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.