Electrokinetic and Pressure Driven Flow in Capillaries and Interconnects: A Study using Laser Induced Fluorescence Imaging and Computational Fluid Dynamics
David Simpson, *Sandy Yates, John Knox and Pat Langridge-Smith
University of Edinburgh, Department of Chemistry, King's Buildings, West Mains Road, Edinburgh, EH9 3JJ, Scotland.
George Alder
University of Edinburgh, School of Mechanical Engineering, King's Buildings, Mayfield Road, Edinburgh, EH9 3JL, Scotland.
Abstract
A combination of computational fluid dynamics and laser induced fluorescence imaging has been used to characterise electrokinetic and pressure driven flow in open tube capillaries. Particular attention has been paid to the geometrical configuration required for efficient capillary interconnects that minimise band dispersion across the joint. As a consequence of these flow visualisation and modelling studies, new strategies for post-column interconnects have been identified.
A. Introduction
With support from the EPSRC Analytical Science Programme we are developing new instrumentation and methodologies for on-line capillary electrochromatography/mass spectrometry (CEC/MS). The current instrument is based on a hybrid quadrupole ion-trap time-of-flight (TOF) mass spectrometer. The quadrupole ion-trap is used in rf-only mode, with dc-pulse ejection, to provide decoupling of the different timescales required for CEC separation and TOF mass analysis. The ion-trap is capable of storing and accumulating ions prior to TOF analysis enabling efficient ion detection of trapped ions.
As is common with the use of other forms of mass spectrometry for on-line detection, coupling of the working capillary electrophoresis (CE) or CEC column to the mass spectrometer has to be accomplished whilst minimising post-column band dispersion. The flow of fluids through capillaries and microchannels is the basis for many miniaturised high performance separation techniques. Optimisation of these techniques requires an understanding of the fluid dynamics and scalar transport within structures having characteristic dimensions of several microns (chip-based devices) to over a hundred microns (conventional CE and CEC). Such considerations have general ramification for the use of microfluidic systems that will be important in miniaturisation of liquid chromatography (LC) and other chip-based microsystems. This includes microfluidic separation systems for the analysis of very small volumes, such as the analysis of single-cell volumes, which may incorporate micro-solid-phase extraction, microfiltration, microgradients, micromixing chambers and microsampling procedures.
One of the consequences of the very small volumes involved in CE and CEC is the loss in chromatographic separation induced by interconnects required to transport the chromatographic eluent to suitably sensitive detection devices, such as mass spectrometers and NMR instruments. This occurs within less than ten diameter lengths in open tubes, i.e., less than 1 mm. This present study has focused on understanding the flow field in open-tube capillaries and interconnects using a combination of computational fluid dynamics (CFD) and laser induced fluorescence (LIF) imaging. The CFD calculations can be easily extended to include electroosmotic flow (EOF), but in the present work the aim was to investigate the effect of post-column dispersion.
In recent CEC studies, Boughtflower et al. [1] have observed that provided an internal diameter (ID) contraction ratio of more than 4:1 is used for the open-tube post-column section, e.g., 100 mm to 25 mm, then most of the chromatographic separation performance is retained. Over several meters of capillary only 10% additional dispersion is noticeable. This is in stark contrast to the dramatic increase in band dispersion when capillaries of equal diameter are connected. This contraction ratio of 4:1 was determined experimentally, and derived analytically using the appropriately adjusted Taylor and Golay equations. These equations can adequately describe the dispersion introduced by a continuous open-tube.
Consideration of the criteria required to couple capillaries raises questions about the nature of the fluid flow dynamics both at these dimensions, as well as in smaller microstructures, which cannot be satisfactorily addressed using equations that purely describe the bulk flow characteristics in idealised geometries. In order to investigate the fluid dynamics and to better understand the criteria for jointing capillaries, a combination of computational fluid dynamics simulations together with LIF imaging has been used to investigate the optimum geometry for such capillary interconnects.
B. Computational Fluid Dynamics
Recently, Ermakov et al. [2] have performed CFD calculations, with EOF included, for electrokinetic transport in microfabricated devices. Their work focused on transport and mixing in such flow fields. The focus of the work described in this paper was to explore the use of CFD to model the flow field in capillaries and interconnects with dimensions typical of those used in practical applications of CE and CEC. Such interconnects have to be used to couple these separation techniques to on-line detectors such as mass spectrometers and NMR instruments. A specific aim of this work was to identify the criteria for the fabrication of good joints that minimise band dispersion, and the contribution to the linear combination of chromatographic dispersion factors that joints can make.
