Complexity

The brazilian nut effect by void filling: an analytic model

Journal Article

Abstract

We propose an analytic model of the Brazilian nut effect (BNE) that utilizes void filling as the primary mechanism behind the rise to the surface of one large buried intruder particle in an externally driven confined mixture with many small particles. When the intruder rises upward, it creates a void underneath it that is immediately filled by small particles preventing the intruder from sinking back to its previous position. Even though the external driving is only along the vertical direction, the small particles are able to move transversely into the void due to the Janssen effect, which postulates that the magnitudes of the vertically directed and transversely directed forces in a confined granular system are directly proportional to each other. The Janssen effect allows us to calculate the transverse speed distribution in which the small particles fill up the void and the temporal dynamics of the intruder particle in the vertically shaken container. We determine the time‐dependent behavior of the intruder vertical position h, its rise velocity dh/dt, and the phase (dh/dt vs. h) as a function of particle size ratio Φ, container diameter Dc, kinetic friction coefficient μ, and packing fraction c. Finally, we show that the predictions of our BNE model agree well with published experimental and simulation results. © 2010 Wiley Periodicals, Inc. Complexity 16: 9–16, 2011

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