You take some sand in a bowl and you start rotating it in circles, why do the bigger particles settle up?

The smaller particles slip through the spaces between the larger particles, so the smaller particles actually settle top the bottom, pushing the larger to the top.

I assume the axis of rotation is in  the centre of the bowl. The sand's boundary inside the bowl will take a paraboloidical( a 3D parabola) shape. This shape is explained by taking into account the different forces acting on the particles, these are gravity, cohesion between similar particles of sand and adhesion between sand and bowl's surface. The reason that bigger particles settle up is that these particles will experience a lesser cohesion due to their large size and hence will be less attracted towards other particles which obviously remain downward. I want to mention that if their weight is very much greater than the smaller ones then they will remain at the bottom as cohesive forces will not be able to counter that weight.

And it's the same reason why stones gradually come to the surface of the garden and the Brazil nuts work their way to the top of the packet of muesli!

I mean it, I'm not kidding.