Violent separation

In keeping with my original plan for this blog, I am now going to teach myself something new.

Here is something I have known about and occasionally seen since I was a kid, and know the name of, but hadn't seen it in operation and didn't actually know how it worked until I decided to write this post and figure it out:

It works exactly the same way as this thing, which I saw for the first time as an adult:

Some of you will have recognized a cream separator in the top image (which I found courtesy of Wikimedia Commons). They've been around for ages: from hand-cranked units to electrically powered, the design really hasn't changed much in the past century.

The bottom image stands about as tall as a person, and is also a centrifuge. It just happens to not deal in milk.

In both cases, I knew that they spin really fast, up in the thousands of rotations per minute, and by spinning generate very high pseudo-gravity, and by high gravity make two substances of different densities separate faster than they would if you put them in a bucket and left them to sit for a few days. What I didn't know was exactly how they did that separation. What's actually inside that centrifuge case?

A lab centrifuge spins vials and packs the heavy stuff at the bottom. It's pretty straightforward, but it's not something that runs continuously the way the two centrifuges pictured above do. The vials have to be filled and spun and emptied, which is a real pain if you need to process hundreds of cubic metres every day.

It turns out the internals are elegant in their simplicity. It consists of a series of nested bowls with a gap between each one and a hole punched through about midway out to the edge. The mixed feed fluid (whole milk) enters at the centre, where there is no centrifugal force, then is directed to the holes in the internals which distribute it through all the layers of the nested bowls. As the fluid passes through the holes some of it moves between the layers instead of on to the next layer. The whole thing is spinning, so the heavier fluid (milk) ends up collecting at the edge, while the lighter fluid (cream) ends up collecting near the centre, just as they would sitting still in a bucket subjected to the normal pull of Earth's gravity—only faster, because the force of pseudogravity at a thousand RPM is higher than regular gravity. The two areas, edge and centre, are connected to the two outlet ports, so the two separated products can be continuously removed to make room for more incoming mixed fluid.

(The dotted line on the left side of the picture is the centre of the centrifuge, the axis of rotation.)

The cream separator relies on gravity to feed the whole milk down through the centre of the centrifuge from the big container sitting on top, and spins on a vertical axis, throwing the milk to the sides. The big centrifuge spins with its axis horizontal and relies on a pump to fill it up with fresh feed; otherwise it's exactly the same thing as the cream separator, only bigger.

Now I feel like doing some math. What is the force of pseudogravity at the edge of the cream separator's centrifuge bowl? Let's assume the bowl is 10cm from centre to edge and it's spinning at about 6,500 RPM.

The acceleration on a body rotating at constant speed is given by:

\[ A = R ( {2\pi \times \mathrm{rpm} \over60} )^2 = 0.1\mathrm{m} ( {2\pi \times 6,500\mathrm{min}^-1\over60\mathrm{sec/min} } )^2 = 46,332\mathrm{m/s}^2 \]

Since earth's surface gravity is 9.81m/s2, this is 4723 times earth's gravity at the outer edge of the bowl. On top of that, the edge of the bowl is travelling at 68m/s, or about 245km/hr.

If a 1g piece of the edge of the bowl were to break and fly off, it would have kinetic energy of:

\[{1\over2}mv^2 = {1\over2}(0.001\mathrm{kg})(68\mathrm{m/s})^2 = 2.3 \mathrm{J} \]

Which doesn't actually sound like a lot. It's the same amount of energy as a 4.6kg object travelling at 1m/s, or a slow walk. On the other hand if that big centrifuge, spinning at similar speeds, had an accident, well, things get kind of bad. Just a reminder of what the big one is supposed to look like:

This is one way they're not supposed to look:

Now if you look closely at it, you can see that it isn't even the centrifuge itself that exploded, just a piece between the motor and the centrifuge drive belts, which weighs a lot less. In fact, now you can see the actual centrifuge cover, because the drive guards have been blown off. If you look closely, you might also be able to see why this chunk of the power train stayed close to where it should have been:

It was tethered by its own drive belts. It's a good thing it was, because if it had gone flying and had hit one of the other six centrifuges and actually broken a centrifuge casing, things could have been catastrophic. As it was, I felt the kaboom with three cinderblock walls between us, and some of the ductwork on the ceiling, easily more than 10m high, had been torn apart by flying debris.

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