101
Anal. Chem. 1989, 61, 101-107
Kinetics of Solvent Extraction-Flow Injection Analysis Charles A. Lucy and Frederick F. Cantwell*
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T 6 G 2G2
The effect of instrumental parameterson the rate of extractlon in solvent extraction-flow injection anaiysls was studied. I n sfrslghffubes, the extraction rate Increases rapidly with decreasing segment length for short segments and Is approximately constant for longer segments. Increasing the h e a r velocity results in less than a proportional increase in the extraction rate. Changes in extractlon rate with tublng diameter are correlated wlth the Interfacial area of the segment and with the segment aspect ratio. The convection wlthin long segments Is torddai wlth the flow streamllnes parallel to the tube wail except near the segment ends, whereas the convectlon In short segments exhibits a slgnlflcant radlal flow component along the entlre segment. I n colled fubes, the extraction rates are much higher than In comparable straight tubes. This enhancement is due to the generatlon of tangential secondary flow withln the segments and is greater for long segments than for short.
Solvent extraction is the most frequently used separation method in flow injection analysis (1). Research on the theory of solvent extraction-flow injection analysis (SE-FIA) has addressed the origin of phase segmentation (21, the dependence of peak area on flow rate (3),the factors influencing peak height ( 4 ) , the efficiency of the separation process (5), the operation of porous-membrane phase separators (6),and the band broadening that results both from film formation in the extraction coil (7) and from the dead volume of the phase separator (8). Until recently, a gap in the theory of SE-FIA has been the lack of understanding of the extraction process itself, by which solute is transferred from the aqueous segments into the organic segments. This process was recently investigated by Nord et al. (9) for segments of 3-40 mm in length. It was found that extraction rate depends on two major factors-the ratio of interfacial area to volume and mass transfer of solute to and from the interface. This work was apparently conducted using coiled extraction tubes. However, the convective/diffusive processes that control mass transfer were interpreted in terms of a simple toroidal circulation pattern within the segments, which, in fact, characterizes only segmented flow through straight tubes. Thus, while the major theoretical principles of solvent extraction in segmented flow have been established in the important work of Nord et al. (91,the significant contribution of secondary flow to convection in coiled tubes, which has been well documented for air-water segmented flow (10-12),has apparently been overlooked. In addition, they studied only long segments (many times the tube diameter) and therefore did not observed the effects of the altered hydrodynamic conditions which occur in short segments. In the present work, the role of secondary flow has been investigated and extensive studies have been done which provide a more detailed and accurate physicochemical model for the extraction process. THEORY Flow Hydrodynamics. When two immiscible solvents flow concurrently through narrow tubing under laminar
conditions, alternating segments of the two phases are formed. This flow is referred to as segmented, bolus (13) or slug flow (IO). If a reference frame moving at the average flow velocity is used to view a relatively long segment flowing through a straight tube, a “toroidal” circulation pattern is observed (9, 10-131, the hydrodynamics of which have been described in the literature (14-16). The fluid at the walls appears to move backward while that along the tube axis moves forward. Alternatively, if the segment is viewed from a stationary reference frame, the cross sectional flow profile, except near the ends of the segment, is parabolic with zero axial linear velocity at the walls and twice the mean axial linear velocity along the axis of the tube (9,13,15). Near the ends of the segments the flow changes rapidly from axial in direction to radial. Another characteristic of segmented flow is that the solvent which has the greater affinity for the wall material forms a thin “wetting film” on the walls of the tubing (7). When flow occurs under laminar conditions through coiled tubing, the resulting centrifugal force acts most strongly on the fastest moving regions of the flow. In segmented flow, like homogeneous laminar flow, this is at the tube center. The fast moving fluid is thrown outward from the coil axis and is replaced by recirculating fluid which flows tangetially along the walls (17,18). Secondary flow augments the convection resulting from the toroidal circulation, such that the rates of solute mass transfer controlled processes within the segment are increased. For instance, in a study of dispersion (band broadening) occurring during the flow of air-segmented aqueous solution, the mixing rate within the aqueous segments was markedly increased by coiling the tube (12).Moreover, in studies of radial mass transfer to the walls of a coiled, wall-coated enzyme reactor, the secondary flow effects were found to be greater in the case of air-segmented aqueous solution than in the case of unsegmented aqueous solution (10). Mass transfer, in the presence of this secondary flow is correlated with the dimensionless velocity parameter De2& (17, 18), where
d,3u2 1 1 De2Sc = -uD d, in which De and Sc are the dimensionless Dean and Schmidt numbers, d, is the inner diameter of the tubing, u is the average linear velocity of the fluid, u is the kinematic viscosity, D is the diffusion coefficient of the solute, and d, is the coil diameter measured at the tube axis. Extraction Model. During segmented flow through Teflon tubing, a solute extracts from an aqueous segment through the ends of the segment into the adjacent organic segments and also radially through the sides of the aqueous segment into the wetting film of organic phase along the walls of the tube (9). If no chemical reaction is involved in the solvent extraction process, or if the chemical reactions are very fast, the extraction will be goverened by the mass transfer to and from the aqueous/organic interface. Mass transfer mediated processes follow an exponential behavior (1%22), and so can be mathematically treated in a similar manner to a first-order chemical reaction, even though no true chemical reaction is involved. The integrated form of the extraction rate expression is
0003-2700/89/0361-0101$01.50/00 1989 American Chemical Society
102
ANALYTICAL CHEMISTRY, VOL. 61, NO. 2, JANUARY 15, 1989
where A,,o and A,,oare either the steady-state absorbance or the peak area due to the analyte in the organic phase at equilibrium and a t time t, respectively, and howis the observed extraction rate constant. This observed rate constant will be a function both of the mass transfer within the segments and of the interfacial area. The interfacial area dependence can be removed by converting the observed rate constant into an overall log mean mass transfer coefficient, (21,22)
I
Waste
“rn 2;:$fiI ,,
:
m
1
.....................................................................................
