碰撞聚合引起液滴数目变化的生灭过程模型

液滴碰撞聚合是气体/液滴两相流动中的重要现象.为研究碰撞聚合引起的液滴数目变化，考虑液相仅包含大小两类尺寸液滴的情形，计算不同尺寸的两个液滴间的碰撞概率，对固定观察区域内液滴的碰撞聚合、迁入及迁出因素作随机分析，建立描述液滴数目变化的生灭过程模型.由无条件概率模型方程，得出模型方程的相应平稳分布.以雨滴下落过程的质量增长为例，说明所得分布在气体液滴两相流动中的应用.

A Birth-Death Process Model for Number of Drops with Collision and Coalescence

Collision and coalescence among drops is an important phenomena in gas/drop two-phase flows. To study change of number of drops caused by collision and coalescence,a special flow field is considered in which liquid phase consists of two classes of drops with big or small sizes. Probability for collision and coalescence between a big drop and a small drop is derived. Considering three factors of immigration,emigration and collision of drops,a model of birth-death process is proposed for number of drops located in a fixed observation region,and relevant unconditional probability model equation is deduced. Finally,stationary distribution is obtained. As an illustration,mass creament of a falling rain drop is calculated.