Pattern Formation at Interfaces with Applications to Biomedical, Materials and Physico-Chemical Processes
October 16, 2006 — October 20, 2006
Coordinators:
- Alexander Nepomnyashchy (Technion-Isr. Inst. of Technol, Haifa, Israel)
- Pierre Colinet (Free University of Brussels, Brussels, Belgium)
Interfacial pattern formation occurs in several natural, technological and medical contexts such as in, e.g., salt lake evaporation, drying of paint films, polymer coating techniques, electro-deposition, semiconductor processing, micro-fluidics, mucus flow in the lungs, dry eye syndrome etc. Modeling these processes requires an understanding of their physics and the knowledge of length and time scales that characterize them. Interfaces play a dominant role at small scales, and their correct modeling is therefore also crucial in the rapidly expanding field of nano-technology.
It is the aim of this course to explain the physics of a number of interfacial phenomena that involve multiple time and length scales and to help the students in mastering their modeling and identifying modern scientific and technological challenges in the field of interface science.
All lectures are presented within the framework of continuous theories and transport phenomena, i.e. mass, momentum and heat transfer. Yet, the investigation of phenomena taking place at interfaces and fronts of phase transition needs the combination of two different kinds of models. In the first approach, the interface or the front are considered as objects of zero thickness; the second approach recognizes the internal “diffuse” structure of the transition zone.
The dynamics of interfaces and fronts are characterized by numerous kinds of instabilities leading to nonlinear patterns and waves. Several challenging physical problems such as phase transition instabilities, front velocity selection and solitary waves on falling films, will be discussed with a view of identifying the relevant physico-chemical processes and incorporating the multiple length scales and time scales into their theoretical and numerical modeling. Generic aspects of nonlinear phenomena will also be emphasized and to complete the picture, experimental evidence of pattern formation at interfaces will be provided.
The course will cover most modern methods allowing to treat interfacial instabilities, such as multi-scale asymptotic expansions, linear stability, weakly nonlinear methods and bifurcation theory. Analytical or fully numerical techniques will be discussed, and experimental results will be presented either to confirm theory, or to illustrate directions for further research. Lectures by Prof. R. Narayanan and Dr. P. Colinet will contain the description of methods for modeling interfacial instabilities leading to patterns and waves, including phase change such as evaporation, as well as front motion in problems of electro-deposition and solidification. Problems involving thin-film dynamics are also described, and a number of industrial applications are also considered. In the lectures of Prof. M. Bestehorn, pure fluids as well as binary mixtures are examined by 3D solutions of the basic hydrodynamic equations. In the case of thin and ultra-thin liquid films, the development of large scale instabilities may lead to the break-up and the formation of dry spots and drops. The lectures by Prof. A. Golovin are focused on solid-solid, solid-liquid and solid-gas interfaces, which are typically met in crystal growth and other materials science processes. The focus is on such characteristic aspects of solid surfaces as effects of anisotropy, dendrite and facet formation, as well as formation of nanostructures in thin epitaxial films. In the lectures by Prof. L. Pismen, the continuous approach is applied to the description of the gas-liquid interface. This approach makes it possible to eliminate the famous paradoxes of the contact line dynamics. The lectures of Prof. A. Nepomnyashchy are devoted to the general aspects of the dynamics of fronts propagating in dissipative systems, with a special attention for the transverse instabilities of fronts that are at the origin of complex spatio-temporal dynamics.
All lectures will be given in a tutorial and pedagogical fashion. The course is intended to graduate students and researchers in physics and engineering, interested in mastering the modern methods of nonlinear stability theory applied to the problems of continuous media mechanics in the presence of interfaces, materials science, as well as biological pattern formation. The attendees are expected to have had a first level course in fluid mechanics or transport phenomena and some background in linear algebra, ordinary and partial differential equations. At the end of the course the participants will be in a position to identify key problems of scientific value, will be able to identify the methods to resolve modeling issues and will see the similarity between a variety of seemingly different physical problems. The exposure will allow the participants to quickly move into an area of physics and engineering that is rich in phenomena and replete in applications.