MIXING, SETTLING, AND THE MOVEMENT OF THE INTERFACE BETWEEN THE MOBILE AND STATIONARY PHASES IN CCC

Abstract

In a J-type centrifuge, wave mixing is the primary method of mass transfer between mobile and stationary phases. It is observed centered about the proximal key node, while settling is observed centered about the Distal key node. A hypothesis using the Kelvin-Helmholtz wave stability criteria gives an explanation of why mixing and settling occur centered around these key nodes. The assumption of constant retention means that the stationary phase has zero linear velocity for all positions within the coil, and that the mobile linear velocity is constant. Closer examination of the Kelvin-Helmholtz wave stability criteria shows that the relative flow of two phases is important in creating waves. The interfacial movement can be viewed as a relative pumping action between the phases that increases the relative linear velocity of the mobile phase at the proximal key node to cause wave mixing. The interface can move within one loop of a coil. This can cause wave mixing at the proximal key node and settling at the distal key node when the lower phase is selected as the mobile phase. The analysis presented, is based upon the following techniques: i) radial and tangential accelerations for helical wound coils on J-type centrifuges, ii) pressure gradient analysis, iii) Hagen- Poiseuille equation for laminar flow in circular bore tubing, iv) hydraulic mean depth to allow for two phase flow in circular bore tubing, v) computational numerical integration. A derived equation links the parameters: centrifuge radius (R), β value, rotational speed (ω), densities of both phases (ρL and ρU), viscosities of both phases (μL and μU), tubing bore diameter (d), and mobile phase volumetric flow rate (Qm). It is hoped, that the derived equation can be used to qualitatively predict the effects of changes to the above parameters on CCC.