Dispersion coefficients from a field-theoretic renormalization of fluid mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Péclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Péclet numbers.