Why is it so hard to mix spaghetti with meatballs? When I cook spaghetti with a sauce that includes meatballs or chopped vegetables, those stay in chunks and won't get uniformly mixed in the pasta.
Is there a simple reason for that?
Has it been studied? you know some people study piles of sand with various grain sizes? 
 A: 
When I cook spaghetti with a sauce that includes meatballs or chopped
vegetables, those stay in chunks and won't get uniformly mixed in the
pasta. Is there a simple reason for that?

I do not know if anyone ever studied spaghetti, if that is what you mean (see below). The reason is very simple: spaghetti are thin and meatballs are big.

How could they ever mix? If you pour the sauce and meatballs on top of spaghetti, even if you stir, they will not mix as they cannot mix: when spaghetti happens to be on the top of a meatball it will slip down along its sides, and the meatball will emerge.
If the meatballs are about the size of spaghetti  like here (polpettine)
(recipe ) then, with a little stir, they will perfectly mix.
The bigger is pasta and the better they'll mix here you have bucatini,
here you have rigatoni


The same applies to vegetables: if they are finely chopped like here: recipe

As you can see in the recipe there are also mushrooms here, but they mix perfectly well.
In a nutshell: what is relevant here is the ratio pasta /meatball

Has it ever been studied?...some people study piles of sand with various grain sizes?

The physical phenomenon involved here is: granular convection "a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes also described as the Brazil nut effect when the largest particles end up on the surface of a granular material containing a mixture of variously sized objects; this derives from the example of a typical container of mixed nuts, where the largest will be Brazil nuts. The phenomenon is also known as the muesli effect since it is seen in packets of breakfast cereal containing particles of different sizes but similar density, such as muesli mix." [wiki]
Smaller grains, because of gravity,  fall into the gaps between other grains created by the shakes, which are to small to be filled by bigger grains. The latter rise when the KE from the shake is greater than the PE needed to scale the diameter of one grain
Experiments made in reduced gravity show that this phenomenon is dependent on gravity
A: I think it's quite a good question. It's certainly something I've observed myself, and while the consistency of the sauce does seem to have an effect (e.g. I seem to remember it changes if you add butter, but I can't remember if this makes it better or worse), there does seem to be a general tendency for the vegetables etc. to cluster in one place instead of being evenly dispersed through the spaghetti.
I suspect it's a nice example of what's called an entropic effect. "Entropic" just means something that happens because there's a lot more ways it can happen than ways it can't. Tangling of cables is often given as an example: if you put all your computer cables in a drawer and let them move around, there are a lot more ways they can be arranged where they're tied in knots with each than ways in which they aren't.*
I suspect that the spaghetti/meatball separation happens for a similar reason. The spaghetti will tend to get tangled up and wound around the other strands of spaghetti, because there are many ways in which this can happen - many ways in which one spaghetti strand can be wound around another one, and many more still if three strands are involved, and so on. But if there's a meatball in the way then that reduces the number of ways in which the spaghetti can get tangled. Although there is more than one way to wind a strand of spaghetti around a meatball, there are fewer possible ways of doing that than winding it around other long strands of spaghetti.
Thus it seems plausible that under the right conditions (e.g. meatball size, spaghetti length and flexibility, sauce stickiness and so on) there could be a much greater number of states in which all the spaghetti is in one big lump than states in which it's evenly mixed with the meatballs, leading to an entropic "force" tending to separate the two types of object.
This is just a hypothesis though - it would be interesting to try and construct some kind of model to demonstrate it, but that could turn into quite a lengthy project! It would also be interesting to know whether the same process can take place on the molecular scale.
*One should be a bit careful with these examples, though - there are other physical processes involved in tangling cables, and if you take care to make sure you don't twist the cables when you store them away, they will tend to tangle a lot less. I'm sure that the entropic effects are also not the only ones at play in a bowl of pasta.
