# Presentation: 343367

## RUI:  Fronts and Patterns in Advection-Reaction-Diffusion Systems Thomas H. Solomon, Bucknell UniversityDMR 0404961 and DMR 0703635

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**RUI:  Fronts and Patterns in ****Advection-Reaction-Diffusion Systems** **Thomas H. Solomon, Bucknell University****DMR 0404961 and DMR 0703635**

- We are performing some of the first experiments to explore how the presence of fluid flows affects the behavior of reacting systems. In the past year, we have initiated studies of large-scale patterns that form in an array of vortices (whirlpools) with chaotic mixing.  At small scales, chaotic mixing between the vortices produces filamentary structures, typical of chaotic processes.  At large scales, though, spiral and target patterns are found, similar to those found in a non-flowing liquid layer.
- Other work recently submitted provides experimental evidence that the pre-sence of vortices in a flow can “freeze” a moving front (e.g., a flame front or a spreading disease) in the presence of a wind that blows across the system.

- Movies showing wave patterns formed in the Belousov-Zhabotinsky chemical reaction.  (a) A double-spiral that generates outward-propagating waves in a thin, stagnant fluid layer in a petrie dish.   (b) Wave patterns in a flow composed of an array of vortices.  Filaments can be seen moving between vortices, but the large-scale pattern is similar to the double-spiral in (a).

- 10 cm

- 25 cm

**Notes:**
There has been a tremendous amount of research about pattern formation and front propagation in interacting systems, including chemical reactions, biological ecosystems (e.g., spread of disease), and systems undergoing phase transitions (e.g., liquid-solid or liquid-gas).  The vast majority of the previous work, however, has considered only the situation in which the system is stagnant with no fluid motion.  But in many natural and industrial systems, there are fluid flows that can dramatically affect the behavior of the system.  We are conducting some of the first experiments to consider the importance of fluid mixing on pattern formation and front propagation in reacting fluid systems.  In previous years, we showed that the tools of chaotic mixing can be used to describe pattern formation in reacting systems, and we showed that reactive fronts moving in a flowing fluid can “lock”, hopping from vortex to vortex in a fixed interval of time.  During the past year, we have initiated experiments that explore how pattern formation in chemical systems is affected by a flow composed of an array of vortices (whirlpools) that oscillate back and forth.  Mixing is chaotic in this flow, and very complicated small-scale chemical structures form, as seen if you look closely at the movie on the right.  But despite the complexity of the small-scale patterns, on a larger-scale, a pattern of rotating spirals forms, and these rotating spirals generate a repeating pattern of waves.  This large-scale behavior is very similar to waves generated in the chemical reaction without any flow at all, as seen in the movie on the left.

We have also studied the effects of vortices and an imposed “wind” on the movement of chemical fronts.  As an example of a front, imagine someone pouring gasoline all over the floor and then dropping a match onto it.  The gasoline will catch on fire, and the fire will move (propagate) across the floor, consuming the gas as it goes.  In this example, the moving flame itself is the front.  Our work is analogous to stirring the gasoline while the flame burns across the floor.  During the past year, we have found that the presence of vortices in a flow (whether ordered or disordered) “freezes” the motion of a chemical front in the face of a uniform wind.  This work is currently under review by Physical Review Letters.

## RUI:  Fronts and Patterns in Advection-Reaction-Diffusion Systems Thomas H. Solomon, PI, Bucknell UniversityDMR-0404961 and DMR-0703635

- Fluid mixing (advection) is significant in a wide range of reacting systems with significant societal impact. Some examples include:  (a) chemical and biological processes, particularly in microfluidic devices; (b) plasmas, e.g., in fusion reactors; (c) developing embryos where flow-induced pattern formation may play a role in segregation of different parts of an embryo into specialized functions; and (d) storm and pressure fronts in the atmosphere.  It is also possible that modeling of a moving population as a fluid might shed insight into spreading of diseases in society.

**RUI:  Fronts and Patterns in ****Advection-Reaction-Diffusion Systems** Thomas H. Solomon, PI, Bucknell UniversityDMR-0404961 and DMR-0703635

**Education:**
- During the past year, three under-graduate students (Mollie Schwartz, Lily Beauvilliers and Jeff Boehmer) contributed to this project. The students also interact with REU students working in the Department of Physics & Astronomy at Bucknell.

**Notes:**
Undergraduate students participate in all aspects of the research, including preliminary discussions about the goals and approaches, designing and testing of the apparatus, collection and analysis of the data, computer modeling of the results, presentation of the work at international meetings, and writing of the research for publication.  All six of the most recent refereed papers have undergraduate students as co-authors; in fact, undergraduates are the first author on five of these papers.  Every undergraduate that has been supported by these grants has either given or will soon give a contributed talk at a national meeting of the American Physical Society.  The experiences here are tremendously valuable to these students as they pursue careers after college, either as research scientists or in industry or teaching.

Students working on these projects during the summer are integrated into the “Research Experience for Undergraduates” program run by the Department of Physics & Astronomy at Bucknell.  In addition to conducting the research, the students participate in weekly meetings with the other students and mentors in which each student gives updates on his or her work.  Weekly seminars, skills sessions (computer skills, poster presentation, giving talks, GRE preparation) and social activities are also part of the summer research opportunities.
As for the research itself, this is an area of research which is still quite new – very few studies have been done to date about the effects of fluid mixing on reacting systems.  But the potential applications are significant, especially for the growing field of microfluidic systems, since chaotic mixing is the dominant mixing process at small scales.  We have listed other potential applications in the column on the right.