Fischer, Benjamin J. and Troian, Sandra M. (2003) Growth and decay of localized disturbances on a surfactant-coated spreading film. Physical Review E, 67 (1). Art. No. 016309. ISSN 1063-651X http://resolver.caltech.edu/CaltechAUTHORS:FISpre03
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If the surface of a quiescent thin liquid film is suddenly coated by a patch of surface active material like a surfactant monolayer, the film is set in motion and begins spreading. An insoluble surfactant will rapidly attempt to coat the entire surface of the film thereby minimizing the liquid's surface tension. The shear stress that develops during the spreading process produces a maximum in surface velocity in the region where the moving film meets the quiescent layer. This region is characterized by a shock front with large interfacial curvature and a corresponding local buildup of surfactant which creates a spike in the concentration gradient. In this paper, we investigate the sensitivity of this region to infinitesimal disturbances. Accordingly, we introduce a measure of disturbance amplification and transient growth analogous to a kinetic energy that couples variations in film thickness to the surfactant concentration. These variables undergo significant amplification during the brief period in which they are convected past the downstream tip of the monolayer, where the variation in concentration gradient and surface curvature are largest. Once they migrate past this sensitive area, the perturbations weaken considerably and the system approaches a stable configuration. It appears that the localized disturbances of the type we consider here, cannot sustain asymptotic instability. Nonetheless, our study of the dynamics leading to the large transient growth clearly illustrates how the coupling of Marangoni and capillary forces work in unison to stabilize the spreading process against localized perturbations.
|Additional Information:||©2003 The American Physical Society (Received 8 March 2002; published 31 January 2003) We gratefully acknowledge financial support for this study from the National Science Foundation through Grant Nos. CTS-9973538, CTS-0088774, and DMR-9809483.|
|Subject Keywords:||surfactants; wetting; surface diffusion; monolayers; surface tension|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||18 Sep 2006|
|Last Modified:||26 Dec 2012 09:03|
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