References for effective viscosity experiments

Presentation

I am studying the following fluid mecanics problem :

let’s consider a domain $Omega$ filled with water. In this fluid, we can find perfectly spherical particles of radius $epsilon h$ where $epsilon$ is a small parameter and $0 leq h leq 1$ , which are periodically disposed in the fluid as pictured below

As the Reynolds number is supposed to be low, the fluid speed $u^epsilon$ satisfy a stationnary Stokes problem with boundary conditions on each particles.

Through mathematical techniques (Homogenization), it is very common to find that the sequences $(u_epsilon)_{epsilon}$ converges toward $u_0$ which satisfies a modified stationnary Stokes problem in the domain $Omega$, without particles this time, but with a different viscosity for the fluid. This new viscosity $nu_0$ is called effective viscosity since it depicts pretty well the real flow, and there exist a lot of studies on this topic.

My questions

I would like to know if you have ever heard of such fluid configuration being experimented in a laboratory ? I was wondering if it would be possible to measure the viscosity, so as to emphasize the mathematical and numerical results I have on this precise issue.

What i’m fearing is that it will be impossible to respect the periodic repartition of the particles in the fluid. I also fear that the rugosity of the real particles will interact with the flow, since I have considered perfectly spherical particles for the mathematical analysis.

Any help or references are welcomed, I’ll be glad to furnish you with more details on the subject.