Xiaohong Yan

Dispersion in retentive pillar array columns

The method of volume averaging is applied to estimate the Taylor-Aris dispersion tensor of solute advected in columns consisting of ordered pillar arrays with wall retention of the type used in chromatographic separation. The appropriate closure equations are derived and solved in a unit cell with periodic boundary conditions to obtain the dispersion tensor (or the reduced plate height) as a function of the Peclet number (reduced velocity); pillar pattern, shape and size; partition coefficient; and resistance to mass transfer. The contributions of the velocity profile, the wall adsorption, and the mass transfer resistance to the dispersion tensor are identified and delineated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns containing ordered pillars. The model is then used to study the effect of pillars shape and pattern on the longitudinal dispersion coefficient (plate height).

Numerical investigation into the effects of ordered particle packing and slip flow on the performance of chromatography

The pressure drop and the plate height of chromatography columns packed with particles in the face-centered cubic, the body-centered cubic and the simple cubic configurations are calculated by a volume averaging method model. It is found that the Kozeny-Carman equation provides a reasonable prediction of the pressure drop when particles are in the face-centered cubic configuration, but overestimates the pressure drop when particles are in the body-centered cubic and the simple cubic configurations. The face-centered cubic configuration has the advantage to provide a smaller longitudinal dispersion coefficient than the body-centered cubic, the simple cubic, and the random configurations. The pressure drop and the plate height for slip flow through particles in the face-centered cubic configuration are lower than that for no-slip flow. The values of the smallest reduced plate height of columns packed with particles in the face-centered cubic configuration for no-slip flow and slip flow are about 0.084 and 0.059, respectively. The plate height of the ordered particle packing structures is smaller and the effect of slip flow on the plate height is less remarkable than results reported in literature.

Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes

In this paper, first, the Navier―Stokes equations for incompressible fully developed flow in microchannels and microtubes with the first-order and second-order slip boundary conditions are analytically solved. Then, the compressible Navier―Stokes equations are numerically solved with slip boundary conditions. The numerical methodology is based on the control volume scheme. Numerical results reveal that the compressibility effect increases the velocity gradient near the wall and the friction factor. On the other hand, the increment of velocity gradient near the wall leads to a much larger slip velocity than that for incompressible flow with the same value of Knudsen number and results in a corresponding decrement of friction factor. General correlations for the Poiseuille number (fRe), the Knudsen number (Kn), and the Mach number (Ma) containing the first-order and second-order slip coefficients are proposed. Correlations are validated with available experimental and numerical results.

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.

Simulation of solute dispersion in particle packs by the volume averaging method

Abstract The ability to predict solute dispersion behavior in homogeneous random particle packs by the volume averaging method is evaluated. Unit cells with periodic boundaries and random pore connectivity are numerically constructed. The asymptotic longitudinal and transverse dispersion coefficients are predicted by the volume averaging method in terms of these unit cells. The Peclet number is in the range of 0–1000. The Reynolds number is less than 1. Dispersion coefficients of eighteen unit cells with different sizes and pore geometries are compared. It is found that a significant scatter of dispersion coefficients exists when the size of the unit cell is small. The scatter decreases with increasing size of the unit cell. The predicted dispersion coefficients are compared with correlations obtained according to experimental and simulation results for homogeneous random particle packs and reasonable agreements are observed when the size of the unit cell is suitable.

Predictive model of solute transport with reversible adsorption in spatially periodic hierarchical porous media.

Solute transport in hierarchical porous media with reversible adsorption is predicted by the volume averaging method. A transient macroscopic advection-diffusion equation is derived to describe the multiscale solute transport problem. The theoretical expression of the dispersion tensor is obtained which is the function of pore-scale velocity profile. Steady closure equations are derived to calculate the dispersion tensor. With the aid of pore-scale simulation in unit cells of the hierarchical porous media, the dispersion tensor can be calculated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns comprised of ordered, porous pillars. It is straightforward to use the model to predict the solute transport behavior in fixed beds packed with particles.