用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用，用修正的BGK模型描述粒间碰撞效应，建立了封闭的颗粒相PDF输运方程。运用Chapmar-Enskog迭代法求得方程的二阶近似解，获得颗粒相脉动速度二阶矩和三阶矩闭合关系。模型与颗粒流模型相容，与液相湍流闭合模型是否相容依赖于扩散模型的具体形式，并据此比较了不同的涡-颗粒作用模型。模型与二维明渠流轻质沙和天然沙试验资料符合很好。表明细小粒径颗粒能够充分跟随水流运动；大粒径颗粒的相间平均速度差和壁面滑移速度明显，近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流，并存在一定程度的颗粒碰撞效应。

Starting with the kinetic theory for dilute solid/liquid two-phase flow, a mathematical model is established to predict the flow in a horizontal square pipe and the predictions are compared with LDV measurements. The present model predicts correctly two types of patterns of the vertical distribution of particle concentration observed in experiments, and also gives different patterns of the distribution of particle fluctuating energy. In the core region of the pipe, the predicted mean velocity of particles is smaller than that of liquid, but near the pipe bottom the reverse case occurs. In addition, full attention is paid to the mechanism for the vertical distribution of the average properties of particles such as concentration and mean velocity. From the kinetic-theory point of view, the cause of formation for different patterns of the vertical concentration distribution is not only related to the lift force exerted on a particle, but also related to the distribution of particle fluctuating energy.