https://doi.org/10.1140/epjst/e2016-60228-8
Regular Article
Parametric excitation of oscillatory Marangoni instability in a heated liquid layer covered by insoluble surfactant
1 Department of Physics, Sam Houston State University, Huntsville, TX 77341, USA
2 Embry-Riddle Aeronautical University-Worldwide, Daytona Beach, FL 33114, USA
3 Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
a e-mail: amik@shsu.edu
b e-mail: nepom@technion.ac.il
Received: 15 July 2016
Revised: 5 August 2016
Published online: 2 May 2017
This paper is a continuation of our previous research reported in the two last IMA conferences. While in our previous works the driving modulation was a modulation of the temperature gradient, here the temperature gradient is fixed in the whole liquid layer and the liquid is vertically vibrated with some fixed driving frequency. Two kinds of waves can be generated in this system. The first kind of waves are transverse (capillary-gravity) waves. The second kind of waves are longitudinal (Marangoni) waves caused by the dependence of the surface tension on the temperature and the surfactant concentration. A linear analysis with arbitrary wave numbers is performed. Two different heating regimes were considered. Multiple instability regions depending on the heating conditions are analyzed. Among three possible modes of the system's response to external forcing, the most “dangerous” one is the subharmonic instability mode.
© EDP Sciences, Springer-Verlag, 2017