B
8 = kobsd/ ( a / v)
(3)
The term a / V is the interfacial area to volume ratio for a segment. ,8 has the units of velocity, and its r e c i p r d is often viewed as the “resistance to mass transfer” (20-22). This overall mass transfer coefficient is related to individual mass transfer coefficients by the expression
where PWand Po refer to mass transfer to the interface through the aqueous phase and away from the interface through the organic phase, respectively, KD is the distribution coefficient of the solute, and Pi refers to transfer across the interface itself (20, 23). In the absence of surface-active solutes l/Pi is negligible (20,23,24). Furthermore, if KD is large, as it usually is in SE-FIA, then BJin is much larger than Paq, and the organic phase acta like a “sink” for solute. Thus the extraction rate is governed by mass transfer within the aqueous phase only
B = Paq
(5)
Since solute exits the aqueous phase via both the ends and the side of the aqueous segment, Paqcan be considered the s u m of two aqueous phase mass transfer coefficients, one for axial maas transfer to the ends and one for radial masa transfer to the sides of the aqueous segment
The radial component of the extraction is analogous to the radial mass transfer that has previously been studied in a wall-coated open tubular enzyme reactor with air segmented flow ( I O ) . Solute, once extracted into the organic phase, experiences band broadening. This is due to transport “backward” of organic solvent into following organic segments via the wetting film (7). Similar phenomena have been reported in air segmented flow (II,12,25). In spite of this band broadening, extraction rates, which are measured in the present work by monitoring the absorbance of the organic phase, correctly reflect the rate of extraction of solute out of the aqueous phase as long as the distribution coefficient of solute between the organic and aqueous phases is large. This is true whether the measured signal is a steady-state absorbance, as used in experiments employing constant feed, or whether it is a peak area, as used in experiments employing sample injection. EXPERIMENTAL SECTION Apparatus. Figure 1 provides a schematic diagram of the SE-FL4 instrument used in these studies. Solvents are pumped by using two liquid chromatographic pumps, P1and P2(Model B-lWS, Eldex Laboratories, Inc., San Carlos, CA), equipped with pulse dampers (Model LP-21 LO-Pulse, Scientific Systems, Inc., State College, PA). Restrictor columns (15 cm X 1mm i.d. X ’/.,
J.
Wstte
j&p,e’ j
................................................................................................................
i
Figure 1. Diagram of extraction-FIA instrument used for kinetic
studies. See Text
for
details.
in. 0.d. packed with 40-pm glass beads), not shown in diagram, ensure sufficient back pressure for proper action of the pumps and pulse dampers. Valve VI (part no. R6031 V6, Laboratory Data Control (LDC), Riviera Beach, FL) is a six-port rotary valve that allows selection of any one of a number of solutions as the aqueous carrier stream. Valves V2 (part no. CAV3031, LDC)are three-port valves that direct flow to either the extraction system or to waste. Valve V, (part no. CSVA-10, LDC) is a 10-pL slider injection valve that is actuated by an air solenoid valve (part no. SOL3-24-VDC, LDC) controlled by an electronic timer (3). The two solvent streams meet at the segmentor, S. Both Technicon A-8 (26) and tee design (2)segmentors were used. The resulting segmented flow passes through the extraction tube, E, in which the extraction between the aqueous and organic phase occurs. Various lengths of 0.3,0.5, 0.8, and 1.0 mm i.d. Teflon tubing were used as the extraction tube. These tubes were held straight in all studies, except thme specificallyexamining the effect of coiling. Coiled tubing was helically wound around a cylindrical template and held in place with elastic bands. After exiting the extraction tube, the segmented flow stream enters the porous membrane phase separator, PS, where a portion of the organic phase is separated. The phase separator is based on a design described by Apffel et al. (23,where two grooves are separated by a hydrophobic membrane. The groove on the downstream side of the membrane has a nominal volume of 8 p L and the upstream groove is 11 pL for all studies except those involving the longer segments in 1mm i.d. tubing, for which the upstream grmve was 18 pL. The hydrophobic membrane consists of one piece of 4-mil, 10-20 pm pore size Zitex Teflon membrane (no. E249-122, Chemplast, Inc., Wayne, NJ). The organic phase passing through the membrane is directed to the 8-pL flow cell of the UV-vis photometer, D (SF770 Spectroflow, Schoeffel Instrument Corp). The detector signal is fed to either a recorder (Fisher 5000) or an integrator (Model 3390A, Hewlett-Packard), R/I, depending on the experiment. The membrane flow is regulated by a downstream peristaltic pump, P3(Minipuls, Gilson, Instruments, Ville-de-Belle, France), which is connected to the detector by 30 cm of 1.5 mm i.d. Teflon tubing to dampen pulsations from the peristaltic pump. The extraction system is thermostated at 25 1OC in a water bath shown as dashed lines in Figure 1. An adjustable rail system allows clamping of the segmentor and phase separator to ensure that the extraction tube is straight. Reagents. Water was demineralized, distilled, and finally distilled over alkaline permanganate. Reagent grade chloroform (Caledon Laboratories, Ltd.) was distilled and washed with distilled water shortly before use. The pH 4.0 buffer solution (ionic strength = 0.1) was prepared from citric acid (Caledon Laboratories, Ltd.) and sodium hydroxide (BDH), and was equilibrated with washed chloroform shortly before use. Caffeine (Aldrich Chemical Co.) was used as received. Measurement of Extraction Rates. Experiments were performed by using either injection of sample or continuous feed of sample, as described below. Time (t in eq 2) is varied by varying the length of the extraction tube at a constant flow rate. Measurements were made prior to the attainment of equilibrium using extraction tubes between 5 and 85 cm in length, while equilibrium
