Effect of inertia on the Marangoni instability of twolayer channel flow, Part II: normalmode analysis
 M. G. Blyth,
 C. Pozrikidis
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The effect of inertia on the Yih–Marangoni instability of the interface between two liquid layers in the presence of an insoluble surfactant is assessed for sheardriven channel flow by a normalmode linear stability analysis. The Orr–Sommerfeld equation describing the growth of small perturbations is solved numerically subject to interfacial conditions that allow for the Marangoni traction. For general Reynolds numbers and arbitrary wave numbers, the surfactant is found to either provoke instability or significantly lower the rate of decay of infinitesimal perturbations, while inertial effects act to widen the range of unstable wave numbers. The nonlinear evolution of growing interfacial waves consisting of a special pair of normal modes yielding an initially flat interface is analysed numerically by a finitedifference method. The results of the simulations are consistent with the predictions of the linear theory and reveal that the interfacial waves steepen and eventually overturn under the influence of the shear flow.
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 Title
 Effect of inertia on the Marangoni instability of twolayer channel flow, Part II: normalmode analysis
 Journal

Journal of Engineering Mathematics
Volume 50, Issue 23 , pp 329341
 Cover Date
 20041101
 DOI
 10.1007/s106650043691z
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 channel flow
 immersedinterface method
 Marangoni instability
 surfactants
 Industry Sectors
 Authors

 M. G. Blyth ^{(2)}
 C. Pozrikidis ^{(1)}
 Author Affiliations

 2. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
 1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California, 920930411, USA