4.Rayleigh and Marangoni convections
We are motivated by the potential of using thermally generated convection patterns in moving droplets for mixing. We investigate the Marangoni-Bénard instability for a three-layer system with deformable interfaces undergoing Poiseuille flow.
Linear stability analysis shows that at small wave numbers a deformable interface is of the orders of magnitude less stable than a non-deformable interface. At large wave numbers, both a rigid and a deformable interface have the same stability. Furthermore, a base planar Poiseuille flow affects the linear stability of the system and the type of instability when the interface is allowed to deform. Flow stabilizes an already unstable system and works to destabilize a stable system.
References
- Alvarez, N.J. and Uguz, A.K 2013 The Impact of Deformable Interfaces and Poiseuille Flow on the Thermocapillary Instability of Three Immiscible Phases Confined in a Channel Physics of Fluids, 024104.1-024104.15 (DOI: 10.1063/1.4790878)
General references
- L. Johns and R. Narayanan, Interfacial Instability (Springer-Verlag, New York, 2002).
- S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981)
- W. Guo, G. Labrosse, and R. Narayanan, The Application of the Chebyshev-Spectral Method in Transport Phenomena: Lecture Notes in Applied and Computational Mechanics (Springer-Verlag, Berlin/Heidelberg, 2013), Vol. 68.
- G. Labrosse, Méthodes Spectrales (Ellipses, Paris, 2011).
- ImageJ : http://imagej.nih.gov/ij/
