Fractal-Dominated Chemistry

Why does cream poured into coffee swirl the way it does? A new study of how chemical reactions proceed establishes new equations for reaction rates by taking mixing abnormalities more into account. Many existing equations assume efficient mixing of ingredients, but this is far from the case.

Before reactions can take place, proper mixing has to occur, and as two Hungarian physicists now discover in their simulations of mixing under more realistic fluid flow conditions, reactions often occur along a fractal frontier. Indeed, much real-world fluid chemistry is chaotic in nature and takes place not in general solution but along a many-filamented fractal surface. Some previous studies of the steady time-independent fracticality of chemical reactions occurring in open flows, those in which fluid continuously flows into and out of a container.

According to Gyorgy Karolyi (Budapest University of Technology and Economics) and Tamas Tel (Eötvös Loránd University), their new study is the first to address the tougher problem of a closed flow, one in which the fluid remains in the container; in this case, the resultant filamentary fractal is not steady but instead evolves through time, gradually filling up more and more of the container volume. They derive the relation between reaction rate and fractal dimensionality (the extent to which surface of the filaments lies between that of a two dimensional and three dimensional object).

Fractal mixing is suspected in the disposition of several natural systems, such as plankton in the ocean, sea ice floating in the ocean, and cloud patterns (see satellite image). Karolyi (karolyi@tas.me.bme.hu) suggests that the new equations might provide new insights for those who design microfluidic devices such as micromixers used in printing and medical equipment.

Karolyi and Tel, Physical Review Letters, upcoming article