Abstract: In the first part of this lecture we review modeling and analyses that have been carried out in the past for electrically driven jet flows and the associated instabilities with important applications in electro-spinning. Next, we consider the relevant governing equations for both linear and nonlinear electrically driven jet flows and their associated temporal and spatial instabilities. Such jets can be driven by either constant or variable applied field. Under certain assumptions, scaling and conditions, we will derive mathematical models for the linear & nonlinear stability systems. We then determine linear and nonlinear solutions for some modes of instabilities of the resulting systems. We explain the properties of these solutions and conditions under which they can be dominant. We also compare the results with the available experimental results. More recent developments including instabilities under different equilibrium states as well as significant jet radius reduction due to certain instabilities and the implications with respect to production of nano-scale fibers will be discussed. In the last part of the lecture, we point out at future studies, directions and important questions that need to be resolved by future investigations on this topic.

Brief Biography of the Speaker:
Daniel N. Riahi served as Full Professor at The University of Illinois at Urbana-Champaign (UIUC) from 1995 to 2005, as Professor Emeritus at UIUC since 2005 with the home Dept of Mechanical Science and Eng (MechSE), and as Full Professor in the Dept of Math at University of Texas-Pan American since 2006. Dr. Riahi’s research work & interest include studies in convection, flow instabilities & turbulence, flow during solidification & crystal growth, electromagnetic applications, and math modeling and theoretical developments with applications to eng and physical sciences. His research accomplishments include new theories and a number of discoveries in fundamental areas of convective and shear flows, some of which were already confirmed by the experimental studies.
Professor Riahi received Appreciation Letters, Service Recognition Award & Certificates, Honorific Title Award & Research Awards from UIUC. He is member of over seven professional societies and a Fellow of Wessex Institute of Great Britain. He is author of Chapters in a book that won the Best Basic Science Book-Award by IAA. He was awarded NSF Grants, UIUC-RB & UTPA-FRC Grants, NCSA Awards and supervised NASA Sponsored Res. Projects. He presented many Invited Lectures and several Plenary Lectures at National & International Conferences. He is Editor and Editorial Board Member of over 20 technical journals and book series. He is author of over 330 publications mostly published in rigorously refereed journals, including books, invited articles, review articles and chapters of books.