Experimental evidence for the stochastic theory of particle flow under gravity

Abstract

Experimental evidence is presented for a recent stochastic theory of flow which represents the convergent flow of cohesionless particles under gravity toward an open orifice as equivalent to a counterflow of voids from the orifice upward through the bed by biased random flight; the theory is summarized in a new phenomenological form. Data, taken from the literature, were obtained from cells initially loaded with alternate layers of differently colored granular material. The theory predicts that after a fixed flow, each layer develops a depression such that if z o is the original height of a given layer above the orifice and z m is the corresponding height of the depression minimum, then for three-dimensional flow a plot of z m 2 vs. z o 2 for different layers will yield a straight line of slope one; the intercept gives statistical information concerning the equivalent void jumps. For two-dimensional flow, the corresponding theoretical plot is z m 3 2 vs. z osu 3 2 Data plotted from several sources conform closely to the above predictions, provided z o is not too large for a given flow. The latter discrepancy is qualitatively explained by a transient effect requiring the density to fall to a certain level before steady-state flow can occur.