Thank you very much.

Thank you to all the participants and also remotely.

So as you said, we are the collaboration

by supervising Dr. Schuster.

So that was a few years ago.

So I'm going to talk about particle-free interactions.

And the link between the two parts

will be how the particles are triggering instabilities

and the transition to turbulence.

So the first case, the first configuration

is very simple in the sense that it is only awake instability.

And the second one is a bit more complex

because that is a real transition to turbulence

in a particulate flow.

So that would be two parts of about 20 minutes, I hope.

So the question I would like to address is very simple.

When you have particles in the flow,

do we enhance perturbations or do we

damp perturbation in order to be able to know

the overall response of that mixture?

So do we increase the level of turbulence

or do we decrease the level of turbulence?

And you see that with the few answers that I proposed,

that the answer is not unique.

So for example, when you add particles in the fluid,

you know that you increase the mixture of viscosity

because the presence of the particles in the region where

you have strain will dissipate energy

because they cannot deform.

So they exert extra dissipation to the mixture.

So we may expect that adding particles in the fluid

will damp perturbations.

But if you have inertial particles,

so the density is different from the fluid,

when you increase the inertia, you

know that inertia is the mechanism

at the onset of turbulence.

So we may expect that when you have inertial particles

in the fluid, you may increase the level of turbulence

or the onset of turbulence.

When you have inelastic collisions, lubrication,

you know that all these effects are dissipative.

So again, you may think that this is a damping effect

when you have a mixture of particles in fluids.

Gravity, so gravity-induced settling,

because of the settling, you have the wake.

You have the boundary layers along the particles.

And that will generate perturbation.

So in that sense, we can expect that the presence of particle

will enhance the level of agitation in the fluid