TY - JOUR
T1 - Scaling behavior of coarsening Faraday heaps
AU - van Gerner, Henk Jan
AU - van der Weele, Ko
AU - van der Meer, Devaraj
AU - van der Hoef, Martin A.
PY - 2015
Y1 - 2015
N2 - When a layer of sand is vertically shaken, the surface spontaneously breaks up in a landscape of small conical “Faraday heaps,” which merge into larger ones on an ever increasing time scale. We propose a model for the heap dynamics and show analytically that the mean lifetime of the transient state with N heaps scales as N −2 . When there is an abundance of sand, such that the vibrating plate always remains completely covered, this means that the average diameter of the heaps grows as t 1/2 . Otherwise, when the sand is less plentiful and parts of the plate get depleted during the coarsening process, the average diameter of the heaps grows more slowly, namely as t 1/3 . This result compares well with experimental observations.
AB - When a layer of sand is vertically shaken, the surface spontaneously breaks up in a landscape of small conical “Faraday heaps,” which merge into larger ones on an ever increasing time scale. We propose a model for the heap dynamics and show analytically that the mean lifetime of the transient state with N heaps scales as N −2 . When there is an abundance of sand, such that the vibrating plate always remains completely covered, this means that the average diameter of the heaps grows as t 1/2 . Otherwise, when the sand is less plentiful and parts of the plate get depleted during the coarsening process, the average diameter of the heaps grows more slowly, namely as t 1/3 . This result compares well with experimental observations.
U2 - 10.1103/PhysRevE.92.042203
DO - 10.1103/PhysRevE.92.042203
M3 - Article
VL - 92
SP - -
JO - Physical review E: covering statistical, nonlinear, biological, and soft matter physics
JF - Physical review E: covering statistical, nonlinear, biological, and soft matter physics
SN - 2470-0045
IS - 4
M1 - 042203
ER -