*
ANALYTICAL CHEMISTRY, VOL. 61, NO. 2, JANUARY 15, 1989
measurements were made using an extraction tube of 310 cm wound in a 4-cm coil diameter. If this equilibrium tube were straight, it would correspond to 41/2 half-lives for the slowest extraction observed. However since secondary flow enhances the extraction rate (see below), this coiled tubing corresponds to greater than 10 half-lives (Le. equilibrium) for all extractions studied. The various lengths of tubing were run in random order to avoid systematic errors in the rates from any slight instrument drift. Once a measurement had been completed for a given extraction tube, the aqueous and organic flow was stopped by using valves Vz, and the segment length was measured by using the formula (7)
where La, is the length of the aqueous segments, X is the total distance measured, N is the number of aqueous-organic segment pairs measured, and Fa and F, are the aqueous and organic flow rates, respectively. For the sample injection experiment the instrument was used as shown in Figure 1. Peak areas were measured with a digital integrator. To set the integrator measurement parameters, all peaks were declared to be “solvent” peaks to ensure integration of the entire tailed peak. The injected sample was 5 X lo4 M caffeine in citrate buffer and the detector wavelength was 278 nm. All other parameters were varied as described in the Results and Discussion section below. Either straight or coiled tubes were used, as specified. In the steady state experiment a base line was first established by pumping chloroform with pump P1 and an aqueous blank solution with pump Po. Aqueous sample solution was then substituted for blank by switching V1 and was fed continuously into the system. The difference between the steady-state sample absorbance and the blank absorbance was measured. The extraction tubing in this experiment was always 0.8 mm i.d. Teflon. The chloroform flow rate, F,, was 3.0 mL/min, the aqueous flow rate, Fa, was 3.0 mL/min, and the flow rate of chloroform through the porous membrane in the phase separator, F,,,, was 1.9 mL/min. Sample solutions were 1.0 x lo“, 9.9 x lo“, and 1.0 X 10” M caffeine in citrate buffer and the blank solution was citrate buffer. The “tee” type segmentor was used. The detector M caffeine and 278 nm for the wavelength was 295 nm for other caffeine concentrations. RESULTS AND DISCUSSION Extraction within a SE-FIA instrument is a mass transfer controlled process. Therefore factors that affect the convection within a segment will influence the kinetics of the extraction. The influences exerted by phase ratio, segment length, flow rate, and tube diameter on the extraction rate observed in straight tubes was investigated and are reported herein. The effect of secondary flow on the extraction rate was studied by varying the coiling of the extraction tube. T o ensure that the extraction rates studied were controlled by the toroidal and secondary flows associated with segmented flow through the extraction tubing, it was necessary to control or eliminate extraction occurring within the other components of the instrument and as a result of random turbulence in the segments. I n s t r u m e n t a l Considerations. Random turbulence within segments in the extraction tube was minimized by taking the following precautions: (i) The solvents were preequilibrated; otherwise their mutual dissolution when they meet a t the segmentor would lead to interfacial turbulence (23,28). (ii) The extraction system was thermostated to avoid thermal gradients which would enhance mixing within the segments and to avoid changes in the equilibrium constants and diffusion coefficients. (iii) The aqueous phase contained a buffer to maintain constant pH and ionic strength. (iv) Surface-active compounds were avoided, since the presence of adsorbed solute at the liquid-liquid interface would reduce the circulation within the aqueous segments (23,28) and may introduce an interfacial resistance to mass transfer (24). (v)
103
al C
0.6
9
8
9
0 ”
0.4
tj
x
P
0.2
tj 0.0 0
10
20
30
310
Extraction Tube Length, cm Flgure 2. Extraction of caffeine into chloroform. Measured absorbance in organic phase for a constant feed of 9.9 X lo-’ M caffeine at extraction tube lengths from 0 to 25 cm and also at the equilibrium tube length of 310 cm. Pulsations in the flow were minimized because they would result in irregularities in the segmentation and affect convection (29). (vi) The extraction tubing was held straight to avoid any secondary flow that would result from coiling. Extra-Tube Extraction. In order to study the extraction occurring within the extraction tube, it is necessary to minimize and control the extraction occurring in the segmentor and phase separator. In an extraction rate measurement, which involves fixed flow rates and varied extraction tube length, both the segment formation time and segment size are constant. Therefore the amount of extraction occurring in the segmentor will be constant. In the porous membrane phase separator, extraction will occur in the chamber on the