https://en.wikipedia.org/wiki/Granular_convection "Granular convection, or granular segregation, is a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes 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." Cool! This sounds like a great topic for a math physics PhD (theoretical) or a terrific HS science project (experimental). There must be some *critical* numbers -- e.g., in a mixture of ball bearings of two different sizes, there must be a critical ratio of sizes, or a ratio of percentages (or both), where the increased density (per unit volume) of the larger ball bearings outweighs (!) the Brazil Nut Effect. Alternatively, adjust the mass density ratio of the larger to the smaller ball bearings until the effect disappears. Also, I don't know if the *slipperiness* of the ball bearing surfaces have any effects; e.g., what if all the ball bearings are covered in a light oil? One could make a Carnot-like "heat engine" in which the larger ball bearings *do work* as a result of the shaking -- e.g., perhaps by some magnetic coupling. Extra credit: what happens in 2D (shaking "discs/rings" instead of ball bearings) or 4D ? This is exactly the sort of problem that would have interested Maxwell -- I wonder if he thought about it? At 09:35 AM 12/10/2018, Veit Elser wrote:
On Dec 10, 2018, at 12:16 PM, Henry Baker <hbaker1@pipeline.com> wrote: Has this problem been studied before?
Try searching "Brazil nut effect".
-Veit