Dispersion in round tubes and its implications for extracolumn dispersion

Computational Fluid Dynamics Study of the Dispersion Caused by Capillary Misconnection in Nano-Flow Liquid Chromatography

It is well known that high-speed/high-efficiency separations in nano-flow liquid chromatography (LC) are very sensitive to the quality of the connections between the column and the rest of the instrument. In the present study, two types of connection errors (capillary misalignment and the occurrence of an inter-capillary gap) have been investigated using computational fluid dynamics. Interestingly, it has been found that large degrees of capillary misalignment (assuming an otherwise perfect contact between the capillary end-faces) can be afforded without introducing any significant dispersion over the entire range of investigated relative misalignment errors (0 ≤ ε/dcap ≤ 75%), even at the largest flow rates considered in nano-LC. On the other hand, when an inter-capillary gap is present, the dispersion very rapidly increases with the radial width Dc of this gap (extra variance ∼Dcn with n even reaching values above 4). The dependency on the gap length Lc is however much smaller. Results show that, when Dc ≤ 30 μm and Lc ≤ 200 μm, dispersion losses can be limited to the order of 1 nL2 at a flow of 1.5 μL/min, which is generally very small compared to the dispersion in the capillaries (20 μm i.d.) themselves. This result also reconfirms that zero-dead volume connectors with a sufficiently narrow bore can in theory be used without compromising peak dispersion in nano-LC, at least when the capillaries can be matched perfectly to the connector in- and outlet faces. The results are also indicative of the extra dispersion occurring inside microfluidic chips or in the connections between a microfluidic chip and the outer world.

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.

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.

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.

Implications of dispersion in connecting capillaries for separation systems involving post-column flow splitting

It is common practice in liquid chromatography to split the flow of the effluent exiting the analytical column into two or more parts, either to enable parallel detection (e.g., coupling the separation to two destructive detectors such as light scattering and mass spectrometry (MS)), or to accommodate flow rate limitations of a detector (e.g., electrospray ionization mass spectrometry). In these instances the user must make choices about split ratio and dimensions of connecting tubing that is used between the split point and the detector, however these details are frequently not mentioned in the literature, and rarely justified. In our own work we often split the effluent following the second dimension (²D) column in two-dimensional liquid chromatography systems coupled to MS detection, and we have frequently observed post ²D column peak broadening that is larger than we would expect to result from dispersion in the MS ionization source itself. For the present paper we describe a series of experiments aimed at understanding the impact of the split ratio and post-split connecting tubing dimensions on dispersion of peaks exiting an analytical column. We start with the simple idea - based on the principle of conservation of mass - that analyte peaks entering the split point are split into two parts such that the analyte mass (and thus peak volume) entering and exiting the split point is conserved, and directly related to the ratio of flow rates entering and exiting the split point. Measurements of peak width and variance after the split point show that this simple view of the splitting process - along with estimates of additional dispersion in the post-split tubing - is sufficient to predict peak variances at the detector with accuracy that is sufficient to guide experimental work (median error of about 10% over a wide range of conditions). We feel it is most impactful to recognize that flow splitting impacts apparent post-column dispersion not because anything unexpected happens in the splitting process, but because the split dramatically reduces the volume of the analyte peak, which then is more susceptible to dispersion in connecting tubing that would not cause significant dispersion under conditions where splitting is not implemented. These results will provide practitioners with a solid basis on which rational decisions about split ratios and dimensions of post-split tubing can be made.

Compartment Model of Mixing in a Bubble Trap and Its Impact on Chromatographic Separations

Chromatography equipment includes hold-up volumes that are external to the packed bed and usually not considered in the development of chromatography models. These volumes can substantially contribute to band-broadening in the system and deteriorate the predicted performance. We selected a bubble trap of a pilot scale chromatography system as an example for a hold-up volume with a non-standard mixing behavior. In a worst-case scenario, the bubble trap is not properly flushed before elution, thus causing the significant band-broadening of the elution peak. We showed that the mixing of buffers with different densities in the bubble trap device can be accurately modeled using a simple compartment model. The model was calibrated at a wide range of flow rates and salt concentrations. The simulations were performed using the open-source software CADET, and all scripts and data are published with this manuscript. The results illustrate the importance of including external holdup volumes in chromatography modeling. The band-broadening effect of tubing, pumps, valves, detectors, frits, or any other zones with non-standard mixing behavior can be considered in very similar ways.

