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.
- http://www.haverford.edu/physics-astro/Gollub/lab.html - Nonlinear Physics Lab, Haverford College