Theoretical tools for predicting optimal cross-sectional shapes in micro-gas chromatography

It is meaningful to explore the possibility of improving the micro-GC column performance by adjusting the column cross-sectional shape. The objective of this study was to seek the column cross-sectional shape that results in larger plate number per meter than other shapes with the same cross-sectional area and the same flow resistance coefficient. We applied a model based on the volume averaging method to derive the expression of plate height for columns with arbitrary cross-sectional shapes, and conducted the shape optimization by combining the model and an optimization tool. By varying flow resistance coefficient, we obtained a series of optimal shapes. It is found that, the optimal shape with larger flow resistance coefficient is shallower and the related plate number per meter is larger. We predicted and optimized the performance of a micro-GC column reported in literature. The prediction agrees reasonably with experimental data. More than twice the plate number per meter of the original column was predicted by using a hypothetical column with one optimal cross-sectional shape.