upstream side of the membrane where the two phases are in contact. Reducing the chamber size and minimizing the mixing within this chamber should reduce the extraction contribution of this device. However miniturization of the phase separator is limited by the need to constantly wet the porous Teflon membrane with the organic phase. As a compromise, a phase separator with an ll-wL groove on the segmented side of the membrane was used. In addition, it was found that increasing the fraction of phase flowing through the membrane decreased the extraction occurring within the phase separator, because this reduces the mixing time within the segmented stream chamber. The degree of extraction reached a minimum plateau value when the flow through the membrane was greater than 40% of the total organic flow. In all subsequent studies the grooved phase separator was used and the membrane flow was maintained between 40% and 65% of the total organic flow. Using these conditions the fraction of the extraction occurring outside the extraction tube ranged between 20% and 6070, being highest for the shortest segment lengths. Extraction Rate. Data for a typical extraction rate experiment are presented in Figure 2, which shows the steady-state absorbance in the organic phase at various extraction tube lengths for the extraction of a continuous sample feed of caffeine. Results from sample injection experiments look the same, except that peak area is used instead of steady-state absorbance. The ordinate intercept reveals that about 33% of the extraction occurred in the extra-tube portion of the instrument. For these conditions the extraction has reached 90% of its equilibrium value by 25 cm. A plot of In [A,,,(AqP, versus t , according to eq 2, yields a straight line with slope 1.29 f 0.07 s-’ and intercept 0.40 0.02, where the uncertainties are standard deviations. The slope is kobd and the intercept reflects the extra-tube extraction. If the extraction of caffeine is a mass transfer controlled process, kobsd should be independent of the sample concen-
104
ANALYTICAL CHEMISTRY, VOL. 61, NO. 2, JANUARY
15, 1989 1.2
Table I. Rate Constants for the Extraction of Caffeine Using Continuous Sample Feed" concn, M
kobsd,' sK1
1.0 x 10-6 9.9 x 10-6 1.0 x 10-3
1.42 f 0.11* 1.29 f 0.07b 1.36 f 0.15b
"Fa= 3.0 mL/min; F, = 3.0 mL/min; portion of organic flow passing through membrane, 63%; tubing, 0.8 mm i.d. Teflon, coiled. Uncertainty is given as the standard deviation of the slope of the first order kinetic plot. Value of kowmeasured in a sample injection experiment was 1.26 f 0.11 s-l (see text).
Table 11. Effect of Phase Ratio on Extraction Rate Constant Measured in Sample Injection Experimentso La,,, mm
phase ratiob
kow,s-*
0.9 0.9
2:l 1:1
0.63 f 0.03 0.65 f 0.05'
2.8 2.8
1:3 1:l
0.25 f 0.01 0.22 f 0.03
3.3 3.3
1:4 1:l
0.23 f 0.01 0.20 f 0.02'
"Total flow rate 4.0mL/min (u = 13.3 cm/s); portion of organic flow through membrane, 60%; sample injected, 10 rL of 5 X IO4 M caffeine in pH 4.0 citric acid buffer; tubing, 0.8 mm i.d. Teflon, straight. bPhase ratio = Fo/F,. CInterpolatedfrom the curve for 4.0 mL/min shown in Figure 3. Uncertainties are based on the relative standard deviation of the points making up the curve. tration. The values of kommeasured at three concentrations of caffeine using continuous sample feed are shown in Table I. They are statistically equivalent at the 95% confidence level. Injection of a sample, as opposed to continuous sample feed, results in a sample zone comprised of a peaked concentration profile. However, since the extraction is mass transfer controlled, and therefore independent of concentration, it should be possible to monitor the extraction rate by using sample injection just as well as by using continuous sample feed. Under the same experimental conditions that pertain to Table I, an extraction rate constant of 1.26 f 0.11 s-l was observed for injections of 2 pL of 5 X M caffeine. This is statistically equal to the rate constants in Table I, indicating that sample injection is a valid procedure for measuring kom. All subsequent studies employed sample injections, as this is the manner in which flow injection analysis is generally performed
(30). Phase Ratio. Extraction rate constants observed a t organic-to-aqueous phase ratios of 2:1, 1:3, and 1:4, at a constant total flow rate of 4.0 mL/min (u = 13.3 cm/s) are given in Table 11. Also shown in Table I1 are rate constants observed using aqueous segments of the same three lengths and using the same total flow rate, but at a phase ratio of 1:l. For reasons discussed later, kobsdis larger for smaller aqueous segment lengths. However, the important observation here is that the two values of komfor a given aqueous segment length are equal to one another and independent of organic segment length. This indicates that the distribution coefficient of caffeine between chloroform and water (101.3measured in this work and in ref 31) is sufficiently high to make the mass transfer in the organic phase fast compared to that in the aqueous phase (20). Thus $ is equal to pa, (eq 5) and only convection within the aqueous segment need be considered in studying the extraction rate. Segment Length. In Figure 3 is shown the dependence of the extraction rate constant on aqueous segment length in a straight tube, for three flow rates. At a given flow rate, koM
1.o
0.8 r
'VI
0.6
0.0
'
0
1
2
3
4
5
6
7
I
8
Segment Length, mm Flgure 3. Observed extractbn rate constant versus the segment length at three flow rates: (a) 2 mL/min (A);(b) 4 mL/min (X); (c)6 mL/min (m). Phase ratio, 1:l; tubing diameter, 0.8 mm; tubing orientation,
straight.
