Hydrocyclones residence-time theory

Each theory in this category offers a relatively simple correlation for the static pressure drop and the cut size of a hydrocyclone described by a few (but often not all) dimensions. The theories fall into two main groups the equilibrium orbit theory and the residence time theory. 

Another theoretical approach to cut size prediction that can be classified as another version of the residence-time theory is that of Trawinski. In direct analogy with gravity settling Trawinski used Stokes law, an effective clarification area and an average acceleration in a hydrocyclone to derive an expression for the cut size. The same author also proposed a rather simplistic correlation for the pressure drop-flow rate relationship. 

A number of physical models have been proposed for the separation process in a hydrocyclone (Driessen MG, 1951 Bradley and Pulling, 1959 Fahlstrom, 1960 Kelsall, 1952 Rietema, 1961 and Schubert and Neesse, 1980). Among these, different phenomenological approaches have led to the development of two basic theories the equilibrium orbit theory and the residence time theory. 

Residence Time Theory. Residence time theory is based on the consideration of whether a particle will reach the cyclone wall in a given residence time. In the development of this theory, the distribution of all particles across the inlet is assumed to be homogeneous (Rietema, 1961). The cut size will be the size of those particles that enter the center of the inlet pipe and just reach the wall within the residence time. Using this theory coupled with extensive experimental test data, Rietema was able to estabhsh a set of empirical correlations and suggest a criterion (a characteristic cyclone number) for optimum design of hydrocyclones. 

Despite the very different approaches and assumptions, the forms of correlations obtained by the equih-brium orbit theory and residence time theory are similar. For specific hydrocyclone designs, both theories provide their respective empirical equations for determining the cut size and pressure drop in terms of three dimensionless groups, the Stokes number at cut size, Stkso, the Euler number, Eu, and the Reynolds number, Re (see discussions in Sec. 5.4 below) ... 

The major deficiency of the equilibrium orbit theory lies in its lack of consideration of the effect of turbulence flow on particle separation and the residence time of the particles in the hydrocyclone (as not all particles are able to find equilibrium orbits within their residence time). In spite of such weaknesses, it proves to be a reasonable approach for determining the hydro-... 

---