The BuffonLaplace needle problem in three dimensions
Abstract
We generalize the BuffonLaplace needle problem, one of the earliest statistical calculations, to three dimensions, account for finite widths, and find the probability for particles of arbitrary length l to make contact with a 2D sievelike mesh. We assume a frictionless interaction with the mesh to account for particle rotations that occur after contact, and find that the probability for a stable intersection goes to 1 for long particle lengths as P(l) = 1(0.5 ± 0.02)l^{1.00 ± 0.01}. This approach represents the first step toward modeling the efficacy of a squaregrid mesh for filtering rodlike granular particles from solution, assuming that the volume fraction phi is kept low, so particles cannot cooperatively jam. We argue that our approach results in an upper bound on the filtration probability and confirm this with comparison to a simple experiment in which cylindrical particles are filtered with a squarehole mesh.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2009
 DOI:
 10.1088/17425468/2009/09/P09010
 Bibcode:
 2009JSMTE..09..010D