Computational fluid dynamic (CFD) simulation of a cuboid packed-bed chromatography device

On the contribution of the top and bottom walls in micro-pillar array columns and related high-aspect ratio chromatography systems

We report on a steady-state based, and hence highly accurate numerical modelling study of the effect of the top and bottom wall in the current generation of micro-pillar array columns. These have a mesoporous retention layer that not only covers the pillar walls but also the bottom wall. Our results show that the performance of these columns can in general not be improved by also covering the top wall with the same layer, despite the increased column symmetry this approach would offer. The reason for this is that the local species retardation caused by a retentive layer is much stronger than the pure flow arresting effect of an uncovered wall. At least, this has a crucial impact in high aspect-ratio systems such as micro-pillar array columns because these require a small inter-pillar distance to promote mass transfer together with a large channel depth to enable a sufficiently high flow rate. On the other hand, a notable improvement could be made if micro-pillar array would be produced without having a retentive layer at the bottom. At Péclet number Pe = 50 and aspect ratio AR = 5 for flow-channels, this gain amounts up to about 4.5 h-units at a zone retention factor k'' = 2 and 1.75 h-units at k'' = 16 (gain scales almost linearly with Pe). To verify these results, we also considered another high aspect-ratio system with a simplified geometry: the open-tubular channel with a flat-rectangular cross-section. This led to very similar observations, thus confirming the findings for the micro-pillar array. The results produced in the present study also allow us to conclude that the classic modelling paradigm adopted in chromatography, which is based on the independency and hence additivity of the hCm- and hCs-contributions, can lead to large modelling errors in chromatographic systems with a high aspect-ratio, even when their geometry is so simple as that of a straight open-tubular channel with constant cross-section. Indeed, when both zones are treated independently, the analysis misses how the vertical diffusion through the retentive layer helps suppressing the vertical gradients in the mobile zone. The diffusion through this layer occurs in a ratio of k''Ds/Dm (Dm being the diffusion coefficient in mobile phase zone and Ds being the diffusion coefficient in stationary phase zone), such that at high retention factors this diffusion contribution even becomes the dominant one.

An alternative general model for the effective longitudinal diffusion in chromatographic beds filled with ordered porous particles

The two-zone moment-analysis method for the determination of the dispersion tensor in hierarchical retentive porous media has been adopted to compute and model the effective longitudinal diffusion Deff, or equivalently the B-term band broadening, in chromatographic beds filled with ordered porous particles. On the one hand, this approach offers accurate numerical results for Deff while keeping computational expenses low. On the other hand, it also gives direct insight for the analytical modelling, readily revealings the two main essential quantities (resp. referred to as the mobile-zone and stationary-zone effective diffusion factors γm and γs) that contribute to Deff. Modelling these two main parameters provided us with two new analytical models for Deff: a general one, valid for diluted and concentrated packings and accurate in the whole range of relevant intra-particle diffusion coefficient Dpz, and an approximate one, reliable for diluted packings and accurate also for concentrated packings with low to intermediate values of Dpz. The large advantage of both models is that they do not need any fitting parameter because all the required information is incorporated into the experimentally accessible geometric obstruction factor in the mobile phase originating from the tortuosity of the through-pore space (limiting case of fully solid particles without any retention). These models hence serve as an alternative to the Effective Medium Theory (EMT) models used so far in the literature. To validate the theory, five ordered geometries have been investigated. The accuracy of the general model proposed has been quantified and found to be comparable with that of the 3rd order approximate Torquato model for four geometries, even for macro-porosities close to the close-packing limit. The case of a 2-d triangular array of ellipsoidal particles with different elongations is also investigated to show the general validity and applicability of the models.

Theoretical computation of the band broadening in micro-pillar array columns

We have investigated the possibility to establish a theoretical plate height expression for the band broadening in the most widely used micro-pillar array column format, i.e., a cylindrical pillar array wherein the pillar walls and the channel bottom are coated with a thin layer of meso‑porous material. Assuming isotropic diffusion in the shell-layer, it was found that the vertical diffusive transport along the porous shell-layer covering the pillar walls significantly suppresses the band broadening originating from the vertical migration velocity gradients. As the vertical transport in the shell-layer increases linearly with the retention equilibrium constant K, this leads to an anomalous dependency on the retention factor. Indeed, instead of increasing with k'' and following the classic (1+ak''+bk''2)/(1 + k'')2-dependency governing a classic Taylor-Aris system, the variation of the mobile zone mass transfer resistance term hCm in a 3D pillar array with bottom-wall retention goes through a maximum (resp. factor 1.5 (k''=4) and 2 (k''=16) difference between observed and classic Taylor-Aris behaviour). This effect increases with increasing pillar heights and increasing reduced velocities. Because of this complex k''-dependency, it proves very cumbersome to establish a general plate height equation covering all conditions. Instead, a plate height expression was established that is limited up to k''=4, but remains accurate for higher k''-values for cases where the ratio of pillar height over inter-pillar distance remains below 5. It can however be anticipated the proposed analytical model is only valid in a rather limited range around the presently considered external porosity of ε=0.5.