One advantage of CFD studies is that flow fields can be modelled for situations that are difficult to test directly by experiment without complex deconvolution of the many contributing factors to band dispersion. For example, with CFD it is possible to label volumes of fluid and to observe the time evolution of that specific volume.
The circular capillaries commonly used for CE and CEC have a natural axial symmetry. Therefore, only two dimensions are required for modelling the flow. Since the linear flow rate in a typical CE or CEC experiment is only a few millimetres per second, the Reynolds number is very low, i.e., much less than one. This excludes any turbulence, and means that specific laminar flow modelling can be performed.
The equations governing fluid motion in two dimensions, in the absence of turbulence, are:
Click here to view continuity equation
Click here to view Navier-Stokes equation
Click here to view species transport equation
where x and r are the axial and radial spatial co-ordinates, u and v are the components of velocity, p is the pressure, and ma is the mass (or molar) fraction of chemical species a.
The above equations assume constant density (r) throughout the flow field, so that the only time-dependent term occurs in the species transport equation. It is also assumed that the viscosity (m) and the diffusion coefficient (D) are constant. In the modelling calculations water was used as the fluid of interest, using an appropriately scaled diffusion coefficient.
(i) Boundary Conditions
The boundary conditions are illustrated in Figure 1. Fluid enters from the left with a uniform velocity u1. The left boundary concentration is a piecewise time-series, simulating a Gaussian profile of standard deviation d, being transported out of the CE or CEC column into the capillary entry section of length L1. This was achieved by labelling a volume of fluid that could be followed as the time steps were advanced.
Figure 1: Boundary conditions
There is a transitional section, of length L3, between the capillary with ID d1 (100 mm) and the final capillary with ID d2 (25 mm). The influence of the geometry of this transition section has been investigated. For butt connection of the two capillaries the value of L3 was set to zero.
The concentration time history at a transverse section, Lm, in the smaller capillary was used to compare the effect of different connection configurations. This method of monitoring the flow provided a representation of a line-of-sight absorption cell. This enabled the data to be represented in a format that would be familiar to chromatographers. In addition to this, other flow characteristics, such as the concentration field, flow streams, and flow velocity vectors can also be displayed. The form of the incoming volume of labelled water, e.g., Gaussian, can also be tailored to meet the desired requirements of the experimentalist. In this respect, the modelling process is quite distinct from any practical experiment that can be performed. For example, one can arbitrarily select the width and 'concentration' of the volume of labelled water. Very narrow widths, e.g., 1 mm and 5 mm, could be used to reveal different aspects of the flow field. In the initial calculations square volumes of labelled water were used to observe the time-dependent evolution of the flow field.
(ii) Numerical Calculations
The Fluent software suite (Fluent 4.44, Fluent Inc.) was used to solve the equations of motion over the domain of interest on a structured, finite-volume grid. An example of the grid used is shown in Figure 2. This grid forms the basis of the calculation matrix and it is critically important to the calculation.
Figure 2: Finite-volume grid for the square joint CFD calculation. The geometry allows 2D axi-symmetric representation with curved corners
Advantage was taken of the axial symmetry to reduce the calculation to a two dimensional problem. The grid shown in Figure 2 represents the upper half of the capillary. Notice that the corners are not square. This was done to improve the matching of the grid to the geometry. As can be seen in Figure 3 this has only a slight effect on the results, but it improves the convergence time of the calculation. The grid can be generated manually, or automatically using a grid generating module.
The procedure for modelling involved: (i) generation of the two-dimensional grid and setting up the appropriate flow parameters, (ii) solving the time-dependent equations for the flow at the particular time-step and then (iii) stepping to the next time value and repeating this processes as required by the model. On completion of the calculation, the results were then interrogated using a post-processor that was used to examine the results graphically.
Figure 3: Comparison of effect of square edge or curved edge on concentration profile
Figure 4 shows the velocity flow field resulting from the CFD calculations for a butt joint. In this calculation a linear bulk flow velocity for water of 1 mm s-1 was used. The most noticeable feature is the high central velocity in the smaller capillary, which infers a large acceleration of the fluid as it enters the smaller capillary. This is the intuitive physical situation that would be expected based on mass flow conservation. However, the CFD calculation can provide the compete velocity field at any point, which goes far beyond the predictive power of any bulk flow calculation.
Figure 4: Velocity flow field for the square joint from the CFD calculations
A sequence of images are shown in Figure 5, below, depicting the flow as it evolves with each time step. In order to mimic the incoming chromatographic separation, a labelled volume of water, with a Gaussian distribution, was allowed to enter from the left. The first time step shows that the flow profile is already evolving into a Poiseulle flow profile. Indeed, other calculations showed that the full flow profile develops within a few hundred microns. This is the origin of the loss in separation encountered when even a short length of open tubing is used as an interface from any highly efficient CE or CEC separation.
