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While I know (and can observe) that solids don't settle easily in a turbulent flow, I struggle with understanding why exactly this is the case. Here' my problem:
Conceptually, turbulence means high Re-number (or vice ersa), and that means the inertail forces are far stronger than friction/viscous forces. But friction keeps the particle suspended, and I would see bouyancy and gravity as inertial forces.
In a non-moving fluid, the only forces acting on a particle are friction (pointing upwards with a sinking particle) and gravity/buoancy, with a net force pointing up or down and/or movement of the particle.
In a perfect turbulent flow, I would expect no dominant direction of flow. So, the fluid 'tugs' at my particle in one direction one moment and somwhere else the next moment - the net force from the friction over a long enough time will be zero, but bouyancy has a preferred direction.

Here's how I would explain why solids don't settle in turbulent flows and I ask you to poke holes into this explanation:
In turbulent conditions, friction is generally proportional to $v^2$, with $v$ beeing the velocity of the particle relative to the fluid. So compared to the same particle in the same fluid but in laminar conditions, the friction resulting from a specific downward (or upward) velocity is higher. This is compunded by the fact that for a particle sinking, any surrounding upward flow will have a stronger effect than a surrounding downward flow with the same speed relative to the particle. Hence, solids settle far slower in turbulent flows.

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You're right that turbulence is the relationship of inertial forces to viscous forces:

$Re=\frac{u L}{\nu}$

but the thing is, the viscous forces don't change in a fluid. So Turbulence is usually a result of an increase of velocity or length scales... not a decrease of viscosity (friction forces).

The drag on your particles (assuming they're spheres), can be expressed as:

$D = 0.5 C_d \rho u^2 A$

An increase in velocity will result in an increase of drag on your particles. Since the turbulence is chaotic, and has motions in all directions, this drags the particles up and down and left and right, preventing them from settling in their normal downward direction.

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