Anal. Chem. 1989, 61, 973-979
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Optimization of Confluent Mixing in Flow Injection Analysis Gregory D. Clark, James M. Hungerford,' and Gary D. Christian*
Center for Process Analytical Chemistry, Department of Chemistry, BG-IO, University of Washington, Seattle, Washington 98195
I t Is demonstrated that the mixing length In a stralght llne system Is llnear wlth the flow rate. The mixing tlme Is, however, Independent of flow In the case for the 90'-90' confluent tee, and the mlxlng tlme decreases wlth Increasingflow and 30'-150' confluent tees, due to rate In the 30'-30' lncreaslng secondary flow upon exltlng the tees. A mixing tee, wlth angles of Intersectionof each stream of 30' wlth the merged stream (3Oo-3O0 tee), provides the most efflclent mixing, reduclng the thne requlred for mixing. I t is postulated that such tees establish a secondary flow proflle, which promotes radlal mixing. Cdllng the reactor also promotes mbtlng In the slde-by-slde streams, establishing secondary flow patterns. Secondary flow transports molecules from the center of the tube to Its wall, and vice versa, reducing the distance necessary for dlffuslon to occur. The mixing tlme Increases wlth the analyte stream vlscoslty when the dlluent stream has a fixed vlscoslty, In a nonlinear fashion (wlth the vlscoslty exponentlal being less than unlty). Colled, and In particular, knotted reactors decrease the tlme requlred for mixing. Mlxlng of a viscous stream wlth a nonviscous stream Is more efflclent wlth these reactors than wlth the stralght4lne tube. Knotted reactors should prove especially useful In the dllutlon of serum or other high-vlscoslty samples. Comparlsons of experlmental results wlth the radial mlxlng model for a stralght llne reactor show agreement for flow-rate dependence and also for vlscoslty dependence when the vlscoslty Increase Is present In both analyte and dlluent streams.
INTRODUCTION Flow injection analysis (FIA) is a means to selectively analyze for a component in a mixture by allowing chemistry to occur in a well-defined, closed system. In many FIA applications, the sample is injected into a carrier stream containing a reactant used to chemically modify the analyte. This modification is performed in such a way as to allow selective, reproducible, and quantitative detection. Such single-line methods are attractive because of their simplicity. Often, however, the chemistry used for the determination may require multiple step reactions, the reagent may exhibit a background signal that is affected by the injected sample, or the sample may need pretreatment before reaction or detection. In these cases, a confluent streams technique is often used (1-3). The confluent streams technique is simply the mixing together of two streams with a mixing tee. One stream is the carrier, which may contain the analyte. The second or merging stream contains the diluent stream, a second reagent, or both. In a series of dispersion experiments, Ruzicka and Hensen ( 4 ) determined the effect the flow rate of the diluent stream has on peak height and width. Frei et al. reviewed mixing tees and suggested the most favorable configuration of confluence between the two confluenced streams and the resultant stream
* To whom correspondence should be addressed.
Present address: Seafood Product Research Center, USFDA, Federal Office Building, Seattle, WA 98174.
is 30" (5). Silfwerbrand-Lindh et al., however, did not notice a difference in mixing resulting from the 30-30 and 90-90 tee (6). Ruzicka and Hansen pointed out (ref 7, p 131) that a commercial instrument also made use of the increased efficiency of mixing by using a tee with the confluence-effluent angles of 30". Mardsen and Tyson (8)pointed out that using an optimized mixing tee yields a more stable base line than that which is produced by a 90-90 tee. Zagatto et al. reported that the use of the confluent streams technique helps reduce peak-to-peak overlap (9). It is imperative that reproducible mixing occur. Mixing must also be sufficient to allow adequate product formation for measurement. In this context, mixing means equilibrating the contents of two confluent streams. Practitioners of FIA have used various methods for promoting mixing. Employing efficient tees, using coiled (IO), knotted (II), or imprinted meandering reactors (12),and optimizing the flow rate have been studied and put into practice as ways to optimize mixing. (Packed (13) and single bead string reactors (14)are also used frequently in FIA. They were not, however, considered here.) Crowe et al. (15) recently studied the factors affecting peak height in a merging zones experiment. In the merging zones technique, a sample is injected into a carrier stream, with a reagent injected concurrently (or nearly so) into another carrier stream. The two streams merge and the sample and reagent boluses are allowed to mix and react. The intended uses of the merging zones and