Figure 5: Band progression through a butt joint
Within the working capillary section, where the flow is electrokinetically driven, the flow profile is flat, i.e., plug-like. However, upon entering the connecting capillaries, where the flow is pressure driven, it very rapidly develops into the classical Poiseulle flow profile. It can also be seen from the simulations that in the final time step, there is detachment between the main flow and the fluid in the corner of the joint. There is a clear rupture in the isoflow contours at the entrance to the smaller capillary.
These flow profile sequences show that even when a butt joint connection is used, employing the theoretically predicated best internal diameter contraction ratio of 4:1, there is a stagnation volume in the corner of the larger capillary where a small amount of the original labelled volume is trapped. It can also be seen that even when the main band has progressed a significant length along the smaller connecting capillary, there is still a small amount of the original labelled volume trapped. Given that the original incoming band had a symmetric Gaussian distribution, the band exiting the interconnect develops significant tailing. This would be detrimental to any chromatographic separation. Moreover, the velocity field in the corner is very slow. Therefore, it is likely that diffusion would play a significant role in the dispersal of this trapped volume in the corners of the larger capillary. The competition between mass transport and diffusion could easily be modelled to establish which process dominates in this case.
Great care was taken in performing these CFD calculations, since CFD modelling can yield unreliable results when not used appropriately or without a detailed knowledge of fluid mechanics. The dependence of these results on the computational grid chosen was tested by doubling the number of grid points. The results presented in Figure 5 are quantitatively unchanged with an increase in the grid density. Similarly, the number of discrete time-steps was doubled, so that the time interval between each calculation was reduced. Again, no dependence on the time-step interval was found. The Fluent software suite is ideally suited to modelling the type of problem presented here, as there is a special module designed for use with laminar flows.
An improved way of coupling the two capillaries would be to use a tapered joint. To examine the flow profile using this geometry the computational grid shown in Figure 6 was used.
Figure 6: Computational grid for a tapered joint
The resulting flow velocity field is shown in Figure 7.
Figure 7: Flow velocity field resulting from a tapered joint
As for the butt joint, the flow velocity in the smaller capillary is much greater than that in the larger capillary. This is dictated by conservation of mass flow.
The flow dynamics using this tapered joint are shown in two time step sequences in Figure 8. These calculations were also carried out using a labelled incoming volume of water with a Gaussian distribution.
Figure 8: Band progression through a tapered joint
A comparison of the results obtained from these CFD calculations for these two jointing geometries is shown in Figure 9. The data shown was obtained by integrating the concentration transversely at the same distance downstream from the connection between the two capillaries; 2.5 mm. In the case of the butt joint, the dispersion introduced by this interconnect is a factor 2.5 times greater than that introduced using the tapered connection. Not only is there a significant increase in chromatographic resolution when a tapered connection is used, but it is also noticeable that the maximum concentration is higher. This is related to the fact that the integrated area for each peak is the same. Since the dispersion is greater for the butt joint, the peak concentration must be lower.
Figure 9: Comparison of dispersion factors between butt and tapered interconnects
Prompted by these results we have recently developed a method for manufacturing tapered capillary interconnects. The procedure involves etching the 25 mm ID capillary, using hydrofluoric acid, to increase its ID to 100 mm. In this way a natural taper develops. The end of the taper is then lapped so that it forms a good connection. When a contraction from 100 mm to 25 mm is used there is a very good retention of chromatographic resolution over several meters. [1] This has significant advantages when detection has to be performed a long way downstream of the working CE or CEC capillary.
These CFD modelling studies were used to optimise the geometry of capillary interconnects. Clearly, it is necessary to consider the overall dispersion of the separation system. If a long entrance capillary is used upstream of the interconnect, the original labelled volume would already suffer significant dispersion prior to traversing the interconnect. Since these effects are additive, if only low chromatographic separation efficiency is achieved, then the relative influence of the dispersion due to the capillary interconnect is less significant. However, for systems that exhibit very low band dispersion and very high chromatographic efficiency, then the contribution to the overall dispersion due to the capillary interconnect is important. This is obviously significant when highly efficient miniaturised separation systems are employed. Thus for microseparation and analysis systems, the additional band dispersion is of great concern, and care needs to taken that the inherent performance of the such systems are not to lost due to dispersion arising from the interconnect. It is worth noting that the CFD modelling studies described here can be extended to complete microfluidic systems of all types. Such studies are in progress.
