Matar, Omar K. and Troian, Sandra M. (1997) Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film. Physics of Fluids, 9 (12). pp. 3645-3657. ISSN 1070-6631. http://resolver.caltech.edu/CaltechAUTHORS:MATpof97
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Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactant monolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are self-similar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows.
|Additional Information:||©1997 American Institute of Physics. (Received 17 March 1997; accepted 11 August 1997) This work was supported by an NSF Research Initiation Award through Grant No. CTS-9409579 and an NSF CAREER award through Grant No. CTS-9624776. The authors would also like to acknowledge interesting discussions with M. Göz, M. Kostin, R. Jackson, S. H. Lam and S. A. Orszag.|
|Subject Keywords:||flow instability; monolayers; wetting; liquid films|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||15 Sep 2006|
|Last Modified:||26 Dec 2012 09:02|
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