On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes

TL;DR

This paper investigates the validity of the law of mass action in three-dimensional coagulation processes, revealing significant deviations caused by fluctuations and establishing a connection between microscopic details and macroscopic decay rates.

Contribution

It introduces a renormalization group approach to systematically incorporate fluctuations and derives an exact relation linking microscopic physics to macroscopic decay behavior.

Findings

Strong violation of the law of mass action observed.

Fluctuations lead to a universal correction term in kinetic equations.

Microscopic details influence the macroscopic decay rate.

Abstract

Diffusion limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long wavelength fluctuations and is a universal function of the macroscopic decay rate.