Comparison between one- and two-way coupling approaches for estimating effective transport properties of suspended particles undergoing Brownian sieving hydrodynamic chromatography

Simplified one-way coupling approaches are often used to model transport properties of diluted particle suspensions for predicting the performance of microcapillary hydrodynamic chromatography (MHDC). Recently, a one-way coupling approach was exploited to optimize the geometry and operating conditions of an unconventional double-channel geometry with a square cross-section, where a Brownian sieving mechanism acting alongside the MHDC separation drive (BS-MHDC) is enforced to boost separation resolution. In this article, a cylindrical geometry enforcing the same BS-MHDC separation drive is thoroughly investigated by following a two-way coupling, fully three-dimensional approach, and results are compared with those obtained enforcing the one-way coupling analysis. Device geometry and operating conditions are optimized by maximizing the separation resolution. The effective velocity and dispersion coefficient of spherical, finite-sized particles of different diameters are computed, and two-phase effects are discussed in detail. Similar to the square channel device, the cylindrical double-channel geometry allows for a sizable reduction in the column length and in the analysis time (a factor above 12 for the length and a factor larger than 3 for the processing time) when compared to the standard MHDC configuration ensuring the same separation resolution. As expected, the one-way coupling approach overestimates the separation performance of both the BS-MHDC and the standard MHDC devices with respect to the two-way coupling analysis. But, surprisingly, the enhancement factor of the BS-MHDC over the standard MHDC is underestimated by the single-phase approximation as it doubles when wall/particle interactions are properly accounted for with a two-phase description.