**16. Conclusions**

In my conclusions for this chapter, I must first pay tribute to the pioneers of the *Two-Layer Model*: Professors K.C. Wilson and C.A. Shook. They motivated the lengthy process of precise definition of the interface layer, calculation of holdup ratio, accurate estimation of the contact load, estimation of the velocity for a stationary bed, the locus of points for a stationary bed and the calculation of the centre of concentration. The algorithm has a long and useful history, which has been punctuated by a series of incremental modifications. A guiding principle in this model has been to keep trialcorrection iterations to a minimum and the two-stage iteration process works extremely well in this endeavour. The first stage — six calculations using an empirical value for the holdup — invites the second stage in which all the variables (including the holdup and contact load) are refined. **Figures 6** and **9** show the progress of the calculations for two widely different examples. They also show how the bed depth reduces as pipe velocity is increased.

Much of the original terminology (from reference (4)) has endured, and the author has been careful to keep to the original symbols where possible. This said much of the *2LM* model described in the foregoing pages is truly new. From a rather unstable computation, a robust and widely applicable system has emerged. In its present form, it has already been used by the author in many calculations for particle-bearing liquids.