Mechanistic Modeling of Preparative Column Chromatography for Biotherapeutics

Chromatography has long been, and remains, the workhorse of downstream processing in the production of biopharmaceuticals. As bioprocessing has matured, there has been a growing trend toward seeking a detailed fundamental understanding of the relevant unit operations, which for some operations include the use of mechanistic modeling in a way similar to its use in the conventional chemical process industries. Mechanistic models of chromatography have been developed for almost a century, but although the essential features are generally understood, the specialization of such models to biopharmaceutical processing includes several areas that require further elucidation. This review outlines the overall approaches used in such modeling and emphasizes current needs, specifically in the context of typical uses of such models; these include selection and improvement of isotherm models and methods to estimate isotherm and transport parameters independently. Further insights are likely to be aided by molecular-level modeling, as well as by the copious amounts of empirical data available for existing processes.

Preliminary Capillary Flow Experiments with Amyloid-β, Possible Needle and Capillary Aβ Adsorption, and a Proposal for Drug Evaluation Under Shear Conditions

Amyloid-β (Aβ) solution injections into an aqueous mobile phase moving through narrow bore stainless-steel capillary tubing results in adsorption of at least 99% Aβ within the tubing or injection valve. However, if flow is stopped for a period of 5-10 minutes, then started, wall desorption yields Aβ-containing molecules in the new effluent. The amount of desorbed Aβ-containing effluent depends on flow rate, period of flow cessation, and number of successive Aβ injections into the same tube without cleaning between injections. Unexpected multiple chromatographic peaks in these experiments seem to imply "separation" of released, previously adsorbed Aβ-containing products in the empty capillary tubing. These preliminary experiments raise questions about possible errors in Alzheimer's disease (AD) spinal tap analyses, which use stainless-steel needles of approximately the same inner diameter and encounter similar flow rates as those in our capillary experiments. Microliter syringes and HPLC connectors also contain stainless-steel tubing that have similar inner diameter dimensions and similar flow rates. The capillary system involved in these experiments has previously been proposed as a model system for studying the effects of shear on Aβ within the brain because it offers a research environment that provides highly restrictive flow through very small dimension channels. A suggestion is made for the use of this system in exploratory anti-amyloid drug studies in which both the drug and Aβ are injected in the same solution so that both drug and Aβ are subjected to the same shear environment. Reduction in adsorbed Aβ is suggested as an indicator of effective anti-Aβ drugs.

Shear-Induced Amyloid Formation in the Brain: II. An Experimental System for Monitoring Amyloid Shear Processes and Investigating Potential Spinal Tap Problems

Liquid sheared amyloid-β (Aβ) initiates amyloid cascade reactions, producing unstable, potentially toxic oligomers. There is a need for new analytical tools with which to study these oligomers. A very small bore capillary flow system is proposed as a tool for studying the effects of liquid shear in amyloid research. This simple system consists of injecting a short cylindrical liquid sample plug containing dissolved amyloid into a liquid mobile phase flowing through an empty, very small internal diameter capillary tube. For liquid samples containing a single protein sample, under conditions in which there is laminar flow and limited sample protein molecular diffusion, chromatograms monitoring the optical protein absorbance of capillary effluent contain either one or two peaks, depending on the mobile phase flow rate. By controlling the sample diffusion times through changes in flow rate and/or capillary diameter, this tool can be used to generate aliquot samples with precise, reproducible amounts of shear for exploring the effects of variable shear on amyloid systems. The tool can be used for producing in-capillary stopped flow spectra of shear-stressed Aβ monomers as well as for kinetic studies of Aβ dimer- and oligomer-forming reactions between shear stressed Aβ monomers. Many other experiments are suggested using this experimental tool for studying the effects of shear on different Aβ and other amyloid systems, including testing for potentially serious amyloid sampling errors in spinal tap quantitative analysis. The technique has potential as both a laboratory research and a clinical tool.

Extra-column dispersion of macromolecular solutes in aqueous-phase size-exclusion chromatography

A set of dextran standards was used to study the extra-column dispersion in conventional chromatographic equipment at a broad range of molecular weights, different mobile phase flow rates and connecting tube lengths and diameters. All known correlations for the tube dispersion at laminar flow, including those for short tubes, overestimated the values of the variance of the outlet concentration signal. The difference increased with the solute molecular weight and the flow rate. It was assumed that the discrepancy was due to the effect of natural convection invoked by the density differences of the injected dextran solutions and water. A suitable approximation of the relative band spreading was suggested in a form of a power function of the Reynolds and Schmidt numbers. A significant decrease of the dispersion was observed when the chromatography tubing was coiled into a circle. This decrease was successfully predicted combining the existing correlations for long coiled tubes and short straight tubes.