confluent streams techniques are different. The merging zones technique seeks to reduce the sample and reagent volumes (ref 7, p 63), while the confluent streams approach serves to provide dilution, additional reagents, or other sample pretreatment (16). This paper examines mixing of two confluent streams in FIA. The factors that promote, or hinder, confluent mixing are discussed. Recommendations are made for promoting mixing in aqueous samples under conditions often employed in FIA. THEORY Mixing in Straight Tubes. Confluent mixing, as defined above, is the equilibration of the contents of two merging streams through convective, diffusive, and secondary flow forces. It is well accepted that at low Reynolds numbers, Re, laminar flow profiles are established. The Reynolds number, Re, is defmed as Re = 2 q p / ~ R qwhere , q is the volumetric flow rate in mL/min, p is the density in g/mL, R is the channel radius in cm, and q is the viscosity in centipoise (cP). In laminar flow, streamlines of flowing liquid do not cross each other (Figure la). There exists a parabolic flow velocity profile with the maximum velocity at the center of the tube, which is equal to twice the average linear flow velocity. The linear flow velocity is zero at the walls. In straight tubes, diffusion is the only mechanism that allows molecular migration across the streamlines. A model that predicts the length, and therefore the time, required for radial mixing was proposed by Huber et al. (17). Their model assumes an initial point source concentration at the tube's center, which is then subjected to laminar flow conditions at flow rate q (given in mL/s). They calculated the length of tubing required for one standard deviation of
0003-2700/89/0361-0973$01.50/00 1989 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 61. NO. 9. MAY 1, 1989 a
syringe pump b
Figure 1. (a) Parabolic flow profile. Smam lines are denoted by the lighter. parallel lines. (b) Secondaiy flow pattern with direction of Row
given by arrows.
U
the radial distribution profile to reach the walls of the tube to be
where a is a numerical factor that depends on the criteria for total mixing and the initial radial distribution of the compound b e i i mixed. It was considered to be unity for the point source example. D, is the diffusion coefficient of the mixing compound. The volumetric flow rate can be written as 4 = U, rR2, where U, is the average linear flow velocity. Substituting this into eq 1,and dividing both sides by U,, an expression for the mixing time, t. in seconds, is obtained
t, = aR2/2D,
v
Fieure 2. (€4 Simplifiedschematic of apparatus used for determhing mixing lengm and time as a function of Row rate, tee geometly. rea&# geomehy,and viscoaily. The term reactor Indicates a generic reactw. which was changed throughout the experiment. The mixing point indicated is t!w point alter which basic bromthymol blue could not be seen. Schematic of confluent streams mixing length. The mixing length. L.. is the length required for neutralization of basic BTB. Alkaline BTB is shown in the heavy cross-hatch. Neutralized BTB is shown in light cross-hatch. HCI is shown to be clear.
(2)
The mixing time may prove intuitively useful than the mixing length when designing a confluent streams system. This form of the equation is reminiscent of the diffusion a.
(3) where t D is the diffusion time and (9) is the mean-square displacement. The sample volume in the present work is essentially infinite as compared to the point source sample volume employed by Huher et al. In spite of this discrepancy, Huber's model is used as a first approximation because both situations allow for mixing facilitated only by convection and diffusion. Thus to a first approximation, the model s e e m adequate. As shown below, the model correctly predicts certain trends in the mixing length. This paper will discuss the parameters in the equations above and discuss conditions where the model fails. Mixing in Curved Tubes. It is well-known that secondary flow promotes mixing. Secondary flow patterns are established in response to centrifugal force (19).Secondary flow patterns bisect the tube, which reduces the diffusion distance by a factor of 2. Perhaps more importantly, radial secondary flow causes effective mass transport, which interchanges material in a slower moving streamline with material in a faster streamline (Figure lb). Curved and coiled tubes should, therefore, give better radial mixing. They would, as suggested by Huber et al. (In,by analogy, result in more efficient confluent mixing. Effects of Viscosity on Mixing Time, t,. Carrier solution viscosity manifests itself in the mixing process as an inhibitor of diffusion. The WilkeChang formula for the diffusion mfficient of a solute molecule with a molar volume, V,, in a solvent with molecular weight, M2, association factor, q2(which is unity for nonpolar solvents and 2.6 for water), viscosity, q, and temperature, T,given by Giddings (20), is
b.
E.
