Articles Anal. Chem. 1995, 67, 2743-2749
A Coaxial Jet Mixer for Rapid Kinetic Analysis in Flow Injection and Flow Injection Cytometry L. D. Scampavia,* G. Blankenstein, J. Ruzicka, and G. D. Christian Department of Chemistry BG- 10, University of Washington, Seattle, Washington 98195
A simple coaxial jet mixer for rapid and efficient confluent mixing under laminar flow conditions (Re < 5 ) is described. This device demonstrates exceptional control of mixing between two laminar streams by creating shear forces due to variable flow velocities at the point of confluence. It is suitable for flow injection and cytometric analyses of rapid kinetic events which require contact mixing of two solutions and subsecond measurements of the evolvingreaction. This apparatus was devised for flow injection cytometry as performed on a Becton Dickinson FACS Analyzer. Under normal cytometric conditions and at a sample introduction rate of 60 pWmin, the laminar jet mixer is capable of complete mixing of two solutions within 55 ms. Kinetic measurements can be performed on the FACS Analyzer in a variable time range of 100 ms to 3 min with 14-30 ms temporal resolution of the studied event. Since no boost in core flow is required, potential spectral distortions due to core flow variations are eliminated. This coaxial jet mixer can be easily constructed and employed on a variety of cytometers as well as conventional flow injection analysis systems, since it is an effective mixer under most flow conditions. Research in flow injection analysis (FIA) and cytometry is increasingly focused on investigating dynamic biochemical interactions that require subminute to subsecond resolution of the kinetic event. The dynamics of ligandheceptor interactions, Ca2+ signaling, and subsecond modulation of G proteins are some examples of rapid events where investigation is quite limited by current cytometric instrumentation.’-Il Although several devices (1) Posner. R. G.; Fay. F. P.; Domalewski, M. D.; Sklar, L. A. Mol. Pharmacol. 1994,45. 65-73. ( 2 ) Dunne. J. F. Cytometiy 1991,12, 597-601. (3) Sklar. L. A.; Fay, S. P.: Mueller, H.; Freer, R. J.; Muthukumaraswamy, N.; Madde, D. Agents Actions Suppl. 1991.35, 11-16. (4) Meshhulan. T.; Herscovitz, H.: Casavant, D.; Bemardo. J.; Raman, R.; Haugland. R. P.; Strohmeier. G . S.; Diamond, R. D.: Simons. E. R. J. B i d . 21465-21470. Chem. 1992,267, (5) Shawn, F. P.: Posner. R. G.; S w a m W. N.; Sklar. L. A. Biochemistiy 1991, 30. 5066-5075. (6) Koenderman. L.: Tool, A. T. J.; Hooybrink, B.; Roos, D.; Hansen, C. A,; Williamson, J. R.; Verhoeven, A. J. Fed. Eur. Biochem. Soc. 1990,270,4952. (7) Neubig, R. R.: Sklar, L. A. Mol. Pharmacol. 1993,43, 734-740. (8) Monk, P. N.; Partridge, L. J. Biochem. J. 1993.295, 679-684. (9) Sklar. L. A. Annu. Rev. Biophys. Biophys. Chem. 1987,16, 479-506. 0003-270019510367-2743$9.0010 0 1995 American Chemical Society
for subsecond reagent addition and analysis are available,2J2J3J4 remarkably little documentation about their mixing effectiveness exists. Kinetic analysis of subsecond events has often required mixing devices capable of producing rapid homogeneity under laminar flow conditions. Instantaneous reagent contact times are especially desirable in elucidating chemical and biological interactions under diffusion-limited control. Flow injection studies have extensively examined the phenomenon of static mixing under laminar flow conditions.15 Mixing tees and simple junctions clearly demonstrate the existence of a laminar separation of the converging streams. This postmixing separation in turn generates an axial as well as a radial concentration gradient as these fluids move forward. The radial concentration gradient can typically require 23 s to mixing completion at flow rates of 5 500 pL/min.16 Although these gradients are highly reproducible and therefore form the basis of flow injection @I) techniques, their presence is undesirable when rapid kinetic studies are to be performed. As a consequence of inadequate mixing, diffusion-limited interactions can result in enigmatic interpretations with respect to reagent efficacy, af6nity, response time, and overall kinetic interaction. To illustrate the limitation of diffusional mixing, let us consider a fairly mobile reagent such as fluorescein (332 Mw), which has an estimated (Hayduk and Laudie method) diffusivity constant (DBw) of 4.4 x cm2 s-l.17 The Einstein-Smoluchowski equation = 2(D,,)t
where xms is the root mean square of the net displacement (cm) (10) Elmer, J.; Kaever. V.; Emmendorffer, A; Breidenbach, T.; Marie-Luke, L. M.; Roesier, J. J. Leukocyte Biol. 1992,51, 77-83. (11) Sklar. L. A.: Finney, D. A; Oades, Z. G.; Jesaitis, A. J.; Painter, R. G.; Cocharne, C. G. J. Biol. Chem. 1984,259, 5661-5669. (12) Cytek Cytometry Flow Products. Time Zero System; Time Window System; Cytek Development, Fremont, CA. 1994. (13) Kelly. K. A. Cytometiy 1991,12, 464-468. (14) Lindberg, W.; Scampavia, L. D.: Ruzicka,J.; qhristian. G. D. Cytomety 1994, 16, 324-330. (15) Ruzicka. J.: Hansen, E. H. Flow Injection Analysis. 2nd ed.; John Wiley & Sons: New York. 1988. (16) Clark. G. D.; Hungerford, J. M.: Christian, G. D. Anal. Chem. 1989,61, 973-979. (17) Lyman, W. J.; Reehl, W. F.; Rosenblatt. D. H. Handbook ofchemicalProfJetty estimation methods: environmental behavior of organic compounds, American Chemical Society: Washington, DC. 1990.
Analytical Chemistry, Vol. 67, No. 17, September 7, 1995 2743
and t is the elapsed time (s), predicts a -30-90 pm (rms) diffusional displacement of fluorescein in a 1-10 s time frame. Moreover, immunoglobulin G (-153000 MW) with a slower diffusivity (&OW) of -4 x lo-’ cmz s-’ would only travel across the path of one to three cells (-10-30 pm (rms)) in the same period. Consequently, mixing within the sample introduction conduit (typically hundreds of micrometers inner diameter) is critical to providing accurate assessment of rapid kinetic events. Efficient subsecond mixing is therefore essential in extending cytometric analysis to elucidating diffusion-limited reactions, such as those involved in low-affinity receptor/ligand ~ t u d i e s . ~ In this paper, the construction and evaluation of a coaxial jet mixer for use in rapid dynamic analysis is shown. Furthermore, a methodology suitable for future evaluations of other mixing devices is proposed and demonstrated. The coaxial jet mixer described features are as follows: rapid and complete mixing withii 55 ms under laminar flow conditions; sample analysis within 100 ms on a FACS Analyzer cytometer (60 pL/min); temporal resolution of kinetic events at 14-28 ms intervals (60-120 pL/ min); variable timing of reagent addition, with a time range of 100 ms-3 min. Theoretical Considerations. In the mixing of fluids, the Reynolds number plays an important part. It indicates the relative significance of the inertial and viscous forces of a moving fluid. The Reynolds number (Re) can be defined in a tubular conduit as
Re = q~/15ndp where q is the flow rate hWmin), d is the internal diameter (mm), p is the fluid viscosity in centipoise (cP), and e is the density of
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various sizes can be used in a coaxial mixer; however, the mixing dynamics can differ greatly depending on the relative sizes and thus will require different operating conditions for optimization. Practical considerations such as shear stress, linear velocity, and pressure drops can be calculated from established chemical engineering formulas shown in Figure L2@
the fluid (g/cm3). For a low Re (2000), the transition to turbulent flow can readily occur. In cytometry, sample introduction to the sheath flow must have a low Re value ( E
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equilibrium value.23 An important convention used in mixing engineering is to calculate the absorbance variance (a2)about the equilibrium value as a function of time.19,21*23
This convention eliminates unimportant differences in experimental parameters (i.e., varying flow ratios), spectrophotometer setup, and multiple calibration curves and allows all experiments to be interpreted in a like manner. Furthermore, a precise measurement of the mixing time can then be defined as the intersection of the variance decay curve at two standard deviations (2u) from the equilibrium value. For example, a variance plot of the above data (Figure 4) is shown in Figure 5 with the mixing time defined at 13 s. Mixing Efficiency as a Function of Total Flow Rate. Evaluation of the coaxial jet mixer at various flow rates has demonstrated that mixing time is independent of the volumetric flow rate after the point of confluence. An example of this finding is shown in Figure 6, where a 1:lflow ratio ([IC]:[OC]) was used for a total flow range of 50-200 pL/min. Despite a Cfold change in the total flow rate, there is no statistically signiticant changes in the mixing times. This relationship was also observed in other (23) Buslik,
D.H.C1-4 CHISA '75 August 25-29,
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flow ratios tested and confirms earlier findings reported in flow injection analysis.16 In the above case, the 1:l flow ratio is calculated to produce a shear stress ratio of 1.11:l.OObetween the annular and inner core flows with a Re of 58. As expected, no signilicant physical alterations of the laminar streams can occur as they merge. At the 1:l flow ratio, the coaxial jet mixing efficiency appears to be principally controlled by d f i s i o n across two separate laminar streams. Optimization of the Mixing Time. In principle, by varying the flow ratio of the inner core to the annular outer core ([IC]: [OC] ratio), a high-velocity stream could impact a lower velocity stream such that the lower velocity fluid becomes entrained into the faster moving stream. If this turbulence can be generated, then eddy diffusion effects can be used to aid in the rapid mixing processes. In order to study the effect of variable flow rates, all experiments were kept at a postcontluence flow rate of 120 pL/min. The [IC]:[OC] flow ratios tested ranged from 11.O:l.O to 1.0:12.3. A summarization of the averaged mixing times is shown in Table I. Generally, mixing times lessened as the difference in the flow ratio became greater. However, the best results were obtained when the outer annular flow rate was significantly faster than the inner core flow. In Figure 7A and B, the variance-time profiles of the 1.O:l.O to 1.012.3flow ratios are shown. Note that in Figure 7B, a progression of quicker mixing times relative to higher flow ratios can be seen. At a flow ratio of 1:9.9, the variance curve becomes erratic and unpredictable. But as the flow ratio increases above the k9.9 ratio (Le., 1:11 and 1:12.3) all variances disap peared, indicating very rapid mixing. The erratic behavior of the 1:9.9 flow ratio was interpreted as a transition point between a laminar and turbulent flow regime. A shear stress (kPa/cm? ratio of 1.0:9.9 at the [IC]:[OCl boundary ratio was calculated for the 1.O:ll.O flow ratio. To demonstrate that the observed mixing phenomenon is real and not due to poor spectroscopic resolution, the 1:11flow ratio was reversed to a 11:l flow and the results are shown in Figure 8. This experiment clearly establishes that the flow ratio and the relative orientation of this relationship are both important in producing effective and rapid mixing. Mixing Time Determination at a 1:1 1 Flow Ratio. Due to the physical limitation in locating the inner capillary tip with Analytical Chemistry, Vol. 67, No. 17, September 1, 1995
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Figure 9. Mixing time for a 1 :11 flow ratio at different overall flow rates. As the total flow rate increases, a higher temporal resolution is possible and the variance decay cuwe is finally revealed at 480 pllmin. The mixing time was repeatedly observed to be 55 ms (&5 ms).
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Figure 7. Mixing times as a function of the [IC]:[OC] flow ratio (A, top) A closeup view (6, bottom) demonstrates a decrease in mixing times with an increased dissimilarity of the two flow rates. All experiments shown were performed with a total flow rate of 120 ,uU min.
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also demonstrated rapid mixing, but no improvement in mixing time was found. Application of Coaxial Flow Mixer to Cytometry. Sample introduction into a cytometer requires a highly laminar flow prior to hydrodynamic focusing. Consequently, the coaxial jet mixer does require additional time to reestablish a laminar flow profile after the point of confluence. The minimal time required for achieving 99%parabolic flow profile can be estimated through the Boussinesq-Langharr equation?
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Figure 8. Coaxial jet mixing efficiencies for 1 : l l and 11 :1 flow ratios. A stable laminar jet is found with a 11:l flow ratio, which retards overall mixing. However, the 1 :11 flow ratio produces turbulence at the point of confluence and substantially reduces the mixing time. Total flow rate 120 ullmin.
greater precision, the mixing time under optimal run conditions (1:11 flow ratio) could only be estimated to be
