Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

J. M. Ottino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of "microstructures" whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context of the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.

Original languageEnglish (US)
Pages (from-to)1417-1430
Number of pages14
JournalPhysics of Fluids A
Issue number5
StatePublished - 1991

ASJC Scopus subject areas

  • Engineering(all)


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