Flow behavior of protein solutions in a lab-scale chromatographic system

A fluid dynamics model has been developed to describe flow behavior in a lab-scale chromatographic system dedicated for protein processing. The case study included a detailed analysis of elution pattern of a protein, which was a monoclonal antibody, glycerol, and their mixtures in aqueous solutions. Glycerol solutions mimicked viscous environment of the concentrated protein solutions. The model accounted for concentration dependences of solution viscosity and density, and dispersion anisotropy in the packed bed. It was implemented into a commercial computational fluid dynamics software using user-defined functions. The prediction efficiency was successfully verified by comparing the model simulations in the form of the concentration profiles and their variances with the corresponding experimental data. The contribution of the individual elements of the chromatographic system to protein band broadening was evaluated for different configurations: for the extra-column volumes in the absence of the chromatographic column, for the zero-length column without the packed bed and for the column containing the packed bed. The influence of the operating variables, including: the mobile phase flowrate, the type of the injection system, i.e., the injection loop capillary or the superloop, the injection volume and the length of the packed bed, on band broadening of the protein was determined under nonadsorbing conditions. For protein solutions having viscosity comparable with the mobile phase, the flow behavior either in the column hardware or in the injection system made major contributions to band broadening, which depended on the type of the injection system. For highly viscous protein solution, the flow behavior in the packed bed exerted a dominant influence on band broadening.

Moment analysis for predicting effective transport properties in hierarchical retentive porous media

We report on a new homogenization approach to solve, with drastically improved speed and accuracy, the general advection-diffusion equation in hierarchical porous media with localized diffusion and adsorption/desorption processes, thus opening the way to a much deeper understanding of the band broadening process in chromatographic systems. The proposed robust and efficient moment-based approach allows us to compute the exact local and integral concentration moments and hence provides exact solutions for the effective velocity and dispersion coefficients of migrating solute particles. Innovative to the proposed method is also that it not only produces the exact effective transport parameters of the long-time asymptotic solution, but also their entire transient. The analysis of the transient behaviour can be used, for example, to properly identify the time and length scales needed to achieve the macro-transport conditions. If the hierarchical porous media can be represented as the periodic repetition of a unit lattice cell, the method only requires the solution of the time-dependent advection-diffusion equations for the zeroth order and first-order exact local moments, exclusively on the unit cell. This implies an enormous reduction of the computational efforts and a significant improvement of the accuracy of the results when compared to the direct numerical simulation (DNS) approaches which require flow domains that are long enough to achieve steady-state conditions, and hence often cover tens to hundreds of unit cells. The reliability of the proposed method is verified by comparing its predictions with DNS results, in one, two and three dimensions, in both transient and asymptotic conditions. The influence of top and bottom no-slip walls on the separation performance of chromatographic columns with micromachined porous and nonporous pillars is discussed in detail.

Fundamental investigation of the dispersion caused by a change in diameter in nano liquid chromatography capillary tubing

We report on a Computational Fluid Dynamics (CFD) study of the extra dispersion caused by the change in diameter when coupling two pieces of capillary tubing with different diameter. In this first investigation into the problem, the focus is on the typical flow rates (0.25≤F≤2μL/min) and diameters (d≤40μm) used in nano-LC, considering both the case of either a doubling or halving of the diameter. The CFD simulations allow to study the problem from a fundamental point of view, i.e., under otherwise perfect conditions (perfect alignment, zero dead-volume). Flow rates, capillary diameters, diffusion coefficients and liquid viscosities have been varied over a range relevant for nano-LC (Reynolds-numbers Re ≤ 1), with also an excursion made towards high-temperature nano-LC conditions (Re ≥ 10 and more). The extra dispersion caused by the change in diameter has been quantified via a volumetric variance σ²_conn, defined in such a way that the overall dispersion across the entire capillary system can be easily reconstructed from the known analytical solutions in the individual segments. When the two capillaries are longer than their diffusion entry length, covering most of the practical cases, σ²_conn converges to a limiting value σ²_conn,∞ which varies to a close approximation with the square of flow rate. Under the investigated nano-LC conditions, the σ²_conn,∞-values are surprisingly small (e.g., on the order of 0.01 to 0.15 nL² in a 20 to 40μm connection) compared to the dispersion occurring in the remainder of the capillaries.

Microchromatography integrated with impedance sensor for bioprocess optimization: Experimental and numerical study of column efficiency for evaluation of scalability

In the last decade, there has been a growing interest in developing microfluidic systems as new scale-down models for accelerated and cost-effective biopharmaceutical process development. Nonetheless, the research in this field is still in its infancy and requires further investigation to simplify and accelerate the microfabrication process. In addition, integration of different label-free sensors into the microcolumn systems has utmost importance to minimize result discrepancies during the scale-up process. In this study, we developed a simple, low-cost integrated microcolumn (26 µl). Micromilling technology was employed to define the geometry and shape of microfluidic structures using poly(methylmethacrylate) (PMMA). The design of PMMA microstructure was transferred to polydimethylsiloxane (PDMS), and interdigitated planar microelectrodes (IDE) were integrated into the system. To evaluate the scalability of the developed microcolumn column, column performance was assessed and compared with a conventional 1-ml prepacked column. Computational Fluid Dynamics (CFD) studies were performed for both columns to understand the differences between theoretical and experimental results regarding retention time and peak broadening. Despite obtaining an acceptable asymmetric factor for the microcolumn (1.03 ± 0.02), the reduced plate height value was still higher than the recommended range with the value of 4.14 ± 0.18. Nevertheless, the consistency and significant improvement of microcolumn efficiency compared to previous studies provide the possibility of developing robust simulation tools for transferring acquired experimental data for larger-scale units.

