The ‘multiphase particle-in-cell coupled with population balance equation’ (MP-PIC-PBE) method is introduced for simulating multi-scale multiphase particulate flows. This method couples the meso-scale fluid dynamics simulated by the MP-PIC method with the simulation of the micro-scale particle size distribution. The homogeneous population balance equation is calculated for each discrete particle tracked in a Lagrangian frame, after the MP-PIC numerical procedure is followed at each time instance. This approach allows the particulate phase to accommodate the particulate stresses using spatial gradients and allows the Lagrangian description to predict particle properties by the PBE. For the antisolvent crystallization of Lovastatin in a biradial mixer, the proposed method is compared to an existing method that simulates the spatiotemporal evolution of the particle distribution by combining a multi-environment probability density function with the spatially varying PBE. The MP-PIC-PBE method has lower computational cost and provides more detailed information, such as particle age and location.

引入了“多相粒子与种群平衡方程耦合”（MP-PIC-PBE）方法来模拟多尺度多相粒子流。该方法将通过MP-PIC方法模拟的中尺度流体动力学与对微观尺度粒度分布的模拟相结合。在每个时间点遵循MP-PIC数值程序之后，针对在Lagrangian框架中跟踪的每个离散粒子计算均质的种群平衡方程。该方法允许颗粒相使用空间梯度来适应颗粒应力，并允许拉格朗日描述通过PBE预测颗粒性质。为了在双径向混合器中洛伐他汀的抗溶剂结晶，将该方法与现有方法进行了比较，该方法通过将多环境概率密度函数与空间变化的PBE相结合来模拟粒子分布的时空演化。MP-PIC-PBE方法具有较低的计算成本，并提供了更详细的信息，例如粒子年龄和位置。