Brownian sieving enhancement of microcapillary hydrodynamic chromatography. Analysis of the separation performance based on Brenner's macro-transport theory

In a recent article [Analytical Chemistry, 93(17), 6808–6816 (2021)], an unconventional device configuration enforcing a Brownian sieving mechanism was proposed as proof of concept for the efficient implementation of microcapillary hydrodynamic chromatography (MHDC). In this article, we perform a thorough analysis of the device geometry and of operating conditions, in order to single out the optimal configuration maximizing separation resolution. Brenner's macro-transport theory provides the technical picklock to perform the search for the optimum over a wide choice of device geometries and for a range of values of the particle Péclet number covering most conditions encountered in practical implementations of MHDC. Specifically, effective transport coefficients defining the dynamics of the suspended phase are obtained by the solution of a two-dimensional steady-state advection-diffusion equation defined onto the channel cross-section. The eigenvalue/eigenfunction structure of the associated transient problem is exploited in order to quantify the timescale for reaching the macro-transport regime conditions. Based on this timescale and on the effective transport parameters, an estimate of the column length necessary to achieve a prescribed level of separation resolution is obtained. We identify device geometry and operating conditions where the capillary length is shrunk down by a factor above ten compared to the standard MHDC configuration. Lagrangian stochastic statistics of particle ensembles are used to validate the results obtained through Brenner's macro-transport approach. The method proposed can be readily generalized to other classes of device geometries enforcing the same Brownian sieving mechanism.