A single experiment with variable low-pressure air flow through a packed bed leads to two methods for determining particle size

Two piston-in-cylinders, charged with air at ambient temperature and pressure, are moved from rest to a constant displacement rate in a syringe pump. The air is pumped to a packed column and an elevated steady state pressure, measured just upstream of the bed, is quickly attained. Upon stopping the pistons' motion, the pressure decays back to its ambient level. The growth and decay phases are described by material balances and the Blake–Kozeny laminar-flow model. The unknown parameters in solutions to the resulting first-order differential equations are determined by fitting the pressure–time data. For the growth phase, the fit leads to the determination of the initial system volume and the steady state pressure, whereas for the decay phase the fit gives a pseudo-time constant. This provides sufficient information to calculate the permeabilities and mean particle sizes—the Sauter mean diameters—for both phases. Packed columns of Aldrich Sand, sieve-size range 0.211–0.297 mm, and glass beads, nominal size 1 mm, give the following means: for Aldrich sand, 0.26 ± 0.02 and $0.27 ± 0.02$ mm; for the glass beads, $1.11 ± 0.06$ and $1.09 ± 0.06$ mm, for the growth and decay phases, respectively. Analogous experiments with a capillary tube, internal diameter $0.485 ± 0.001$ mm, give the following internal diameters: $0.492 ± 0.007$ and $0.501 ± 0.007$ mm for the growth and decay phases, respectively.