Theoretical framework for mixer design for noise reduction and gradient fidelity

The mixing of two or more solvent streams to deliver a stable and accurate solvent composition is crucial to the performance, repeatability and reproducibility of a liquid chromatographic separation. We provide a theoretical treatment of axial mixing of a sequence of solvent packets with the framework of continuous stirred tank reactors (CSTRs) in series and investigate the tradeoffs presented between the primary goal of mixers (noise reduction) and it's necessary side-effects of gradient deformation and asymmetry. An experimental setup to mimic CSTR conditions was created using a stop-flow setup where the fluid flow was periodically paused and sonicated within pods of a certain volume. The effects of mixer volume relative to the volume of pump strokes and gradient volumes were investigated and discussed. A total mixer volume that is six-fold the pump stroke volume was found to be necessary to achieve sufficient (95%) noise reduction necessary for certain applications. A series of two or more CSTR elements was found to outperform a single CSTR element for larger mixer-to-pump stroke volume ratio in dampening baseline noise. For linear gradients, a gradient volume that is ten times larger than the mixer volume was found to sufficiently maintain gradient fidelity. For very small gradient volumes relative to the mixer volume, deformation of linear gradients was found to be significantly greater than predicted by the analytical solution. Furthermore, the nature of the solvent gradient deformation was asymmetric, with the latter half of the solvent gradient deforming significantly more than the first half. Combining analytically and numerically derived solutions for multiple CSTRs connected in series with experimental data, several suggestions can be made on mixer dimensions and design for a certain pump system and method transfer, given a pump stroke volume and gradient time.