My problem is, that I also want to remove those particles from my flow domain that hit the wall of my geometry. That's why I think I need to track the particle trajectories. If I only use a scalar value for the particle phase I don't see a chance to remove the particles, that hit the wall.

So my approach would be now:

1. Create a particle material

2. Define a fluid particle mixture

3. At the inlet assign that mixture

4. Add expression for particle sink at wall and diffusion between mesh cells

You can put factors into the scalar approach to handle things like this but they tend to be approximations and can involve some tricky maths to derive.

It is much simpler to implement this sort of thing in a Lagrangian frame work. But note you are going to have to require enough particles to create a good estimate of the billions of particles there are in reality.

So you are going to have to add your Brownian motion stuff and removing particles which hit the wall to the Lagrangian model. Removing particles which hit the wall is easy (just use 0 coefficient of restitution).

This thread reminds me of my problem.
 

My contribution is more of my problem. My study is to show the effect of reinforcing materials on the viscosity of a nano particle reinforced metal matrix composite in molten form. I feel its an experimental problem but my supervisor feels its something I should solve numerically, pls I need advice I don't seem to know how to go about it.

I have no idea what the important physics of that would be so cannot help you. Your supervisor seems to know, why not ask him?

Sorry for my late reply! What I ended up doing in the end is exactly what Glenn Horrocks recommended right from the start. Instead of simulating the particles in a Lagrangian framework I used an Euler-Euler approach, in particular the quadrature method of moments. You can have a look at the method e.g. in the paper "Simulation of nanoparticle coagulation under Brownian motion and turbulence in a differential–algebraic framework: Developments and applications" by Guichard et al.