Influence of the geometry of extra column volumes on band broadening in a chromatographic system. Predictions by computational fluid dynamics

A computational fluid dynamics method was used for prediction of flow behavior and band profiles of small- and macro-molecule compounds eluting in extra-column volumes (ECV) of an Äkta chromatographic system. The model compounds were: acetone, bovine serum albumin and an antibody. The construction of ECV was approximated by different types of geometries, starting from the simplest two-dimensional (2D) arrangement consisting of a straight capillary tube, and ending with a three-dimensional system (3D), which accounted for the flow path curvature of individual elements of ECV, including: injection loop capillary, multi-way valve, connecting capillary and detector cell. The accuracy of the model predictions depended on the flow path length and the eluent flowrate. 2D-geometry models reproduced pretty well the shapes of band profiles recorded at the lowest eluent flowrate used, but they failed for increased flowrates. The 3D-geometry model was found to be sufficiently accurate for all conditions investigated. It was exploited to analyze band broadening in the individual ECV elements. The simulation results revealed that the flow behavior in the injection loop capillaries strongly influenced the shape of band profiles, particularly at higher eluent velocities. This was attributed to the formation of Dean vertices triggered by centrifugal forces in curved parts of the eluent flow path.

A cuboid chromatography device having short bed-height gives better protein separation at a significantly lower pressure drop than a taller column having the same bed-volume

Simultaneously reducing the bed-height and increasing the area of cross-section, while keeping the bed-volume the same, would substantially reduce the pressure drop across a process chromatography column. This would minimize problems such as resin compaction and non-uniformity in column packing, which are commonly faced when using soft chromatographic media. However, the increase in macroscale convective dispersion due to the increase in column diameter, and the resultant loss in resolution would far outweigh any potential benefit. Cuboid-packed bed devices have lower macroscale convective dispersion compared to their equivalent cylindrical columns. In this paper, we discuss how and why a flat cuboid chromatography device having a short bed-height gives better protein separation, at a significantly lower pressure drop, than a taller column having the same bed-volume. First, we explored this option based on computational fluid dynamic (CFD) simulations. Depending on the flow rate, the pressure drop across the flat cuboid device was lower than that in the tall column by a factor of 6.35 to 6.4 (i.e. less than 1/6^th the pressure). The CFD results also confirmed that the macroscale convective dispersion within the flat cuboid device was significantly lower. Head-to-head separation experiments using a 1 mL flat cuboid device having a bed-height of 10 mm, and a 1 mL tall column having a bed-height of 25.8 mm, both packed with the same chromatographic media, were carried out. The number of theoretical plates per unit bed-height was on an average, around 2.5 time times greater with the flat cuboid device, while the total number of theoretical plates in the two devices were comparable. At any given superficial velocity, the height equivalent of a theoretical plate in the tall column was on an average, higher by a factor 2.5. Binary protein separation experiments showed that at any given flow rate, the resolution obtained using the flat cuboid device was significantly higher than that obtained with the tall column. This work opens up the possibility of designing and developing short bed-height chromatography devices for carrying out high-resolution biopharmaceutical purifications, at very low pressures.

High-resolution purification of a therapeutic PEGylated protein using a cuboid packed-bed device

PEGylated proteins which are a class of protein-synthetic polymer conjugates that have shown significant promise in the area of biotherapeutics are difficult to purify. A cuboid packed-bed device was used to purify a mono-PEGylated therapeutic protein from impurities such as high molecular weight (HMW) species (e.g., tri- and/or di-PEGylated forms), and low molecular weight (LMW) species such as unreacted protein and polyethylene glycol (or PEG). The separation efficiency of this device was compared with that of an equivalent cylindrical column. The effects of operating conditions such as flow rate, buffer composition, elution gradient, and column loading were systematically compared. An equivalent column with the same bed volume, same resin and same bed height was served as control. In mono-PEGylated protein purifications experiments, the cuboid packed-bed device exhibited sharper peaks and gave better resolution at all conditions examined in this study. The purity of mono-PEGylated protein in the samples collected from the cuboid packed-bed device and the column were comparable, i.e., 98.1% and 97.9% respectively. The recovery of mono-PEGylated protein in the pooled eluate from the cuboid packed-bed device was 31.7% greater than that recovered in the pooled eluate from the column. Therefore, significantly higher recovery of mono-PEGylated protein was obtained with the cuboid packed-bed device while maintaining the same purity specification as obtained with the column.