Cornell Fluids Seminar (CFS): Steven J. Weinstein, Ph.D. (Rochester Institute of Technology), "Algebraic Instabilities on Threshold of Neutral Stability"

Description

Abstract: If a flowing liquid system in a manufacturing process is unstable, i.e., initiated disturbances are magnified, the flow can often easily be disrupted away from a uniform state. This could be a desired outcome, as is the case for liquid fuel atomizers where instability leads to the breakup of a liquid sheet into droplets, or in the case of instability-driven turbulence to enhance mixing processes. Instability is unwelcome in other situations where layer uniformity is essential, such as in the thin films used to coat ink jet and copier papers, printed electronics, and liquid crystal display screens. Thus, it is important for practitioners to control the parameters that influence fluid instability in order to produce a salable product. In this talk, a largely unexplored type of hydrodynamic instability is examined: long-time algebraic growth. Such growth is possible when the dispersion relation extracted from classical stability analysis indicates neutral stability. A physically motivated class of partial differential equations that describes the response of a system to disturbances is examined. Specifically, the propagation characteristics of the response are examined in the context of spatiotemporal stability theory. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. One similarity in the responses is that the characterization of absolute and convective instabilities are relevant. Whereas exponentially unstable responses have a well-defined range of component wave speeds that grow at large times, algebraically unstable responses have growth that occurs at precisely one wave speed and algebraic damping at all others. The overall response, however, is smooth and broad since those speeds associated with damping exhibit transient growth. One key implication of this work is that systems that are characterized as neutrally stable from classical stability analysis may actually have responses that grow or decay. Bio: Dr. Steven Weinstein received his B.S. in Chemical Engineering from the University of Rochester and his MS and PhD in Chemical Engineering from the University of Pennsylvania. He worked for Eastman Kodak Company for 18 years after receiving his PhD. He is well published in the field of coating, and has focused on thin film flows, die manifold design, wave stability, curtain flows (flows in thin sheets of liquid), and web dynamics; he also has 7 patents in these areas. Dr. Weinstein joined the faculty of the Department of Mechanical Engineering at Rochester Institute of Technology (RIT) in January of 2007, and along with teaching graduate and undergraduate courses in fluid mechanics and applied math, founded the Department of Chemical Engineering in the fall of 2008. In addition to performing his administrative duties as department head and serving on a variety of college and university committees, he teaches chemical engineering courses on material balances in reactive systems, fluid dynamics, chemical thermodynamics, reactor design, separation processes, and applied mathematics. Dr. Weinstein also serves as a core faculty member in the Mathematical Modeling PhD Program at RIT.