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Background story: I put my duvet (synthetic filling) into a washing machine, and the machine was unable to spin-dry it. My mom told me: "It's because it is full of air".

I was not satisfied with the answer. So: Why is it problem for a washing machine to spin-dry a synthetic duvet? From my point of view, the only important factor is the momentum of inertia, that depends only on the weight and distribution of the weight.

I do not think that the momentum can be significantly higher for a single duvet than for a large lot of casual clothes.

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It couldn't spin it? Or it did not come out dry after being spun? – Jaime Jan 3 '13 at 19:50
It couldn't spin, it tried several times, but failed. – yo' Jan 3 '13 at 20:32
Probably you did not distribute the weight homogeneously. If that is the case, when trying to spin the axis would experiment torques larger than the allowed for protection reasons, and some internal mechanism prevents this by stopping. – rmhleo Jul 19 '15 at 8:58
@rmhleo But this happens also when you have some standard clothes there, and I think it happens even more. But I don't know... – yo' Jul 19 '15 at 9:57
Well is not clear what the conditions were. Maybe it happened that the weight exceeded the capability of the washing machine. In any case, if it did not spin it looks like a technical problem, or an engineered mechanism, rather than a physics related issue. – rmhleo Jul 20 '15 at 8:32

As noted in the comments, weight must be evenly distributed or the washing machine will spin off center and shut down.

Clothes are a lot of small pieces. When spinning starts, they fly to the outside. Usually they are uniformly distributed.

A duvet is a single large piece. It is easy for it to be off center. For example, if you wrap it around the outside, the ends may overlap. When spinning starts, the place where the ends are is not uniform. The ends try to pull the whole duvet over. You may succeed if you carefully arrange the duvet when the spin cycle starts.

You may also destroy the duvet. Down comforters and sleeping bags are particularly susceptible. They have internal compartments to keep the feathers uniformly distributed. The compartments are made of very thin material to keep comforter or sleeping bag light. They are not strong enough to hold wet feathers against centrifugal force.

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The solution has to have with the 'surface tension' of the exterior surface.
Google for 'surface tension' satin water repellent synthetic tissue and find:
'Liquid water is prevented by surface tension from penetrating' on Polyester Microfilament Woven Fabrics

Conclusion : the exterior surface of the duvet (and not the interior material) is blocking the water flow, much similar to the properties of bird's feathers.

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