Influence of chemical kinetics on postcolumn reaction in a capillary Taylor reactor with catechol analytes and photoluminescence following electron transfer

Postcolumn derivatization reactions can enhance detector sensitivity and selectivity, but their successful combination with capillary liquid chromatography has been limited because of the small peak volumes in capillary chromatography. A capillary Taylor reactor (CTR), developed in our laboratory, provides simple and effective mixing and reaction in a 25-microm-radius postcolumn capillary. Homogenization of reactant streams occurs by radial diffusion, and a chemical reaction follows. Three characteristic times for a given reaction process can be predicted using simple physical and chemical parameters. Two of these times are the homogenization time, which governs how long it takes the molecules in the analyte and reagent streams to mix, and the reaction time, which governs how long the molecules in a homogeneous solution take to react. The third characteristic time is an adjustment to the reaction time called the start time, which represents an estimate of the average time the analyte stream spends without exposure to reagent. In this study, laser-induced fluorescence monitored the extent of the postcolumn reaction (reduction of Os(bpy)3(3+) by analyte to the photoluminescent Os(bpy)3(2+)) in a CTR. The reaction time depends on the reaction rates. Analysis of product versus time data yielded second-order reaction rate constants between the PFET reagent, tris(2,2'-bipyridine)osmium, and standards ((ferrocenylmethyl)trimethylammonium cation and p-hydroquinone) or catechols (dopamine, epinephrine, norepinephrine, 3, 4-dihydroxyphenylacetic acid. The extent of the reactions in a CTR were then predicted from initial reaction conditions and compared to experimental results. Both the theory and experimental results suggested the reactions of catechols were generally kinetically controlled, while those of the standards were controlled by mixing time (1-2 s). Thus, the extent of homogenization can be monitored in a CTR using the relatively fast reaction of the reagent and p-hydroquinone. Kinetically controlled reactions of catechols, however, could be also completed in a reasonable time at increased reagent concentration. A satisfactory reactor, operating at 1.7 cm/s (2 microL/min) velocity with solutes having diffusion coefficients in the 5 x 10(-6) cm2/s range, can be constructed from 8.0 cm of 25-microm-radius capillary. Slower reactions require longer reaction times, but theoretical calculations expect that a CTR does not broaden a chromatographic peak (N = 14 000) from a 100-microm-capillary chromatography column by 10% if the pseudo-first-order rate constant is larger than 0.1 s(-1).

Electroosmotic and pressure-driven flow in open and packed capillaries: velocity distributions and fluid dispersion

The flow field dynamics in open and packed segments of capillary columns has been studied by a direct motion encoding of the fluid molecules using pulsed magnetic field gradient nuclear magnetic resonance. This noninvasive method operates within a time window that allows a quantitative discrimination of electroosmotic against pressure-driven flow behavior. The inherent axial fluid flow field dispersion and characteristic length scales of either transport mode are addressed, and the results demonstrate a significant performance advantage of an electrokinetically driven mobile phase in both open-tubular and packed-bed geometries. In contrast to the parabolic velocity profile and its impact on axial dispersion characterizing laminar flow through an open cylindrical capillary, a pluglike velocity distribution of the electroosmotic flow field is revealed in capillary electrophoresis. Here, the variance of the radially averaged, axial displacement probability distributions is quantitatively explained by longitudinal molecular diffusion at the actual buffer temperature, while for Poiseuille flow, the preasymptotic regime to Taylor-Aris dispersion can be shown. Compared to creeping laminar flow through a packed bed, the increased efficiency observed in capillary electrochromatography is related to the superior characteristics of the electroosmotic flow profile over any length scale in the interstitial pore space and to the origin, spatial dimension, and hydrodynamics of the stagnant fluid on the support particles' external surface. Using the Knox equation to analyze the axial plate height data, an eddy dispersion term smaller by a factor of almost 2.5 than in capillary high-performance liquid chromatography is revealed for the electroosmotic flow field in the same column.

Rapid breakthrough measurement of void volume for field-flow fractionation channels

A peak breakthrough technique is described and evaluated for measuring the void volume of field-flow fractionation (FFF) channels, particularly those used for flow FFF. This technique uses a high-molecular-mass macromolecular or particulate probe that can be displaced rapidly by flow through the FFF channel with minimal transverse diffusion. The particles that emerge first are those carried through the entire length near the channel centerline at the apex of the parabolic flow profile. These particles generate a sharp breakthrough profile. The measured breakthrough time is two thirds of the void time, thus making it possible to calculate both the void time and the associated void volume. This method, although applicable to all FFF channels (and capable of extension to open tubes), is particularly useful for flow FFF because conventional low-molecular-mass void probes can diffuse into the permeable walls and thus distort void measurements. The theoretical basis of the breakthrough technique and an explanation for the sharpness of the breakthrough front are given. A method for compensating for deviations from perfect sharpness is developed in which the breakthrough time is identified with the time needed to reach 85-88% of the breakthrough peak maximum. Preliminary experimental results are shown using various protein probes in four different FFF channel systems.