Basic relationship for the particle motion

As is well known, the regularity of the particle motion is a result of the combined action of various forces. In the stream(s) three forces act on the particle (1) The field force, which is the gravitational force in irrotational flows (2) The buoyancy force 

Equation (2.1) can be simplified or reformed for various specific cases. 

with the subscript x denoting the motion direction being saved for the onedimensional motion of a single particle, Eq. (2.1) can be simplified to 

In order to focus attention on the basic feature of the oscillation movement of the particle, the assumption Tamir [5] made that the gas velocity is uniformly distributed in the whole flow field, i.e., ug = constant, is still employed here. The experimental results obtained by Enyakin [41] illustrated that this assumption can give relatively good approximate results. 

According to the above analysis for Fig. 2.1, the motion of the particle in the impinging streams is divided into various stages. 

---