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This is kinda cool, but it would take _forever_. With 3D scanners getting cheaper and cheaper by the day, it's a cool hack, but that's it.
yeah, for example http://www.nextengine.com is a good one, and only 3K$.
The problem with the NextEngine is (from what I understand) that it's so vibration sensitive that you pretty much have to set it on a timer and leave the room...

There are a few companies working on getting some cheap scanners out there, it's pretty exciting.

Only when you are scanning at very high 3D DPI. Another problem is shinny surfaces on your model that introduce noise and holes on the 3D mesh (because the lasers reflect in odd directions from them). They provide some kind of powder to damp that, but still annoying.
There must be a cheap way of automating the adding of milk... Some kind of really slow pump.
There's a long discussion in the comments about how to automate the milk, but most of them are wrong.

The goal is to raise the level of the milk on the model by, let's say, 1mm and take a snapshot. In fact the method of adding 3 tbs for each picture is wrong - because adding 3tbs may raise the milk level by less than 1mm when the current section of the model is thin and more than 1mm where the model has a thick profile. If you're doing it by hand, you want a scale on the side of the container and you should add enough milk to raise by 1mm for each photo.

More wrong answers: You can't use a pump with a constant rate, for the same reason as above. Using a screw drive alone doesn't do that either, because if you lower by 1mm the milk rises more than 1mm, and has the same variance-due-to-thickness problem.

Right answers: Someone proposed a black bar on the side of the tank, and a pump with constant rate of flow. That's not a bad idea - you can use the height of the black bar in the photos to judge what the current milk height is, and use that as the z position for the current heightmap.

If your heightmaps must be evenly spaced, there's one more right answer - use a screw drive to lower the model into the milk and a drainhole halfway up the container and a pump to maintain the level of the milk. Now when you lower by the model by 1mm the level of the milk rises by 1mm on the model.

Did I miss another right answer?

Very cool. Except for the using milk part (but that can likely be replaced with other things).

You could automate this with a drip. Drips of opaque coloured liquid slowly drop into the container. The camera could even figure out when a drop hits the liquid to wait for the ripple to finish - and take a snapshot.