Critical beta-values of all coil planet centrifuges

I-type, J-type and non-synchronous centrifuges are all coil planet centrifuges. Analysing the motion of I-type and J-type centrifuges has advanced the understanding of how to manufacture and use these centrifuges. This paper analyses the motion of non-synchronous centrifuges producing equations of motion that can be applied to all coil planet centrifuges. This has also produced simple equations to determine the critical beta-values for any coil planet centrifuge. This paper also demonstrates that I-type centrifuges also have 2 critical beta-values when it was thought that beta-value did not influence the understanding of the processes within I-type centrifuges. For the I-type instrument both of these critical values are at bobbin radii approaching infinity. In practice this means all I-types function within one beta-value range hence the unilateral distribution and type/effectiveness of the mixing is consistent. Finally the paper shows the influence that the tangential velocity has on the Archimedean screw effect and thus the unilateral distribution of the upper and lower phases in the columns of coil planet centrifuges. This explains why the maximum stationary phase retention in an I-type centrifuge is limited to 50%.