Flgure 3. Mixing tees usad in the experlment, directions of flow Indicated: (a)tee with 90' angle of intersection of both input streams with the effluent stream;(b) tee with 30' angle of intersedim of input
streams with the effluent stream; (c) tee with angles of intersection between the input streams and the effluent of 30' and 150'. In the straight line system L, contains a factor of the diffusion coefficient in the denominator (eq 1). If the WilkeChang formula for D , is considered a valid approximation, then the mixing time would be proportional to q. With increasing viscosity, the rate of diffusion decreases, thereby decreasing radial mixing and increasing the mixing time, L, (in a linear fashion). EXPERIMENTAL SECTION Apparatus. The apparatus used in this experiment is depicted in Figure 2. The apparatus consists of a Carnegie Medicin AB CMA/lOO syringe pump that provides constant flow with low amplitude pulsations. Hamilton 1005-LTN 5-mL syringes and Perfektum 1-mL syringes were used for propulsion of both indicator and diluent streams. An Ismatec Mini-S 860 peristaltic pump was also used in this study. Ismatec Tygon pump tubing was used (Cole-Parmer catalog numbers 7616-74 and 7616-78). Micro-Line 1850 0.51 mm inside diameter (i.d.) tubing and Cole-Pawner 0.89 mm id. Tygon tubing (catalognumber 762680) were also used to conduct the streams into and out of the mixing tees. Mixing tees of several geometries were machined in Plexiglas with inside diameters of 0.50 mm and 0.89 mm (Figure 3). The "angle of intersection" in the tee is defined as the angle between an incoming stream (e.g., carrier) and the effluent stream. One tee was constructed such that both angles of intersection were 90' (hereafter referred to as the 9W90 tee). Another had angles of intersection each of 30° (hereafter referred to as the 3C-30 tee). The third had angles of intersection of 30° and 150° (henceforth referred to as the 3W150 tee). The effluent from the tees was passed into 0.51 mm i.d. Microline tubing. A feature of the
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yellow in acidic media. The neutralization of a basic solution with acid is readily seen with this indicator. This work defines the observed mixing time as the length in the tubing after the confluence point required for complete neutralization of the bromothymol blue, as indicated by the conversion of the dye to its yellow, acidic, form divided by the average linear flow velocity. This choice for mixing seemed appropriate because the acid-base reaction accompanied by a color change provided a visible indication of whether or not the basic dye solution was completely neutralized. See Figure 2b. The mixing length was determined for varying volumetric flow rates, mixing tee geometries, solution viscosities, and reactor geometries (i.e., straight, coiled, curved, or knotted). For the case of coiled reactors, the travel length of the solution per revolution of tubing was known. The mixing length measurements were based on the number of turns necessary for complete neutralization, to the nearest eigth of a revolution. The corresponding uncertainty is 0.36 cm and 4 cm for the 0.524 and 4.17 cm radii cylinders, respectively. For measurements of the mixing length resulting from the knotted reactors, marks were made every 5 cm prior to the knotting. Thus the measurements were made to the nearest 2.5 cm. The nominal volumetric flow rates delivered by the syringe pump and the peristaltic pump were verified by using a 10-mL graduated cylinder and recording the time required for delivery of 3-5 mL of the solution. Rhodamine was excited by use of a UV lamp with fiitered light. The light emitted was bright yellow. The fluorescence was filtered to reject stray, ambient light, and the mixing length was determined to be the point after which the fluorescence intensity in both hemispheres of the tube could no longer be visually distinguished. This was confirmed by stopping the flow and observing whether any change in the fluorescenceintensity occurred, which would indicate incomplete mixing.
a.... =&
b*16.4 2.0 em
c m - 4 4 3.0 em
b. Flgure 4. (a) Schematic of coiled reactor. (b) Schematic of knot
configuration in knotted tube reactor. reactor-tee complex is that there was very low dead volume. The tee channel had a diameter that matched the inside diameter of the tubing to within 10 pm. The end of the reactor tubing was inserted into the counterbore of the tee. Thus there was very low discontinuity in the radius of tubing and no discontinuity in the channels experienced by the flowing streams. Four reactor configurations were used. The first was simply a straight length of Microline tubing, held rigidly straight. The second was a curved reactor in which Microliie tubing was curved to have a specific radius. The third was a coiled tube reactor in which Microline was coiled around a glass cylinder and held rigidly in place. Two coiled reactors were used, with radii of curvature, R,, of 0.524 and 4.17 cm. A coiled reactor with a radius of