Can slip walls improve field-flow fractionation or hydrodynamic chromatography?

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.

Field-flow fractionation and hydrodynamic chromatography on a microfluidic chip

We present gravitational field-flow fractionation and hydrodynamic chromatography of colloids eluting through 18 μm microchannels. Using video microscopy and mesoscopic simulations, we investigate the average retention ratio of colloids with both a large specific weight and neutral buoyancy. We consider the entire range of colloid sizes, including particles that barely fit in the microchannel and nanoscopic particles. Ideal theory predicts four operational modes, from hydrodynamic chromatography to Faxén-mode field-flow fractionation. We experimentally demonstrate, for the first time, the existence of the Faxén-mode field-flow fractionation and the transition from hydrodynamic chromatography to normal-mode field-flow fractionation. Furthermore, video microscopy and simulations show that the retention ratios are largely reduced above the steric-inversion point, causing the variation of the retention ratio in the steric- and Faxén-mode regimes to be suppressed due to increased drag. We demonstrate that theory can accurately predict retention ratios if hydrodynamic interactions with the microchannel walls (wall drag) are added to the ideal theory. Rather than limiting the applicability, these effects allow the microfluidic channel size to be tuned to ensure high selectivity. Our findings indicate that particle velocimetry methods must account for the wall-induced lag when determining flow rates in highly confining systems.