The principle of centrifugal separation

The principle of centrifugation of a particle within a rotating flow has already been treated in section 16.6 of Chapter 16 using the BBOT equations. Here, we formulate differently the behavior of a particle in a rotational flow, using a physical approach that sets out the main forces governing the dynamics. 

We consider an axisymmetric fluid flow rotating about an axis Oz. The rotation dominates, that is, Ur ue and ue. This hypothesis is, to a very large extent, 

There is in the fluid a radial pressure gradient which balances the centrifugal force applied on a fluid particle. 

Let us now consider a spherical particle of diameter d and density ps, placed in the fluid flow. We denote by, uep, and u p the radial, azimuthal, and axial components of the particle s velocity in the cylindrical coordinate system of axis Oz. The main results from Chapter 16 are the following  

Since the particle is small, the friction resistance to the relative radial displacement of the particle with respect to the fluid is expressed by Stokes law (Chapter 15, section 15.1)  

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In the following, we successively apply the principle of centrifugal separation to the configuration of discontinuous decanter and then to that of a continuous decanter. 

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