An Improved Model for the Steric-Entropic Effect on the Retention of Rod-like Particles in Field-Flow Fractionation: Discussion of Aspect Ratio-Based Separation

Abstract

Abstract:We developed an improved model for predicting the steric-entropic effect on the separation behaviors of rod-like particles in flow field-flow fractionation. Our new model incorporates the "pole-vault" rotation of a rod-like particle near a wall under shear flow into the original model developed by Beckett and Giddings which considered only Brownian rotation. We investigated the effect of the aspect ratio on the retention ratios and the crosssectional concentration distribution in the separation of rods in field-flow fractionation (FFF). Our analyses involved comparing the results predicted using the original model and those from the new model under various rod geometries and flow conditions. We found that the new model can show the aspect ratio-enhanced elution trend in certain flow conditions for the assumption of non-constant cloud thickness (ratio between the cross flow rate and the rod diffusivity). We also deducted that the flow conditions allowing for the aspect ratioenhanced elution are related to the interplay among the axial flow rate, cloud thickness, and rod geometry. The new model can be viewed as a prototype to qualitatively show the aspect ratio-enhanced trend since its quantitative agreement with the experimental data must be improved for our future work.

Measuring nanoparticles in the size range to 2000 nm

“…Despite some uncertainties of the actual mechanisms by which rod-like particles are separated in A4F devices (Park and Mittal 2015 ; Nguyen et al 2013 ), under a variety of conditions, separations by length actually do occur [Cf. Fig.…”

The Effect of Weak Confinement on the Orientation of Nanorods under Shear Flows

“…The orientation distribution and moments newly obtained from our study can be applied to improve the prediction of flow behaviors or structural configurations of rod-like particle in various flow systems. The model equations in the shear-induced rod migration theory and the subsequent theories on particle separation contains the terms of the average orientation moments [ 12 , 13 ]. A typical approach for evaluating the particle distribution in a flow system is to use the convective-diffusion equation, where diffusivity is usually assumed to be isotropic and constant in the channel [ 41 ].…”

“…We calculated all of the possible combinations of the second-order and the fourth-order orientation moments. However, we only display < p x p y >, < p y 2 > and < p x p y 3 >, which are related to a theoretical model equation for shear-induced rod migration [ 12 , 13 , 25 , 26 ].…”

“…For example, the elution order of gold nanorods in field-flow fractionation, which is a particle separation technique [ 9 ], is not clearly understood yet [ 10 , 11 ]. Therefore, a more accurate calculation of rod distribution under consideration of the steric effect of a wall is required for the prediction of the dynamics and elution behaviors in such a system [ 12 , 13 ]. In this work, we focus on the steric effect of a wall on the rod orientation distribution, more specifically confined in a channel, of which height is larger than the long axis length of a rod.…”

Shape-based separation of micro-/nanoparticles in liquid phases

“…Theoretical models describing the shape effect of rod-like particles on the separation behaviors in FFF have been developed by a series of works by Park and Mittal in 2015, Park in 2014, and Alfi and Park in 2014, based on earlier works by Phelan andBauer in 2009 andGiddings in 1997. As suggested by Beckett and Giddings (1997) as well as Park and Mittal (2015), the condition for each mode is classified in terms of D ⊥ /U where U is the cross-flow rate and D ⊥ is the rod diffusivity perpendicular to its main axis, approximated by slender-body theory (Batchelor, 1970):…”