Granular Segregation
Shake a can of mixed nuts and the largest nuts migrate to the top — the Brazil nut effect. This counterintuitive result arises because small particles fill voids beneath large ones, the effective buoyancy depends on size, and convection rolls carry particles along container walls. The inverse effect (large particles sinking) also occurs under certain conditions.
F_buoy ∝ (ρ_eff − ρ_particle) g V_particle | void-filling probability ∝ r_small² / r_large²
Watch the gold (large) particles rise and the blue (small) ones settle. The bars show mean height of each species. Inverse mode: large particles are denser and sink.
Why do large particles rise?
The Brazil nut effect was first described rigorously by Rosato et al. in 1987. Three mechanisms cooperate:
- Void filling — When a large particle moves up, small particles quickly fill the void beneath it, preventing it from falling back. The probability that a small particle fits under a large one scales as (r_small/r_large)².
- Convection — Shaking drives granular convection cells: particles rise in the center and descend along the cooler walls. Large particles rise with the center flow but are too big to descend through the narrow wall gap, so they accumulate at the top.
- Effective buoyancy — In a fluidized granular medium, denser (larger) particles experience a net upward pressure from the fluctuating granular temperature gradient.
The reverse Brazil nut effect occurs when particles are much denser than surroundings, or when the vibration is in the inertial regime (high amplitude, low frequency) where geometric effects are overwhelmed by inertial sinking.