Abstract
The linear stability of an annular capillary liquid (external or internal) coating, undergoing a uniform axial elongation, is analysed. An appropriate initial-value problem is formulated and solved for the evolution of small perturbations on the free surface of the coating, thereby enabling a thorough description of the amplification envelopes (of maximal growth) and the wavenumbers of the instantaneously dominant perturbations.
Similarly to other related capillary-stability problems, it is observed that the elongational motion has, through the continual stretching of perturbation waves, an inhibiting effect upon perturbation growth. The present results demonstrate that the latter is further suppressed in the practically relevant case of small (relative to the instantaneous radius of the cylindrical surface being coated) coating thickness. It is thus suggested that this phenomenon may be utilised to improve the quality of coating in certain industrial processes where the very production of the coated body involves a significant elongation.
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Biber, E., Frankel, I. Elongational stabilization of capillary coating. Appl. Sci. Res. 52, 355–370 (1994). https://doi.org/10.1007/BF00936837
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DOI: https://doi.org/10.1007/BF00936837