Electrostatically Charged Granular Matter

Abstract

In many industrial applications and experimental situations, the handling of granular matter involves friction and is therefore accompanied by triboelectric charging of the grains. This applies in particular to dry granulates made of insulating material, but also to more complex systems such as powders suspended in a non-polar liquid. In fact, whenever a granular material is processed, stirred or shaken, such that contacts between different grains are continuously established and broken, surface charges are separated to some extent, leading to mutual electrostatic forces. The process of charge separation is a complex phenomenon and depends strongly on the material as well as on the surface properties of the grains. Even the sign of the mean charge may depend on the choice of the material. Therefore, interesting effects are expected if grains of different materials are mixed or if the grains interact with surfaces made of a different material. The study of electrically charged granular matter is particularly fascinating because of the long-range nature of Coulomb interactions. In fact, various electrostatic properties such as the integral charge and the macroscopic electric field can be detected and quantified easily. Sometimes the influence of electrostatic forces can even be seen with the naked eye. For example, simple plastic spheres poured between two plexiglass plates and shaken, become equally charged and arrange themselves in a beautiful pseudo-crystalline configuration because of their mutual Coulomb repulsion (see Figure 11.1). Apart from the material properties, the influence of electrostatic interactions depends significantly on the size of the grains: Since in the case of insulators the charges are located on the surface of the particle, the typical charge per grain will scale with its surface area. Hence the average charge per unit mass will decrease with increasing particle size. Therefore, the influence of Coulomb forces is expected to be particularly strong for very small particles, especially for fine powders. On the other hand, approaching scales of 1 micron or below, the grains are so small that the number of elementary charges per grain is limited or even equal to one. This means that for granular matter on the nanometer scale, the quantized nature of electric charge is expected to play a significant role as well. The purpose of this article is to summarize some interesting recent developments in the theoretical understanding and modeling of charged granular matter. Regarding the theoretical modeling, the simplest system of interest is a granular gas of equally charged particles, which will be discussed in Section 11.2. Another important physical situation, on which we will focus in the present article, is electrically charged granular matter suspended in a non-polar liquid (see Section 11.3). If the suspended particles are very small, the influence of the van