approaches a constant value for segment lengths greater than about 4 mm, but increases with decreasing segment length for shorter segments. The increase in kobd with decreasing segment length at a constant flow rate could reflect an increase in either the interfacial area or pa,. The former factor can be accounted for by converting k,m to Pa, using eq 3. The interfacial area-to-volume ratio for the aqueous segments is given by
where La, is the aqueous segment length calculated by using eq 7 and rt is the tubing radius. This expression assumes hemispherical ends for the aqueous segments and a negligibly thin wetting film of chloroform. The resulting three plots of mass transfer coefficient versus segment length (not shown) consitute a family of curves very similar in appearance to those in Figure 3. Thus, for straight tubes, the increase in interfacial area accompanying a decrease in segment length can explain only a minor portion of the increase in extraction rate, the major portion being due to increased PaT For paqto increase there must be some enhancement in the convection within the segment. Solutions to the Navier Stokes equation for the toroidal circulation (14-16) indicate that for long segments the mid-segment axial velocity profile approaches the parabolic Poiseuille profile, in which the flow streamlines are parallel to the tubing wall; i.e. the radial velocity component is minor. However, when the segment length is reduced sufficiently that the ends of the segment are on the order of a tube diameter apart, the ends interact hydrodynamically to dramatically increase the radial velocity component of the circulation within the segment. This enhances the convective mixing in the segment and thus increases the mass transfer coefficient. In a study of radial mass transfer of solute to the wall during air-segmented flow of aqueous solution through straight tubes, very similar behavior to that shown in Figure 3 was observed (Figure 2 or ref 10). (In the study results were expressed in terms of the dimensionless quantities Nusselt number, segment aspect ratio and Reynolds number rather than by their respective dimensional counterparts-mass transfer coefficient, segment length, and flow rates-as is done here). This suggests that in liquid-liquid segmented flow either the extraction results mainly from the radial mass transfer (p = pradid)or that the axial and radial mass transfer coefficients exhibit the same dependence on segment length. This question is addressed in a subsequent study for the case of
ANALYTICAL CHEMISTRY, VOL. 61, NO. 2, JANUARY 15, 1989
1 -
0.009
105
t
17
1
t
1
I
u'*
0.0
t
0.012
-
o.2
(B) \td)
0.000"" 0
3
"
I
"
6
" " . 1" 2
9
15
18
Segment Aspect Ratio Flgure 5. Repbtting of mass transfer coefficient from Figure 48 versus the segment aspect ratio.
0.000
0
1
2
3
4
5
6
7
8
Segment Length, mm
Figure 4. Observed extraction rate constant (A) and mass transfer coefficient (B) versus segment length at four tubing diameters: (a) 0.3 mm i.d. (A); (b) 0.5 mm i.d. (e);(c) 0.8 mm i.d. (X); (d) 1.0 mm i.d. (0). Linear velocity, 13.3 cm/s; phase ratio, 1:l; tubing orientation, straight.
