An Isaac Newton Institute Workshop

Developments in Experimental Pattern Formation

"Measuring fluid stretching to understand chemical reaction patterns and polymer mixing"

10th August 2005

Authors: Jerry Gollub (Haverford College and U. Penn), Paulo Arratia (Haverford College and U. Penn)

Abstract

Normally when we talk about pattern formation in fluid systems, we are considering the spatial structure of the velocity or temperature or composition field. However, many physical processes, especially mixing and chemical reaction, depend on the local stretching or deformation produced by the fluid. We first show how stretching fields can be computed from high-resolution time-dependent velocity fields. Their patterns can be quite different from the velocity field patterns. Yet, the statistical properties of the stretching probability distributions for various two dimensional flows are similar. Then, we consider chemical mixing, and show that the global progress of an acid base reaction that is limited by advection and diffusion can be expressed in terms of a single function that depends only on the mean Lyapunov exponent, not on the details of the structure of the stretching field. Finally, we show how in a non-Newtonian fluid, the process of fluid stretching and the resulting mixing behavior can be substantially modified.

Work supported by NSF-DMR.

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