Starting from the Boltzmann–Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances for each solid phase. To close locally averaged transport equations, a Maxwellian distribution is presumed for both particle velocity and charge. The hydrodynamic equations for bidisperse solid mixtures are first revisited and the resulting model consisting of the transport equations of mass, momentum, total kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, and charge is then presented. The charge transfer between phases and the charge build-up within a phase are modelled with local charge and effective work function differences between phases and the local electric field. The revisited hydrodynamic equations and the derived charge transport equation with constitutive relations are assessed through hard-sphere simulations of three-dimensional spatially homogeneous, quasi-one-dimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.

中文翻译：

---

具有非均分脉动能的双分散碰撞颗粒流的电荷传输方程

从 Boltzmann-Enskog 动力学方程出发，导出具有接触带电的双分散颗粒流的电荷传输方程，其中每个固相具有单独的平均速度、总动能、电荷和电荷变化。为了关闭局部平均输运方程，假定粒子速度和电荷都存在麦克斯韦分布。首先重新审视了双分散固体混合物的流体动力学方程，然后提出了由质量、动量、总动能（颗粒温度和脉动张量和电荷的轨迹之和）的输运方程组成的模型。相之间的电荷转移和相内的电荷积聚用局部电荷和相之间的有效功函数差和局部电场来建模。通过对三维空间均匀、准一维空间不均匀双分散颗粒气体和具有传导壁的三维分离双分散颗粒流的硬球模拟，评估了重新审视的流体动力学方程和导出的具有本构关系的电荷传输方程。