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Published July 1, 2005 | public
Journal Article Open

Generalized linear stability of noninertial coating flows over topographical features


The transient evolution of perturbations to steady lubrication flow over a topographically patterned surface is investigated via a nonmodal linear stability analysis of the non-normal disturbance operator. In contrast to the capillary ridges that form near moving contact lines, the stationary capillary ridges near trenches or elevations have only stable eigenvalues. Minimal transient amplification of perturbations occurs, regardless of the magnitude or steepness of the topographical features. The absence of transient amplification and the stability of the ridge are explained on physical grounds. By comparison to unstable ridge formation on smooth, flat, and homogeneous surfaces, the lack of closed, recirculating streamlines beneath the capillary ridge is linked to the linear stability.

Additional Information

©2005 American Institute of Physics (Received 4 February 2005; accepted 6 May 2005; published online 24 June 2005) This work was supported by the NASA Microgravity Fluid Physics Program, the U.S. Army TACOM-ARDEC, and the Princeton Research Institute for the Science of Materials. J.M.D. wishes to thank the Air Force Office of Scientific Research for a NDSEG Fellowship and Princeton University for the G. Van Ness Lothrop Fellowship in Engineering. S.M.T. kindly acknowledges the warm hospitality and generous financial support received through the Moore Distinguished Scholar Program at the California Institute of Technology.


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