The three-dimensional model for helical columns on type-J synchronous counter-current chromatography.

Unlike the existing 2-D pseudo-ring model for helical columns undergoing synchronous type-J planetary motion of counter-current chromatograph (CCC), the 3-D "helix" model developed in this work shows that there is a second normal force (i.e. the binormal force) applied virtually in the axial direction of the helical column. This force alternates in the two opposite directions and intensifies phase mixing with increasing the helix angle. On the contrary, the 2-D spiral column operated on the same CCC device lacks this third-dimensional mixing force. The (principal) normal force quantified by this "helix" model has been the same as that by the pseudo-ring model. With β>0.25, this normal centrifugal force has been one-directional and fluctuates cyclically. Different to the spiral column, this "helix" model shows that the centrifugal force (i.e. the hydrostatic force) does not contribute to stationary phase retention in the helical column. Between the popular helical columns and the emerging spiral columns for type-J synchronous CCC, this work has thus illustrated that the former is associated with better phase mixing yet poor retention for the stationary phase whereas the latter has potential for better retention for the stationary phase yet poor phase mixing. The methodology developed in this work may be regarded as a new platform for designing optimised CCC columns for analytical and engineering applications.