curvature, R,,is depicted in Figure 4a. The fourth reactor was a knotted tube reactor in which 29 knots were placed in the reactor as depicted in Figure 4b. An Ultraviolet Instruments UVSL25 ultraviolet lamp was used to excite a rhodamine solution. The lamp, in the high mode, emitted broad band UV light centered around 365 nm. An interference filter was used to filter the light at 546 nm. The filter had a band-pass of 10 nm at half peak maximum. A second interference filter with a cutoff of 590 nm with a 10-nm band-pass was used to filter the fluorescence to allow a better determination of the mixing point. The temperature was not strictly controlled. Ambient temperature, which fluctuated between 19 and 21 “C, was accepted as the temperature. Some measurements were made with the use of a light box such as one uses for drafting. This caused temperature fluctuations, which may account for the few outliers. Reagents. The reagents were prepared according to procedures given in Ruzicka and Hansen (ref 7, p 301). A 0.02 N borax solution was prepared by adding 3.814 g of sodium tetraborate, decahydrate (Matheson, Coleman & Bell) to 1 L of deionized water. The resultant pH obtained by measurement with a Radiometer pH meter was 9.2 at 24 “C. A stock solution of bromothymol blue was prepared by dissolving 0.400 g of bromothymol blue (3’,3”-dibromothymolsulfonephthalein) in 25 mL of 96% ethanol, and then the final volume was brought to 100 mL with the 0.02 N borax solution. Working solutions were prepared by dilution with the 0.02 N borax solution. A stock solution of 0.5 N HC1 was prepared in deionized water, from which a 0.05 N working solution was prepared by dilution. Additionally, sample viscosities were altered by using glycerol according to weight percents listed in ref 21. For viscous HCI solutions the appropriate weight of glycerol was added to a 100-mL volumetric flask along with 10 mL of the stock 0.5 N HCl solution. The resultant solution was brought to a final volume of 100 mL with deionized water. The experimental viscosity was determined with an Ostwald viscometer. Viscous solutions of 0.0239 N sodium hydroxide were obtained by adding the appropriate weight of glycerol to a 100-mL volumetric flask and adding 5 mL of a stock solution of 0.477 N NaOH perpared earlier and 10 mL of the bromothymol blue stock solution. The final volume of 100 mL was made up with deionized water. A3X M aqueous solution of rhodamine 116 perchlorate (Kodak) was prepared by dissolving 0.0036 g of the compound in 2 mL of 96% ethanol, and then a final volume of 100 mL was made with distilled water. Procedure. Bromothymol blue is blue in basic media and
RESULTS AND DISCUSSION Determination of a. Huber et al. (17) derived eq 1 by considering only diffusion and convection. Any reaction that would consume the analyte or carrier would likely affect the mixing length. Therefore an experiment was performed that would allow detection of the mixing time, yet that did not contain a reaction. A stream of rhodamine was merged with a water stream by using a 90-90 tee and a 0.89 mm i.d. reactor. The mixing length was determined for flow rates between 0.10 and 0.4 mL/min. Two distinct hemispheres in the tube were seen. One hemisphere, containing the rhodamine was brightly fluorescent, the other hemisphere containing water had no fluorescence. As mixing progressed, the streams became less distinct in fluorescence intensity, and eventually a point was reached where the intensity difference between the hemispheres, as determined visually, was zero. This point was considered to be the mixing length. The resulting mixing lengths are plotted as a function of flow rate in Figure 2a. The slope of the line was found to be 333 min/cm2 (19980 s/cm2). By use of eq 4,D, for rhodamine was found to be 5.0 x lo4 cm2. The slope is equal to a/2rD,. One can solve this equation for a, which yields a = 0.63. A value for a other than unity is not unlikely, since the initial boundary condition for the derivation of eq 1was such that the dispersing sample was assumed to be a point source in the center of the tube. Mixing was considered to be complete when one standard deviation of the radial concentration distribution was equal to the tube’s radius. A computer program simulating the confluent streams model was developed to study mediating factors in the confluent streams mixing process (22). It corroborates the linear dependence of the minimum length for mixing on the flow rate. The corresponding mixing times were calculated by using eq 2. An interesting feature of the system is seen in Figure 5b when the mixing time is plotted as a function of the flow rate, q. Equation 2 predicts that the mixing time is independent of the flow rate for a straight line system, because
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I t
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Flgure 5. (a) Plot of mixing length vs flow rate for a straight, 0.89 mm i.d. reactor using rhodamine merging with water. (b)Plot of mixing time vs flow for the system in 5a.
