General theory for flow optimisation of split-flow thin fractionation.

Recently, magnetic split-flow thin (SPLITT) fractionation has been developed to separate macromolecules, colloids, cells and particles. However, the previous theory, developed for an infinitely long channel, needs to be improved to consider the flow transit regimes at both inlet and outlet. In this paper, we describe a new approach to optimising flow-rates for particle separation which considers the effect of flow transit region. Surprisingly, the critical particle migration velocities derived by the present theory are identical to the previous simplified theory. Therefore, the previous simplified theory may have wider application than might have been expected. As a test of our theory, a numerical simulation based on solving Navier-Stokes equations has also been carried out for a magnetic SPLITT device. The trajectory of a particle with the critical migration velocity is exactly as expected by our theory. Following experimental validation, this work will facilitate the design of new SPLITT fractionation systems with smaller aspect ratio.