Complications in the System
While their remains a lack of agreement on many fronts, all experiments agree that the larger the bead, which is termed 'intruder' in the literature, the faster it will rise through the vibrating bed. Studies have found that merely two minutes of mixing is sufficient to reach a steady state. Moreover, when the Brazil nut effect is observed, it is distinguishable almost immediately after the vibrations begin.
Differences in scientific findings usually point to the necessity for a more nuanced theory, and this case is no exception. More recent papers have found more and more characteristics on which granular segregation hinges. For example, a recent study by Ulrich et al. found that a transition from reverse Brazil nut effect to Brazil nut effect could be induced simply by waiting long enough. That is, they found that after 25 hours of continuous shaking, or aging, a sharp transition occurred for unchanged driving conditions. Perhaps more telling was their find that after an aggressive cleaning procedure of the glass tube in which the beads were, the system returned to its original position.
Ulrich et al. explained this phenomenon by measuring the friction on the sides of the container. They found that aging the system increased the friction, while cleaning the system decreased the system to its original value. They suggest a two-mechanism system. First the dense particles sink to the bottom because their buoyancy is smaller than their weight, then, the sidewall-driven convection begins to play a part. The way this convection works is that as the container vibrates up and down, a convection roll going downwards at the walls of the container and upwards in the center of the container begins. When the larger particles move upwards in the center, they have a lower probability to enter the downstream layer at the walls of the container. Since an increase in the friction of the walls would strengthen the convective motion relative to the buoyancy, it would strengthen that segregation method.
Can a new mechanism be found that will combine all ten of the currently proposed mechanisms into simple equations? In another paper, Schroter et al. seem to think so. Doing so, however, will take many more years of research efforts. The wonder of children at the segregation of the nuts in the mixed nuts box is not so misplaced nor so easily explained after all.