The trajectory model of dispersed phase drops and distribution model of drop diameters were derived.By numerical simulation,the analytical results indicate that a large number of dispersed phase drops accumulate on the upper plate in different directions and form a hydrodynamic area with the stream-wise location in the range of 0—0.4m,where the flow of trickling film obtains kinetic drive from flowing field.The flowing field of trickling film exhibits an unstable state if the stream-wise location is less than 0.02m,and a stable state otherwise.Moreover,different velocity vectors of drops in the x-y plane result in different interactions between the trickling film and drops.For the non-uniform distribution of drop diameters,there is a stronger interaction between the trickling film and drop if the stream-wise location is less than 0.02m,because the amplitudes of velocity vectors are higher than those in the range of 0.02—1.0m.The result reveals a complexity and diversity of stratified two-phase flowing field.On the other hand,both the basic flowing field and distributions of drop diameters have a great influence on the distributions of comparable kinetic energy of drops.The complicated motions of larger drops are helpful to coalescence because they will consume much more kinetic energy on the trickling film than those of smaller drops.The change of comparable kinetic energy of smaller drops is continuous and steady.The smaller drops are easily entrained by the liquid-liquid flowing field.
The trajectory model of dispersed phase drops and the model of basic flow for drop motion between two inclined parallel plates are derived with the optimized calculation. The analytical results of direct numerical simulation indicate that the basic flow plays an important role in the drop coalescence on liquid-liquid interface. In the stratified two-phase flow field, the smaller droplets are difficult to drain the thin continuous film between the approaching droplets and bulk interfaces and eventually immerse into the trickling film to yield coalescence. They almost attain the velocity of their local surroundings. Moreover, the basic flow exerts a dominant influence on the motion of smaller droplet. The smaller droplets are easily entrained by the basic flow. On the contrary, the larger drop presents advantageous characteristics of coalescence due to its high velocity. The range of 0.3 mm < δR≤ 0.75 mm is the advantageous drop coalescence condition since the rapidly varied velocity and its first derivative theoretically cause the forces acting on a drop to become imbalanced. On the other hand, the thin layer of the continuous phase drained from the interval between the drops and trickling film should not be neglected in the calculation of shearing force since it is important for drop rotation. The drop rotation is an indispensable factor in coalescence.