segmented liquid-liquid flow through a straight tube (32). Flow Rate. Intercomparison of the three curves in Figure 3 shows that, at a given segment length, the extraction rate constant increases with flow rate. In an analogous study in air segmented flow through straight tubing, Bra& was related to the linear velocity u by a power relationship ua where a was observed to be 0.50 for short segments and 0.34 for long segments. For a constant tube diameter, linear velocity and flow rate are directly related. Plots of log kobsd vs log u for the data shown in Figure 3 yielded straight lines, with slopes of 0.89 f 0.08 and 0.68 0.08 for segment lengths of 1.5 and 6.0 mm, respectively. Likewise, if the data for the extraction of caffeine from long (8 mm) segments flowing through 0.7 mm i.d. coiled tubing (Figure 6 of ref 9) are plotted in this double logarithmic fashion, a linear plot of slope 0.58 0.02 is obtained. Thus, mass transfer in both air segmented and liquid segmented flow is related to linear velocity via a power relationship, the power of which decreases with increasing segment length and is greater for corresponding segment lengths in liquid segmented flow than in air segmented flow. The larger value of cy in liquid segmented systems may be understood in the following way. Increasing the linear velocity increases both the circulation within the segments and the thickness of the wetting film on the tube wall (7, 11, 25). However, in SE-FIA the increased film thickness of the organic phase will have no effect on the mass transfer rate, since the rate-determining mass transfer process occurs in the non-film-forming aqueous phase. In air segmented flow, on the other hand, the radial mass transfer occurs in the filmforming phase, and studies of axial dispersion (11,12, %) have shown that there is slow mass transfer within the quasi-static liquid film at the tube wall. Thus, in air segmented flow an increased linear velocity generates two opposing effects. The enhanced convective mass transfer due to increased circulation is partly offset by the decreased diffusional mass transfer within the thicker wetting film. Tubing Diameter. The effect of varying tube diameter on the observed extraction rate is strongly dependent on the
*
*
segment length, as can be seen by intercomparing the curves in panel A of Figure 4 at a constant segment length. For long segments, > 4 mm, the extraction rate increases as the tubing diameter is decreased. However, for shorter segments, a crossover is observed, so that the extraction is fastest in the wider tubing. Conversion of the observed extraction rates into the corresponding mass transfer coefficients eliminates this crossover and greatly simplifies the observed trends, now shown in panel B of Figure 4. This indicates that to a large extent the behavior of kobsd results from the increase in a / V as the segment length is decreased. However, while does appear to become independent of the tubing diameter for extremely long segments, 1 8 mm, it still increases with increasing tubing diameter for shorter segments. The hydrodynamics within a segment are determined by boundary conditions defined by the walls and the ends of a segment. In reflection of this, solutions of the Navier Stokes equation use the dimensionless segment aspect ratio rather than the segment length (14-16). This is the segment length divided by the tubing diameter. Figure 5 is a replotting of the mass transfer coefficients of Figure 4B versus the segment aspect ratio. In this plot the data collected at the four tube diameters follow a single general curve in which two regions of behavior are evident. Above an aspect ratio of about 3, the mass transfer coefficients is constant, whereas below this aspect ratio p increases rapidly with decreasing aspect ratio. This behavior is consistent with the hydrodynamic studies discussed above in which it was found that when the segment length approaches the tube diameter, the segment ends interact hydrodynamically to enhance convection (15,16) and mass transfer. Coiling. For a homogeneous single phase fluid flowing through a coiled tube, the secondary flow is well developed when De2& > lo4 (18). For caffeine, under the segmented flow conditions used in this study, De2Sc ranged between 106 and 1 6 , so coiling of the extraction tube is expected to strongly affect the extraction rate. In Figure 6 are shown the rate constants observed for caffeine extraction in coiled tubing. The reciprocal of the coil diameter is used as the abscissa since the secondary flow is related to this term (17, 18), as is shown in eq 1. Three segment lengths were used, corresponding to the steeply rising region, to the "knee" region, and to the flat region of Figure 5. The results shown in Figure 6 are phenomenologically similar to the results of a study of coiling on the radial mass transfer in air segmented flow (10). In Figure 6 two classes of behavior are evident. For longer segments (curves b and c in Figure 6) k&d first rises rapidly as coil diameter is decreased and then tends to flatten out, whereas for the short segments (curve a) the rapid rise is preceded by a region in which kohd is nearly independent of
B
106
ANALYTICAL CHEMISTRY, VOL. 61, NO. 2, JANUARY 15, 1989
1.2
Table 111. Dependence of Extraction Rate Constant and Mass Transfer Coefficient on Segment Length in Straight and Tightly Coiled Extraction Tubes"
i
straight*
La,, mm
1.6 0.4#
n
1
/
2.8
7.9 I
0.0' 0.0
"
0.2
"
0.4
"
0.6
"
0.8
" 1.0
Figure 6. Observed extraction rate constant for various degrees of (b) 2.8 mm (+); coiling at different segment lengths: (a) 1.6 mm (0); (c) 7.9 mm (XI. Aqueous flow rate, 2.0 mL/min; organic flow rate, 2.0 mL/min; tubing diameter, 0.8 mm i.d.
