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.

A discrete element model (DEM) is developed for investigation of the dynamic behavior of sand grains, in which the motion of individual grains is considered. The DEM has been used for simulating 9000 grains" motion blown by wind, resulting in ripples and saltating paths. Exchange between saltation and creep along the surface is also calculated, which is helpful for revealing the intrinsic mechanism of ripple formation. A critical event in the trajectory of sand grain saltating in the air is its interaction with the surface. As another application of DEM, the numerical experiment of a sand bed impacted by a single grain traveling at 8ms-1 and I 1.5 is performed to quantitatively evaluate the splash process. A normalized Maxwellian distribution function f(uy)=a ucy exp(-b. uyd) is proposed for the vertical velocity distribution of splashed grains, where the parameters a, b. c. and d can be regressed from the vertical velocity component of sahating grains. Generally, the vertical velocity of saltating grains fits the Maxwellian function well, with the correlation coefficients larger than 0.8. The result also shows that the restitution and surface friction coefficients of grains have negligible influence on the Maxwellian function. Therefore, the DEM can simulate sand movement and offer more detailed information as to what happens inside the flow. which could be applied in a wider suitable range in comparison with previous models.