Turbulence enhancement of coagulation: the role of eddy diffusion in velocity

TL;DR

This paper develops a model linking turbulence-induced eddy diffusion to enhanced coagulation rates, providing a theoretical and numerical framework that aligns with gas-kinetic predictions.

Contribution

It introduces a deterministic model with enhanced diffusion derived from a stochastic approach, establishing a precise link between turbulence intensity and coagulation enhancement.

Findings

Numerical simulations confirm the relationship between turbulence intensity and coagulation rate.

A new method proves the formula for mean velocity difference aligns with gas-kinetic models.

The model provides a quantitative link between turbulent velocity fields and coagulation enhancement.

Abstract

A Smoluchowski type model of coagulation in a turbulent fluid is given, first expressed by means of a stochastic model, then in a suitable scaling limit as a deterministic model with enhanced diffusion in the velocity component. A precise link between mean intensity of the turbulent velocity field and coagulation enhancement is obtained by numerical simulations, and a formula for the mean velocity difference, in agreement with the gas-kinetic model, is proved by a new method.