Spontaneous Separation of Charged Grains

In 1867, Lord Kelvin described an experiment in which two streams of water droplets were connected so that each stream amplified the charge on the second stream [W. Thomson, Proc. R. Soc. London 16, 67 (1867).]. We present here a complementary effect in flowing grains that spontaneously separates similar and well-mixed grains into two charged streams of demixed grains. This effect has important consequences for industrial and natural processes.

Figure 1

Demixing of mechanically similar grains. (a) Overview of experiment: grains are supplied by vibrating feeder (top) into charged acrylic collecting cylinder (left). (b) Size distributions of red and blue grains, obtained by passing grains through sequential sieves. Insets to right show micrographs of grains, illustrating similar shapes.

Figure 2

Correlation of charge separation of colored sand with externally applied voltage. Intensity of segregation $I_S$ from processing of digital photos of sandpiles and measured voltage near feeder outlet vs distance from centerline of chute to nearest edge of a positive Van de Graaff generator. Error bars represent standard error over multiple trials. Inset: Geometry used; Van de Graaff generator is moved to right in orientation shown. The black box indicates the approximate location of rectangular array of $2\times 8$ collecting vials used in the experiment of Fig. 3a.

Figure 3

(a) Demixing in arrangement of Fig. 2 (inset) of initially mixed 50–50 blend of acetaminophen (“APAP”: USP special grade, Mallinckrodt, Raleigh, NC) with a common pharmaceutical excipient (“MCC”: PH-200, FMC BioPolymer, Philadelphia, PA). Powder is collected in sampling bins arrayed in ranks within the rectangle indicated in Fig. 2 (inset); bins in the further rank from the chute have consistently lower APAP concentration than bins in the closer rank. (b) Charge densities measured on grains collected in a Faraday cup at the feeder outlet.

Figure 4

(a) Close-up of demixing in arrangement of Fig. 1 showing that blue and red charged grains separate at the outlet. (b) Detail of beard of adhered grains (experiment halted, and background digitally filtered to remove extraneous equipment). (c) 2D simulation of strongly (blue) and weakly (red) charged particles on an inclined and vibrated surface. Grains (cyan) fixed beneath the chute simulate induced negative charges. Simulation uses elastoplastic model of [21] integrated using Euler method for 2D particles with coefficient of restitution 0.16 and kinetic friction coefficient 0.2. Simulation shows state after 500 000 time steps. Computations use dimensionless units with grain $\mathrm{\text{diameter}}=1$, $\mathrm{\text{mass}}=5$, $\mathrm{\text{gravity}}=0.01$, and $\mathrm{\text{time step}}=0.125$. New positive grains are created every 500 time steps at randomized locations $25\pm 4$ units upstream and above the chute. The histogram shows positions of all grains that have fallen 15 diameters below the chute, after which grains are removed from the simulation.