The concept of particle pressure of a suspension of particles in a turbulent flow

TL;DR

This paper applies the Clausius Virial theorem to derive a concept of particle pressure in a suspension within turbulent flow, drawing parallels to Brownian motion and Einstein's diffusion work.

Contribution

It introduces a novel theoretical framework for calculating particle pressure in turbulent suspensions using classical kinetic theory.

Findings

Derived an expression for particle pressure in turbulent suspensions.

Established a relation analogous to the Stokes-Einstein relation for turbulent flows.

Highlighted differences between Brownian motion and turbulent suspension dynamics.

Abstract

The Clausius Virial theorem of Classical Kinetic Theory is used to evaluate the pressure of a suspension of small particles at equilibrium in an isotropic homogeneous and stationary turbulent flow. It then follows a similar approach to the way Einstein (1905) evaluated the diffusion coefficient of Brownian particles (leading to the Stokes-Einstein relation) to similarly evaluate the long term diffusion coefficient of the suspended particles. In contrast to Brownian motion, the analogue of temperature in the equation of state which relates pressure to particle density is not the kinetic energy per unit particle mass.