there is only radial diffusion to account for the radial mixing. Figure 5b has a large, positive intercept. This is due in part to the nonzero intercept seen in Figure 5a. The precision is poorest with the data point corresponding to the lowest flow rate considered. At higher flow rates, however, the mixing time appears to be independent (within experimental error) of the flow rate and has a mean mixing time of 145 s. Dependence of Mixing in a Straight Tube on Flow Rate and Mixing Tee Geometry. To allow better inspection of the mixing length, an alkaline pH indicator dye that would undergo a color change when merged with an acid stream was chosen. The neutralization of the basic, dye-containing solution would introduce a new term in eq l and 2, to account for the change in mixing length due to the chemical reaction. A reagent-consuming reaction would affect its concentration, thereby affecting its migration rate. An alkaline stream of bromothymol blue was merged with an aqueous, acidic stream. The alkaline BTB stream is blue, and the acidic BTB stream is yellow. Two distinct stripelike streams were observed after the confluence point. Silfwerbrand-Lindh (6) also noted this effect. The length of the blue stripe, which corresponds to basic bromothymol, was taken as the neutralization, or mixing length. This neutralization length varied with flow rate. After the tee a stripe of yellow was observed in the clear acidic side that increased in size with increasing length until the point at which the blue color disappeared. Variations in the mixing length were noticed when peristaltic pumps were used, likely due to periodic pulsations. Figure 6a shows the dependence of the length of mixing (neutralization) as a function of flow rate for the three tees used. The effluent tube was held as straight as possible and the mixing time was taken to be the point after which BTB in the basic, or blue, form could not be distinguished. The plots are linear with flow rate. Therefore, the eq 1 prediction
0.2
0.4
0.6
0.8
Flow Rata, q (rnl/mln)
Flgure 6. Plots of (a) mixing length and (b) mixing time against flow rate for (filled diamonds)30-30 tee, (open squares) 30-150 tee, and (filled squares) 90-90 tee.
that the mixing length is proportional to flow rate holds for the case of reaction. By the simple conversion of dividing mixing length by the linear flow velocity, results for each of the three tees were plotted as mixing times in Figure 6b. The plots demonstrate a decrease of the mixing time with the flow rate for the 30-30 and 30-150 tees. The mixing times for the 90-90 tee remain essentially constant over this range. Equation 2 predicts a constant mixing time for the confluent streams experiment in which diffusion is the only mechanism of radial transport. It is apparent, however, that the mixing times are definitely decreasing with increasing flow rate for the case of the 30-30 and 30-150 tees. This suggests that the tees impart secondary flow profiles on the exiting streams that increase in magnitude with increasing flow rate. Figure 6 gives an indication of the relative degree of efficiency of mixing for the three tees studied. The tees vary in the manner in which the two input streams undergo confluence. In the 90-90 tee the two input streams meet in a head-on fashion, and the effluent stream exits perpendicular to this line. The two input streams in the 30-150 stream also meet head-on, but the effluent stream exits at a 30" angle to one of the input streams. The input streams meet at 60" in the 30-30 tee but exit a t 30" from each input stream. Upon inspection of Figure 6a, two differences are apparent among the three plots. The slopes differ, with the 30-30 tee having the flattest slope and the 90-90 tee having the steepest slope. Their intercepts also vary, but in opposite order. If all three plots had a zero intercept, and retained their linearity, the three tees would all have flat curves in Figure 6b. However, since the curve in Figure 6b corresponding to the 90-90 tee has a slightly negative intercept, the corresponding curve in 6b has a slight dip in the curve at low flow rates. The curves for the 30-150 and 30-30 tees have positive intercepts and the mixing times in Figure 6b fall off accordingly at higher flow rates. Figure 6b also indicates that the three tees have a mixing time that overlaps a t low flow rate. The overlap
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
occurs a t a flow rate near 0.1 mL/min. The 90-90 tee has an intercept of 5.75 s at zero flow rate, a value which the 30-150 and 30-30 tees seem to approach. Assuming this time to be the minimum time of mixing for the three tees, the rootmean-square displacement of the diffusing particle can be calculated by rearranging and taking the square root of eq 3 (r2)
= (2Dmt,)'/2
(5)
