If anybody has modeled brownian motion or knows how to model it please enlist the steps. I want to include force due to brownian motion on the particles (micron sized) in the flow field. Also, it would be of great help if anybody can cite any literature on modeling of brownian motion.

I have no help for you, but rather a comment. The continuum hypothesis is failing where Brownian motion becomes observable. This is also the regime where the turbulence cascade ends. It lies between continuum fluid mechanics (CFM) and kinetic theory (KT). It would be an interesting regime to study, but would require a delicate marriage of the two concepts. Maybe one could impose some weak form of CFM on top of KT or vice-versa. How? I don't know.

Brownian motion is modeled much like turbulent dispersion of particles, as a random sampling process. A fluctuating force is applied to the particles to model the effect. The random force is a function of Boltzmann constant, particle diameter, and temperature.

It's often included in simulations of human airways where particles are of this size. One example: Nowak et.al., "CFD Simulation of Airflow and Aerosol Deposition in Human Lungs," Annals of Biomedical Engineering, Vol. 31, pp. 374-390, 2003. Check other papers on human airway simulation too.

Hi,

"It's often included in simulations of human airways where particles are of this size". What size do you refer to? Micron's? Is the solution solved in a langragian or Eulerian form? How do the particles interact with the fluid-flow field? Do you solve an equation or set of equations for the particle motion?

Generally micron or sub-micron size is where Brownian motion becomes significant. For larger particles the effect is negligible.

The random sampling approach I mentioned is for Lagrangian particle tracking. With Eulerian form you would need to form a diffusion coefficient, again a function of Boltzmann constant.

Friedlander's book "Smoke, Dust, and Haze" goes into some of this too.

If you can elaborate a bit more on what turbulent dispersion of particles means it would be great. From what I gather, it is not same as brownian motion.

Sanks

I only mean it's modeled in a similar fashion: you randomly sample from a distribution function to obtain a fluctuation which is applied to the particle force or velocity. You're right, they are very different physical processes.

Turbulent dispersion modeling accounts for the random fluctuations in particle motion due to turbulent kinetic energy. Instead of using the gas velocity alone, you also apply a velocity fluctuation derived from k (the random sampling) and use that in your particle force calculation.

You might start by having a look at two journal articles by J. D. Ramshaw:

Physics of Fluids 22, p. 1595 (1979).

Theoret. Comput. Fluid Dynamics 14, p. 195 (2000).

In addition, there are numerous references in those papers, including to the original work by Einstein.