A new computational algorithm for the interaction between electrically charged particles
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A new computational algorithm for the interaction between electrically charged particles Claus Bissinger1 · Holger Grosshans1 Received: 28 December 2019 / Accepted: 4 April 2020 / Published online: 25 April 2020 © Springer Nature Switzerland AG 2020
Abstract In industrial applications, the dynamics of particles is frequently controlled through electrical charges, e.g., in electrostatic precipitators or during powder coating. However, the electrification of particulates can also cause the formation of deposits, hazardous sparks, and dust explosions. The objective of our work is to propose a new computational method which captures accurately the dynamics of interacting electrically charged particles during their approximation. This model focuses especially on the precise prediction of the contribution of the electrostatic and collisional forces whose time-scales are typically much smaller than the numerical time-step used to compute forces other than the Coulomb force. To this end, binary particle interaction is calculated through the local adaptive refinement of the time-step. We present results that demonstrate the capability of the method to accurately and efficiently describe binary and multiple particle interaction. Further, through comparison with benchmark solutions we elaborate on the conditions, in terms of particle charges and sizes, for which our model is superior to previously employed approaches. Keywords Computational method · Particle interaction · Particle dynamics · Electrostatics
1 Introduction The dynamic interaction of electrically charged particles is an elementary mechanism of many industrial processes. Examples include the control of particle trajectories during electrostatic precipitation [1, 7], powder coating [30], pneumatic conveying [29], or printing [25]. As regards granular media, recent studies demonstrated the huge impact of an excess of electric charges on the interactions between grains [20, 23]. Not only solid material, also droplets can acquire a net excess of electric charges [3]. The influence of these electric charges on the collision between droplets is also primordial as it affects natural phenomena such as thunderclouds [4]. Nonetheless, electrostatics may also alter particle dynamics in an unwanted way such as the attraction of charges on the particle and its image on the surface of transport pipes leading to the formation of deposits [17, 18].
The fundamental physics and mathematical equations underlying this interaction are well-established. Namely, Newton’s second law of motion describes inertial acceleration, Gauss’ law (also known as Maxwell’s first equation) gives the electric field forces, and the Navier–Stokes equations in case aerodynamic interaction is relevant. Albeit being generally accepted, the numerical solution of a coupled system of these equations poses challenges. Let alone the computation of collisions between uncharged particles, two approaches became popular, namely the hardsphere and the soft-sphere approach. In the hard-sphere approach [5], the p
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