The interaction of an externally applied electric _eld with a liquid can give rise to interesting ow instabilities and pattern formation. For example, it has been demonstrated that the application of an electric _eld to an initially at polymer-air or polymer-polymer interface may result in an electrohydrodynamic instability which leads to the formation of columnar structures. This phenomenon could be exploited in order to form well-controlled patterns at the microscale and nanoscale with many practical engineering applications. The scope of the present research project is to achieve fundamental understanding of the electrically-induced ow of viscoelastic liquid _lms and to investigate the e_ect of various factors (e.g. the complex uid rheology, the presence of surface active materials or free charge along the liquid-air or liquid-liquid interfaces, geometric con_guration, etc) that may play an important role in such a process. It is well known that the dynamics and stability of liquid _lms can be very rich and it is characteristic that despite the fact that the _rst attempts to address the stability of a simple system such as a clean (without surfactants) Newtonian liquid _lm under the e_ect of gravity appear in the literature in the late 50's full understanding of the underlying mechanisms was not achieved until recently. One of the goals of the present study was to expand our understanding on the stability of the liquid _lms in the presence of surface active materials (surfactants). The reason for this is threefold. On one hand, the interaction of a surfactant-ladden _lm with an electric _eld is of interest for controlled pattern formation at the micro- and nano-scale. For example, ionic surfactants may interact with the electric _eld thereby a_ecting interfacial concentration and imposing speci_c patterns in the liquid. On the other hand, surfactants attribute non-Newtonian properties to the liquid, because the free surface attains surface elasticity and surface viscosity. Also, at high surfactant concentrations, micelles may form in the bulk and complicate its rheological behavior, rendering the solution viscoelastic. Finally, the governing equation that describes the conservation of surfactant concentration along the interface is identical to the equation that describes the conservation of free charge in the case of dielectric materials. These systems share many similar characteristics and it is possible to draw conclusions from the analogy between them. To this end, we formulated the Orr-Sommerfeld equation for a surfactant-laden _lm with appropriate boundary conditions, and solved it numerically for arbitrary disturbances and analytically for long-wave disturbances. The results from our analysis demonstrate the signi_cant e_ect of surfactant solubility and sorption kinetics on the stability characteristics and provided useful insight in the non-linear dynamics of the ow. The results from this this work have been published to the Journal of Fluid Mechanics. In a subsequent paper that has also been submitted for publication to the Journal of Fluid Mechanics we have investigated the role of surfactants on the mechanism of the long-wave instability in liquid _lm ows. We have also made announcements to several local and international conferences. A second goal of this research project was to develop a robust numerical algorithm capable of handling the ow of viscoelastic material with large interfacial deformations…..