coil diameter. The differences in behavior for the long and short segments in Figure 6 can be understood in terms of the two regions of the curve in Figure 5. In long segments, whose aspect ratio is greater than 3 (curves b and c in Figure 6), the mid-segment axial velocity distribution in a straight tube approaches the parabolic profile characteristic of Poiseuille flow, with the highest velocity along the center of the tube. When the tube is coiled the centrifugal force acts upon this flow in the same way that it does in single phase flow, generating a secondary flow which enhances the convective mixing in the segment and thus the mass transfer from it. However, while the intensity of the secondary flow continues to increase as the coil is made tighter (i.e. De2Sc a l/dc from eq l),the extraction rate constant increases more slowly so that plots of koW vs l/dc in Figure 6 tend to flatten out a t large l / d c values. This less-than-proportional dependence of koM on l/dc is reminiscent of the dependence of koW on the linear velocity, u. An increase in u increases the intensity of the toroidal circulation. In straight tubes, k o u was related to ua where a < 1. It might then be expected that in coiled tubes kobsd would also be related to (1/dJa. For example, for curve b in Figure 6 a plot of log kobd vs log (l/dc) had a slope, a,of 0.35 f 0.04. For the short 1.6-mm segments in straight tubing (l/dc = 0), there is considerable radial convective mixing within the segment due to the hydrodynamic interaction of the segment ends (15). This results in more rapid extraction than in the longer segments, as discussed above in the section Segment Length. The fact that there is a significant radial component of flow at all points along a short segment means that the axial flow profile is less parabolic in a short segment than in a long segment. Thus when the tubing is coiled, there is little velocity differential across the tube, and so consequently the centrifugal forces are more uniformly distributed across the tube. For the parabolic profile characteristic of homogeneous fluid flow, the secondary flow is well developed when De% is greater than lo4. I t might then be speculated that a much greater value of De2Scthan lo4 would be required for a well developed secondary flow to exist within the short segment. This would then account for the initial delay in curve a of Figure 6 in which the coiling had little effect on k o w A similar general behavior has been observed for the radial mass transfer in air segmented flow (10). In Table I11 are shown the rate constants and mass transfer coefficients for extraction within straight and tightly coiled tubing for the same experiments as shown in Figure 6. In order to examine the effect of coiling on the convective mass transfer, free of the influence of changing interfacial area, we will focus on the value of in Table 111. An important conclusion is that coiling produces a relatively greater enhance-
kobsd, 5.'
3, cm/s
0.39 f 0.04 0.0058 f 0.0005 0.22 f 0.03 0.0037 f 0.0005 0.16 f 0.01 0.0031 f 0.0002
-
tightly coiledc
kobd, s-'
3, cm/s
1.31 t 0.08
0.020 k 0.001
1.21 f 0.05
0.020 f 0.001
0.83 f 0.04d 0.015 f O.OOld
'Experimental conditions were as follows: Fa, 2.0 mL/min; F,, 2.0 mL/min; F,,,, F,,, 0.50-0.58; tubing diameter, 0.8 mm i.d.; linear velocity, 13.3 cm/s; sample, 5 X M caffeine in pH 4.0 citrate buffer; injection volume, 10 p L ; wavelength, 278 nm and absorbance range, 0.4 AU. *Data at l/dc = 0 in Figure 6. 'Refers to the portion of the curve after the rapid rise for each segment length in Figure 6; i.e. 11d, > 0.15 for 7.9-mm segments, l/d, > 0.6 for 2.8-mm segments and l/d, > 0.8 for 1.6-mm segments. The mean value of the points in this region are reported. dThe data point at lid, = 0.25 was excluded in calculating the mean on the basis of the Q test; Qob,d = 0.81, Qwn,n=4 = 0.76. ment of 3 for long segments than for short. For example 3 is increased about 5 times upon coiling for the 2.8- and 7.9-mm segments, but only about 3 times for the short 1.6-mm segment. This is a consequence of the reduced secondary flow in short segments resulting from the smaller velocity differential across the tube. These observations me similar to results reported for the radial mass transfer in air segmented flow (IO). In the studies by Nord et al. (9) on the rate of extraction in segmented flow, the segments were between 3 and 40 mm in length. For these long segments almost any curvature in the tubing would be sufficient to induce a strong secondary flow. Thus, in spite of the fact that the extent of coiling, d,, was not specified for their coiled extraction tube, it is clear that the data of Kord et al. should be interpreted in terms of the effects of both the toroidal and secondary flows. In this light, the influence of segment length on the extraction of bromocresol green which they observed (Figure 4 of ref 9) is analogous to the results shown in Table 111 for the tightly coiled tubing.