where ( ~ * ) lis/ ~ the root-mean-square displacement of the diffusing molecule. HCl has a diffusion coefficient of approximately 3.1 X lo" cm2s ref 21, p F-62). The root-mean-square displacement that the diffusing molecules would travel in 5.75 s is calculated to be 0.019 cm. This distance is on the order of the inside diameter of the tube (0.025 cm). Therefore, the occurrence of a minimum mixing time when using these tees appears likely. Figure 6b demonstrates that mixing efficiency is the highest for the 30-30 tee, followed by the 30-150 and the 90-90 tees. The basis for this observation is that for increasing flow rate, above 0.1 mL/min, the 90-90 and 30-150 tees require longer mixing times than the 30-30 tee. This result corroborates work done earlier on the efficiency of mixing tees, which was summarized in the review given by Frei. Frei suggested that the 30-30 tee and the 30-150 tee causes turbulence which allows more efficient mixing. Since turbulence is considered to begin at high Reynolds number (23), the reason for this increased mixing efficiency is suggested here to be a secondary flow pattern, associated with bending an input flow stream around the corner in a mixing tee and merging it with the other input stream. This secondary flow pattern would likely increase with increasing flow rate. Perhaps the 30-30 tee induces a secondary flow pattern that mixes the streams more readily than in the 30-150 tee, which in turn causes mixing more readily than in the 90-90 tee. An alternative explanation may be that, as flow velocity increases, local turbulence at the tees may be induced due to the higher velocities on turning the corner. Mixing i n a Curved Reactor. The mixing time as a function of radius of curvature was determined for the 30-30 and 90-90 tees. The mixing time for the 30-30 tee was plotted in Figure 7a as a function of the radius of curvature, R,. The mixing time was plotted for the 90-90 tee in Figure 7b as a function of the natural logarithm of the radius of curvature, log R,. The linear regression, calculated by Statworks, a Macintosh statistical program, for the 30-30 tee yielded the best results when R, was the abscissa, while a logarithmic form of R, yielded the best results for the W 9 0 tee. However, both lines were closely fit with other regression types and functions of R,. The calculated lines are t, = 0.8474 0.1807RCfor the 30-30 tee, which has a regression coefficient, R, of 0.9980, and t , = 0.6103 1.801 log R, for the 90-90 tee, which yielded a regression coefficient, R, of 0.9989. The appropriate abscissas for Figure 7 were chosen based on these data. The salient features of the plot, other than the linear dependence of the mixing time for the 90-90 tee on log R,, is that decreasing the radius of curvature decreases the mixing time. This effect is attributed to increasing the secondary flow, which inverts the flow profile, thereby mixing the streams more readily. This effect has been documented in conventional FIA experiments where optimization of reactor length, radius of curvature, and flow rate was studied (10). The effect was also noted by Hungerford et al. (24),using a meandering reactor, who found mixing times on the order of s. The meandering reactor provides more efficient mixing than does the coiled reactor; however, the secondary flow effects are much the same. Viscosity Effects on Mixing. An important application, for which the confluent streams technique would be well
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1
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in lS
L
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Flgure 7. (a) Plot of mixing time against radius of curvature, R,, for the 30-30 tee. (b) Plot of mixing time against the logarithm of the radius of curvature, log R,, for the 90-90 tee.
suited, is the dilution of a stream with high viscosity. An example would be the dilution of a stream containing an industrial dye as the analyte. An experiment was performed in which the viscosity of the HC1 stream was increased, while the viscosity in the alkaline BTB stream was held constant at a viscosity near that of water. It was found through titration of the glycerol-HC1 solutions with borax that the 0, 16, and 24% (w/w) glycerol-HC1 solutions had essentially identical end points. These solutions required approximately twice their volume in borax for neutralization. The 48% and 60% glycerol solutions, however, had quite different titration curves. Single volumes of borax were required to neutralize the HC1-glycerol solutions. This disparity would likely alter the mixing length and time observed. Therefore, for this and the next experiment below where higher viscosities were required, 0.0239 N NaOH solutions were used in place of borax such that approximately 2 volumes of the alkaline solution neutralized one volume of the acidic solution. This was done to be consistent with the experiments performed earlier, where a 2:l ratio was also found. The mixing time is plotted as a function of viscosity of the HC1 stream at a T i e d flow rate of 0.51 mL/min of each stream (1.02 mL/min in the reactor) in Figure 8. In one case indicated in Figure 8, the viscosity of the NaOH-BTB stream was held constant at 0.911 cP, at 24 "C. The 30-30 tee was used with 0.89 mm i.d. tubing for the reactor and conduits for transporting the solutions into the tee. It is clear that as the viscosity of the acid stream increases, the time required for neutralization increases. This is conceptually easy to understand. The diffusion coefficient is inversely proportional to the viscosity. Thus, increases in solution viscosity d e c r q e the diffusion coefficient. This in turn reduces the radial mixing attributable to diffusion and also reduces any spurious
