfeld eigenvalue problem. For Derjaguin's solution, we show that the LLD solution is convectively unstable for $\text{Ka}<17$ and absolutely unstable for $\text{Ka} \gtrsim 0.15 \,\text{Re}^{1.7}$ for $\text{Re} > 10$. For water ($\text{Ka}=3400$), the LLD solution is always convectively unstable. The absolute instability is observed only when the dip-coated film is additionally fed from above. |
| title | Absolute and convective instabilities in a liquid film over a substrate moving against gravity |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2312.14613 |