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Rapid optimization of gradient liquid chromatographic (LC) separations often utilizes analyte retention modelling to predict retention times as function of eluent composition. However, due to the dwell volume and technical imperfections, the actual gradient may deviate from the set gradient in a fashion unique to the employed instrument. This makes accurate retention modelling for gradient LC challenging, in particular when very fast separations are pursued. Although gradient deformation has been addressed in method-transfer situations, it is rarely taken into account when reporting analyte retention parameters obtained from gradient LC data, hampering the comparison of data from various sources. In this study, a response-function-based algorithm was developed to determine analyte retention parameters corrected for geometry-induced deformations by specific LC instruments. Out of a number of mathematical distributions investigated as response-functions, the so-called "stable function" was found to describe the formed gradient most accurately. The four parameters describing the model resemble the statistical moments of the distribution and are related to chromatographic parameters, such as dwell volume and flow rate. The instrument-specific response function can then be used to predict the actual shape of any other gradient programmed on that instrument. To incorporate the predicted gradient in the retention modelling of the analytes, the model was extended to facilitate an unlimited number of linear gradient steps to solve the equations numerically. The significance and impact of distinct gradient deformation for fast gradients was demonstrated using three different LC instruments. As a proof of principle, the algorithm and retention parameters obtained on a specific instrument were used to predict the retention times on different instruments. The relative error in the predicted retention times went down from an average of 9.8% and 12.2% on the two other instruments when using only a dwell-volume correction to 2.1% and 6.5%, respectively, when using the proposed algorithm. The corrected retention parameters are less dependent on geometry-induced instrument effects., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 The Authors. Published by Elsevier B.V. All rights reserved.)

In spatial multi-dimensional liquid chromatography (LC) devices the flow of each dimension has to remain in the corresponding region, otherwise the separation efficiency is undermined. Adequate flow-confinement measures are necessary. Here, the use of permeability differences across different compartments of spatial two-dimensional (2D) and three-dimensional (3D) LC devices as a method to guide fluid flow and reduce analyte loss during the first, second- and third-dimension development was investigated with computational fluid dynamics (CFD) simulations. In case of 2DLC devices, it was shown that porous barriers with a permeability on the order of 10 -12 m 2 suffice to keep the total sample spillage from an open 1 D channel under 1%. In case of 3DLC devices, it was shown that flow confinement could be achieved using an open 1 D channel in combination with a highly-permeable monolith (permeability on the order of 10 -12 m 2 ) in the second-dimension ( 2 D) and a less permeable packing with a permeability on the order of 10 -15 m 2 (e.g. 1 μm particles) in the third-dimension ( 3 D). Additionally, the impact of the 3 D flow-distributor has been studied and a novel design, capable of limiting the spillage to the other dimensions to the absolute minimum, is proposed., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2019 Elsevier B.V. All rights reserved.)