Reactive Particles in Random Flows

We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.

Figure 1

Distribution of $B$ particles at time $t=14$, right after the 7th reaction step. The upper left inset illustrates the scaling of $N(\sigma )$ for the region given by $R_0=[-1.5,-0.26]\times [0.2,1.2]$. The result is a well-defined power law, with a fractal dimension of 1.96. The upper right inset shows the time evolution of the number of $B$ particles towards the steady state, where the time $t$ is measured in units of the reaction time $\tau$.

Figure 2

Distribution of $B$ particles at time $t=16$, right after the 8th reaction steps in the counting region $R_0$. The inset shows the scaling of $N(\sigma )$ for $R_0=[-0.8,-0.28]\times [0.1,0.8]$. The measured fractal dimension is 1.94, which is within statistical errors equal to the result of Fig. 1.