Absolute and convective instabilities in a liquid film over a substrate moving against gravity

Abstract

The drag-out problem for small Reynolds numbers ($\mathrm{Re}$) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers ($\mathrm{Ca}$), and Derjaguin's solution for large $\mathrm{Ca}$. 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.

Cited by in corpus (1)

• Linear stability analysis of a vertical liquid film over a moving substrate