A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected particle can be chaotic even with a flow field that is simply time periodic. Similar to the case of ideal tracers, whose dynamics is Hamiltonian, chemical or biological activity involving such particles can be analyzed using the theory of chaotic dynamics. Using the example of an autocatalytic reaction, $A+\overrightarrow{B}2B,$ we show that the balance between dissipation in the particle dynamics and production due to reaction leads to a steady state distribution of the reagent. We also show that, in the case of coalescence reaction, $B+\overrightarrow{B}B,$ the decay of the particle density obeys a universal scaling law as approximately $t^{-1}$ and that the particle distribution becomes restricted to a subset with fractal dimension $D_2,$ where $D_2$ is the correlation dimension of the chaotic attractor in the particle dynamics.

• Received 30 July 2001

DOI:https://doi.org/10.1103/PhysRevE.65.026216