C. Laser Induced Fluorescence Imaging of Fluid Flow
In parallel with the CFD flow modelling studies described above, LIF imaging measurements of the flow and analyte progression through capillaries have also been undertaken. These LIF measurements were used for flow visualisation studies to monitor column performance, and the effect of interconnects on band dispersion. Samples of a highly efficient fluorescent dye, rhodamine 6G were excited (hnEX) on-column using the focused output from an argon laser operating at 514 nm. The resulting fluorescence (hnEM) from the dye is red-shifted with respect to the excitation wavelength.
Figure 10: Schematic diagram of excitation and emission of rhodamine 6G in solution
The fluorescence, which exhibits a maximum in the region of 560 nm, was filtered with a Schott glass filter (OG550, 3 mm) to reject the excitation wavelength, and observed orthogonally though a microscope (Prior Scientific) using a sensitive CCD video camera (Pulnix PU2015). The signal was captured using a frame grabber (Data Translation, DT355) and analysed with an image processing software package (Vision S, Impuls).
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Figure 11: Video frames of LIF images for a solution of rhodamine 6G being driven through a 100 mm ID quartz capillary by EOF. Viewed region 950 x 700 mm
In recent work, this technique was used to image the flow of the injected dye on-column and in the region of the frit and capillary interconnects using electrokinetic pumping. A 100 mm ID fused-silica capillary was used in these experiments. Rhodamine 6G at 0.282 mM in methanol was electrokinetically injected (5 kV for 5 s). The mobile phase was aqueous sodium dihydrogen orthophosphate at 50 mM, adjusted to pH 3.5 with 1 M NaOH. The capillary length was 100 cm, with a distance of 37 cm between the injection end of the capillary and the microscope. A voltage of 20 kV was employed. Figure 11 shows a selection of video frames, recorded on-column of the LIF image obtained for rhodamine 6G being driven through the capillary by EOF. Each image is separated by seven frames (taken at 30 frames per second). The flat plug-like flow profile, which is characteristic of EOF, can clearly be seen in each frame.
Although these flow characteristics are well known, we intend to use this technique to examine the flow profiles at other points on and post-column. These results will make an interesting comparison with recently reported LIF imaging measurements by Behnke et al. [3]
We propose to extend these LIF imaging experiments using photoactivated dyes. Photoactivated dyes are fluorescent dyes that have been rendered non-fluorescent by attaching a moiety that causes the absorbed light energy to be lost through non-radiative transitions. The dye can be rendered fluorescent again by photocleavage, through irradiation at 355 nm (frequency tripled Nd:YAG laser), thereby restoring the highly efficient fluorescence of the dye. Such dyes are often used as probes in molecular biology. The dye is said to be 'uncaged' when it is rendered fluorescent. The uncaged dye can then be excited using argon laser radiation (at 488 nm). This approach provides a means of spatially 'writing' a label on a volume of fluid, enabling evolution of the flow and any consequent dispersion, due to void trapping and recirculation volumes. This approach for flow field imaging was first reported by Lempert et al. in 1995 [4] and has recently been used by Paul et al. [5] to image pressure and electrokinetically driven flow fields in open capillaries.
D. Discussion
The preliminary flow visualisation experiments presented here were carried out to complement theoretical modelling. The CFD modelling employed structured grid methods and time-dependent calculations. Built into the model calculations are the effects of diffusion and the characteristics of laminar flow, with very low Reynolds numbers. It has been shown that it is possible to simulate band broadening effects due to interconnects that are used to interface CE and CEC columns to remote detectors, such as mass spectrometers or NMR instruments. CFD allows flow details to be considered that go beyond those expressed in the Taylor equation for dispersion. These theoretical results are supported by recent experimental work undertaken by Boughtflower et al. [1] As a consequence of these flow visualisation and modelling studies, new strategies for post-column interconnects have been identified.
E. Conclusion
These computational and LIF flow visualisation studies can be extended in a relatively straightforward way to more complex microseparation devices, such as chip-based CE or CEC columns. In future studies we intend to include the effects of EOF in CFD modelling of fluid flow fields in three dimensional microstructures. Moving the modelling to the Fluent 5 platform will allow use of unstructured grids to provide increased grid density in key areas of such devices. We also expect to be able to extend flow visualisation studies using LIF to microfabricated devices.
F. Acknowledgements
We would like to acknowledge financial support from EPSRC for a project grant from the Analytical Science Programme, support from EPSRC and ICI plc for a CASE Studentship (DS), as well as assistance from GlaxoWellcome, Stevenage.
G. References