CONCLUSIONS The experiments reported here, in which both straight and coiled extraction tubes are used, have shown that the rate of extraction of solute from the aqueous into the organic phase in SE-FIA can be quantitatively understood in terms of the established principles of hydrodynamics. The results obtained herein allow a refinement of the guidelines given by Nord et al. (9) for experimentally increasing the rate of extraction in SE-FIA: (i) the extraction rate is increased by increasing the interfacial area to volume ratio which can be best accomplished by decreasing the tubing diameter; (ii) decreasing the segment length increases the extaction rate; (iii) increasing the linear velocity increases the extraction rate with respect to time, but in less than a linear way; (iv) tightening the coiling of the tubing increases the extraction rate with respect to time, in a much less than linear way and to a greater extent for long segments than for short, also for short segments, mild coiling conditions may have little effect on the extraction rate; (v) decreasing the linear velocity or increasing the coiling will increase the extraction rate based on the tube length. However, decreasing the linear velocity is not recommended since experimental studies (27, 33) have shown that the band broadening produced in the extraction coil can be overshadowed by that produced in the phase separator, injector, and detector. Since these components contribute a constant
Anal. Chem. 1989, 61, 107-114
volume variance, their effect is magnified when the flow rate (17) (18) is lowered (27). (19) In subsequent studies, employing a different measuring (20) technique, the relative magnitudes of PaqW and @aq,rau are (21) measured in a straight extraction tube (32). ACKNOWLEDGMENT Hubert Priebe of the Chemistry Department machine shop made the phase separator. The authors thank J. Masliyah for his helpful comments about the hydrodynamics. LITERATURE CITED (I) Valdrcel, M.; Luque de Castro, M. D. J . Chromatogr. 1987, 393. 3-23. (2) Cantwell, F. F.; Swelleh. J. A. Anal. Chem. 1985, 57, 329-331. (3) Fossey, L.; Cantwell, F. F. Anal. Chem. 1982, 5 4 , 1693-1697. (4) Swelleh, J. A.; Cantwell, F. F. Can. J . Chem. 1985, 83, 2559-2563. (5) Shelly, D. C.; Rossl, T. M.; Warner, I. M. Anal. Chem. 1982, 54, 87-91. (6) Persaud, G.; Xlu-mln, T.; Cantwell, F. F. Anal. Chem. 1987, 59, 2-7. (7) Nord, L.; Karlberg, B. Anal. Chlm. Acta 1984, 184, 233-249. (8) Mckstrom, K.; Danielsson, L.0.; Nord, L. Anal. Chim. Acta 1986, 187, 255-289. (9) Nord, L.; Mcksbom, K.; Danlelsson, L A . ; Ingman, F.; Karlberg, B. Anal. Chlrn. Acta 1987, 194, 221-223. ( I O ) Horvath, C.; Solomon, B. A.; Engasser. J.-M. Ind. fng.Chem. Fundam. 1973, 12, 431-439. (11) Snyder, L. R.; Alder, H. J. Anal. Chem. 1978, 48, 1017-1022. (12) Snyder. L. R.; Alder, H. J. Anal. Chem. 1976, 4 8 , 1022-1027. (13) Prothero, J.; Burton, A. C. Blophys. J . 1981, 1 , 565-579. (14) Duda, J. L.; Vrentas. J. S. J . Flu@ Mech. 1971, 45, 247-260. (15) Bugliarello, 0.; Hslao, 0. C. B(ome0lCgy 1970, 7 . 5-36. (16) Lew, H. S.; Fung. Y . C. Blorheology. 1969, 8 . 109-119.
(22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33)
107
Truesdell, L. C., Jr.; Alder, R. J. A I C M J . 1970, 18, 1010-1015. Tljssen, R. Anal. Chlm. Acta 1980, 114, 71-89. Cantwell, F. F.; Frelser, H. Anal. Chem. 1988, 80, 226-230. Danesl, P. R.; Chiarlrla, R. CRC Cdt. Rev. anal. Chem. 1986, 10, 1-128. Cussler, E. L. D/ffus/on. Mass transfer in f/& systems; Cambrldge University Press: New York, 1964 Chapters 9 and 11. Cussler, E. L. CMEMTECH 1986. 18, 422-425. Lo, T. C.; Balrd. M. H. I.; Hanson, C. Handbook of S o h n t EmcHon; Wlley: New York, 1983; Chapters 2.2 and 3. Borwankar, R. P.; Wasan, D. T. Ind. Eng. Chem. Fundam. 1986, 2 5 , 662-668. Pedersen, H.; Horvath, C. I d . Eng. Chem. Fundam. 1981, 20, 181-186. Karlbrg, B.: Thelander, S. Anal. Chlm. Acta 1978, 98, 1-7. Apffel, J. A.; Brlnkman, U. A. Th.; Frel, R. W. Chromatographle 1984, 18, 5-10. Davles, J. T.; Rideel, E. K. Intsrfaclel phenomena; Academic Press: New York. 1961; Chapter 7. Saylor, R. D.; Berman, J. Chem. Eng. Ccinnnm. 1987, 5 2 , 215-235. Luque de Castro, M. D. J . Autom. Chem. 1986, 8 , 56-62. Leo, A.; Hansch, C.; Elklns, D. Chem. Rev. 1971, 71, 525-616. Lucy, C. A.; Cantwell, F. F. Anal. Chem., following paper In thls Issue. Lucy, C. A.; Cantwell, F. F. Anal. Chem. 1986, 58. 2727-2731.
RECEIVED for review June 30, 1988. Accepted October 12, 1988. This work was supported by the Natural Sciences and Engineering Research Council of Canada and the University of Alberta. The postgraduate scholarship provided for C.A.L. by the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. Presented in part at the 3rd North American Chemical Congress, Toronto, