Modeling and Experimental Measurement of Triboelectric Charging in Dielectric Granular Mixtures

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Triboelectric charging, the phenomenon by which electrical charge is exchanged during contact between two surfaces, has been known to cause significant charge separation in granular mixtures, even between chemically identical grains. This charging is a stochastic process resulting from random collisions between grains, but creates clear charge segregation according to size in dielectric granular mixtures. Experiments in grain charging are frequently conducted with methods that may introduce additional charging mechanisms that would not be present in airless environments, and often aren't capable of measuring the precise charge of each grain. We resolved these issues through the development of a model that predicts the mean charge on grains of a particular size in an arbitrary mixture, and through experiments that do offer controlled measurement of precise grain charges. These results can be used to develop methods for electrostatic sorting to enable \textit{in situ} resource utilization of silica-based regoliths on airless extraterrestrial bodies.

Beginning from a basic collision model for a mixture of hard spheres, we developed a robust semi-analytical model for making predictions about the charge distribution in a dielectric granular mixture. This model takes a set of assumptions about a mixture, including the continuous size distribution, collision frequencies, and charge transfered per collision, and calculates the mean charge acquired by grains of each size after all charges have been exchanged. This model allows us to explore experimental results through many different lenses. To test our predictions and provide a repeatable and flexible method for analyzing charging in a variety of granular mixtures, we designed and built our own experimental test stand. This device is housed entirely in a vacuum chamber, allowing us to induce tribocharging in dielectric grains in a controlled airless environment and measure individual charge and diameter of a grain by dropping samples through a transverse electric field.

We observed that mixtures of zirconia-silica grains containing two primary size fractions exhibited size-dependent charge segregation when charged in vacuum. Unlike in other experiments with grains charged by fluidization with a gas, we consistently observed that the small grains charged predominantly positive, while the large grains were primarily negative. We considered a variety of charge transfer mechanisms and generated predicted charge distributions for each using the modeling framework we developed. Comparing these models to the collected data, we are able to assess the viability of each potential transfer mechanism by examining properties of its resulting distribution, including the relative charge magnitudes for each size fraction, the point at which the polarity changes, and the polarity and magnitude of the charge carrier density.

The results of this work provide solid supporting evidence for the role of positive charge carriers in dielectric tribocharging. While some prior work has suggested positive ions from the atmosphere and/or adsorbed water are responsible, we have observed that even when these environmental factors are reduced or eliminated, silica-based materials still exhibit positive charge transfer. The modeling framework developed in search of a descriptive model for this effect is a useful, adaptable tool. The experimental apparatus itself, and especially in conjunction with these modeling tools, overcomes some of the more difficult challenges faced by experimentalists investigating granular tribocharging, enabling further investigation into tribocharging in regolith and other dielectric materials.