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## Main Question or Discussion Point

Hi all,

I want to calculate how tell if a particle in a centrifuge in deep space will move towards the rotation axis or to the rim of the fluid. There is no container walls. This is not a HW problem. I watched the video

and wanted to learn more about this. (it is under the you-tube search subject: rotating fluids microgravity)

As the video shows, less dense particles move towards the rotation axis, more dense particles move towards the rim.

Here's what I have so far.

Suppose I have a centrifuge in a space station in orbit. The rotation axis points along the +Z axis. I have a particle of mass M, volume V, and density ρ[itex]_{p}[/itex]. To keep things simple, the particle remains at latitude 0 degrees (equator, no north and south motion, etc, but it can move radially in or out) The particle is immersed in a fluid of density ρ[itex]_{f}[/itex] and spins at constant angular velocity ω.

Since the particle moves in a circle, by Newton's Laws, its net force is mrω[itex]^{2}[/itex]. mrω[itex]^{2}[/itex] points inwards radially. This term takes the place of "ma" in the usual Newton's Laws. There should be a bouyant force ρ[itex]_{f}[/itex]Vg? that points radially outwards (except that there's no "g" for gravity in this situation, so I don't know how to replace "g" in this context). Since the mrω[itex]^{2}[/itex] is a net force, there must be some force to cause this and overcome the bouyant force to keep the particle moving in a circle. In a centrifuge, the Normal force of the walls of the container on the object would provide the mrω[itex]^{2}[/itex] but I don't know what that force would be if the fluid has no walls.

If I could just write down Newton's Laws with this I would be good to go. I could not find any old HW problems or websites that talked about "Centrifuge Mechanics".

What force works against the bouyant force to move the particle in a circle?

How do I replace "g" in ρ[itex]_{f}[/itex]Vg for this context?

Between the bouyant force and the force that acts towards the center, is there an "ma" to categorize how the particle moves radially until it hits the rotation axis or the rim?

Thanks for you help, as always.

I want to calculate how tell if a particle in a centrifuge in deep space will move towards the rotation axis or to the rim of the fluid. There is no container walls. This is not a HW problem. I watched the video

and wanted to learn more about this. (it is under the you-tube search subject: rotating fluids microgravity)

As the video shows, less dense particles move towards the rotation axis, more dense particles move towards the rim.

Here's what I have so far.

Suppose I have a centrifuge in a space station in orbit. The rotation axis points along the +Z axis. I have a particle of mass M, volume V, and density ρ[itex]_{p}[/itex]. To keep things simple, the particle remains at latitude 0 degrees (equator, no north and south motion, etc, but it can move radially in or out) The particle is immersed in a fluid of density ρ[itex]_{f}[/itex] and spins at constant angular velocity ω.

Since the particle moves in a circle, by Newton's Laws, its net force is mrω[itex]^{2}[/itex]. mrω[itex]^{2}[/itex] points inwards radially. This term takes the place of "ma" in the usual Newton's Laws. There should be a bouyant force ρ[itex]_{f}[/itex]Vg? that points radially outwards (except that there's no "g" for gravity in this situation, so I don't know how to replace "g" in this context). Since the mrω[itex]^{2}[/itex] is a net force, there must be some force to cause this and overcome the bouyant force to keep the particle moving in a circle. In a centrifuge, the Normal force of the walls of the container on the object would provide the mrω[itex]^{2}[/itex] but I don't know what that force would be if the fluid has no walls.

If I could just write down Newton's Laws with this I would be good to go. I could not find any old HW problems or websites that talked about "Centrifuge Mechanics".

What force works against the bouyant force to move the particle in a circle?

How do I replace "g" in ρ[itex]_{f}[/itex]Vg for this context?

Between the bouyant force and the force that acts towards the center, is there an "ma" to categorize how the particle moves radially until it hits the rotation axis or the rim?

Thanks for you help, as always.

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