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8 -
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s
F
-a
0
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ii
0 ~ ~ " " ' ~ " " ' "
Vlscosny, Eta (cP)
Vlscoslly, eta (cP)
Figure 8. Plot of mixing time against viscosity for case when the HCI
stream has increasing viscosity and the base-indicator stream has viscosity of 0.911 CP (open square) and both streams have equal, increasing viscosity (filled diamond). The mixing tee used was the 30-30 tee. secondary flow that may result from small bends in the reactor that may promote mixing. The Cricket Graph logarithmic regression algorithm was used to calculate the line that best fits the data. The logarithmic regression calculated the line to be: L, = 44.8q0.5sQ, with a regression coefficientof 0.99. The first three data points are, however, reasonably linear. These data points are in a region where the viscosity of the acid stream is not very different from that of water. When the difference between the stream viscosities becomes greater, the nonlinearity manifests itself. Thus, it is suggested that L, increases with Furthermore, this nonlinearity becomes more obvious at larger viscosity differences. This is not in agreement with the predicted linear increase in mixing time with the viscosity by eq 1 and 2. Another experiment was performed in which the mixing time was found for the case when the viscosity of both solutions (HCl and NaOH + BTB) was increased commensurably. The results are also shown in Figure 8. Linear regression was performed on the data. The resulting line was L , = 14.8 + 29.27, with a correlation coefficient of 1.0. Thus, L, appears to increase linearly with the solution viscosity, as predicted by eq 1and 2. If eq 1applies for confluent streams, this result demonstrates that the linear dependence on viscosity is valid only when both streams have the same viscosity. The model by which Huber et al. derived their equation also suggests that in order for the viscosity dependence to apply, the viscosities should match in both streams. Reactor Geometry Effects on Mixing. Clearly, allowing 30-40 s for mixing of a viscous stream with a nonviscous diluent stream using straight tubing is not practical. Coiled and knotted tubing has been used extensively to mix streams in FIA. An experiment was performed to determine viscosity effects on mixing in these reactors. The mixing times (t,) for a knotted reactor (Figure 4b) and two coiled reactors with radii of curvature of 0.524 and 4.17 cm (Figure 4a) were determined as a function of viscosity. The neutralization stream consisted
Flgure 9. Plot of mixing time vs 7 for a coiled reactor with R, of 0.524 cm (open square), a coiled reactor with R, of 4.17 cm (filled triangle), and a knotted reactor (filled square) when the acid stream has the indicated viscosity and the viscosity of the alkaline BTB was held constant at 0.91 1 cP.
0
1
2
3
4
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Vlrcorly, eta (cP)
Figure 10. Plot of mixture time vs q for a coiled reactor with a radius of curvature of 0.524 cm, in which both streams are of the same
indicated viscosity. of the 0.0239 N NaOH and bromothymol blue indicator. The data are plotted in Figure 9. The Cricket Graph logarithmic least-squares algorithm was used to fit the lines. The equations for the lines were t , = 2 . 3 9 ~ ' , ~ L ~, ,= 2.58~O."~,and L, = 4.73~7O.~~, respectively. These equations demonstrate that mixing is facilitated through use of a knotted reactor varying the secondary flow
Anal.
Chem. 1980, 6 1 , 979-981
profile, forcing confluent mixing of viscous streams. The coiled reactors are also useful in the mixing process, although not of the same magnitude as the knotted reactors. It is apparent that as the degree of secondary flow increases, the efficiency for mixing of viscous solutions increases in even greater proportion, and so for mixing very viscous solutions, the knotted reactor is very effective. Only 3.40 s was required to mix the solution of 7 = 5.4 CPwith the diluent, whereas 6.10 and 9.92 s were required for neutralization in the 0.524- and 4.17-cm coiled reactors, respectively. A mixing time of 40 s was required for mixing in the straight line reactor. Some applications may require mixing of two viscous streams. Therefore, an experiment in which both streams had the same viscosity was performed by using a coiled reactor. The data are plotted in Figure 10. The mixing time increases dramatically with 7 for the lower viscosities and then apparently levels off. The encouraging result in this experiment is that the coiled reactor using a 30-30 tee will mix two streams of high viscosity with quite good efficiency, if necessary. Under our experimental conditions, the two reactors, coiled and knotted, offer a distinct advantage over straight and curved reactors when mixing two solutions, one with a high viscosity (e.g., blood serum). It is obvious that mixing is promoted in the coiled and knotted reactor by secondary flow, and that either would be useful when faced with sample pretreatment in which one must dilute a highly viscous sample stream.
ACKNOWLEDGMENT The authors thank David A. Whitman for many helpful discussions.
079
LITERATURE CITED Stewart, J. W. B.; Ruzicka, J.; Bergamin Fo, H.; Zagatto, E. A. G. Anal. Chim. Acta 1978, 8 1 , 371. Ruzicka, J.; Stewart, J. W. B.; Zagatto, E. A. G. Anal. Chim. 1976, 81. 387. Stewart, J. W. B.; Ruzicka, J. Anal. Chim. Acta 1978, 8 2 , 137. Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1978, 99, 9. Frei, R. W. Chemical Derivatlzatlon In Analytical Chemistry. In Modern Analytcal Chemistry; Frel, R. W., Lawrence, J. F., Eds.; Plenum Press: New York, 1981; Vd. 1. p 211. Silfwerbrandlindh, C.; Nord, L.; Danielsson, L. G.; Ingman, F. Anal. Chim. Acta 1984, 160, 11. Ruzicka, J.; Hansen. E. H. Flow Inbtlon Ana!&, 2nd ed.;Wiiey-Interscience: New York. 1988. Mardsen, A. 8.; Tyson, F. F. Anal. Proc. 1988, 2 5 , 89. Zagatto, E. A. G.; Reis, B. F.; Maitineili, M.; Krug, F. J.; Bergamin F., H.; Gine. M. F. Anal. Chim. Acta 1987, 198, 153. Tjissen, R. Anal. Chim. Acta 1980. 114, 71. Neue, U.;Engelhardt, H. Chromatographia 1982, 15, 403. Ruzlcka, J.; Hansen, E. H. Anal. Chim. Acta 1984, 181, 1. Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1980, 114, 19. Reijn. J. M.; Van der Linden, W. E.; Poppe, H. Anal. Chim. Acta 1881, 123, 229. Crowe, C. D.; Levln, H. W.; Betterme, D.; Wade, A. P. Anal. Chim. Acta 1987, 194, 49. Whitman, D. E.; Christian. 0. D. 42nd Northwest Regbnai Meeting of the American Chemical Society, Beiiingham, WA, June 17-19, 1987. Huber, J. F. K.; Jonker, K. M.; Poppe, H. Anal. Chem. 1980, 52, 2. Berry, R. S.; Rice, S. A.; Ross, J. physlcal Chemistry. John Wlley & Sons: New York, 1980; p 1104. Golay, M. J. E. J . Chromtogr. 1979, 186. 341. Giddings, J. C. Dynamics of Chromatography, Part I , Princlph and Theory; Dekker: New York, 1985. CRC Handbook of Chemhtry and physics, 64th ed.;Weest, R. C., Ed.; CRC Press: Boca Raton, FL. 1983; p F-48. Pfeffer, J., unpublished results. Hungerford, J. M. Doctoral Dissertation, University of Washington. Hungerford, J. M.; Christlan, G. D.; Ruzicka. J.; Giddings, J. C. Ana/. Chem. 1985, 57, 1794.
RECEIVED for review July
14, 1988. Resubmitted February 3, 1989. Accepted February 3, 1989.
Electrodes Modified with a Film of Phosphatidylcholine: Electrochemistry inside a Lipid Layer Orlando J. Garcia, Pablo A. Quintela, and Angel E. Kaifer* Chemistry Department, University of Miami, Coral Gables, Florida 33124 Prellmlnary results on the behavior of glassy carbon electrades modlfled by cast layers of phosphatldylchdlne(PC) are presented. Redox-actlve amphlphlles are extracted from a Contacting aqueous solutlon Into the cast llpld layer where they undergo electrochemical reactlons wlth the underlylng electrode surface. Once the llpld layer Is loaded wlth electroactlve amphlphlllc materlal, the electrode can be transferred to pure supporting electrolyte solutions wlth retentlon of the electroactlvlty. I n contrast, hydrophlllc electroactlve substrates are kept away from the electrode surface by the PC layer largely preventlng the observatlon of electron transfer reactions wlth the electrode.
In this communication we report the peculiar electrochemical behavior of electrode surfaces covered by a layer of phosphatidylcholine (PC).Redox-active amphiphiles readily partition into this lipid layer from a contacting aqueous solution and undergo electrochemical reactions at the electrode surface. In contrast, more hydrophilic versions of these electroactive compounds are rejected by the lipid layer preventing their electron transfer reactions with the electrode. Several groups are actively investigating the properties of electrode surfaces derivatized with hydrophobic materials. A 0003-2700/89/0381-0979$01.50/0
common approach is based on the self-assembly of electroinactive (1-5) or electroactive (6-12) amphiphiles at the eledrode-solution interface. An alternative methodology uses Langmuir-Blodgett techniques to transfer monolayers (7, 13-18) or multilayers (19) from the air-solution interface to a substrate that is then employed as an electrode. The effects of cast layers of palmitic acid on the electrochemical behavior of several substrates at the underlying electrode were recently reported by Tanaka et al. (20). In their work, these authors noted that the hydrophobic layers hindered substantially the observation of electrochemistry of hydrophilic species. We reasoned that a PC layer could behave as a selective barrier (membrane) on the electrode and perhaps incorporate redox-active lipophilic substrates. We present here preliminary results that clearly indicate both features using the following redox-active substrates.
2 Br-
I R = C,H,, , X = BrR = CH3 , X - = I-
O 1989 American Chemical Society
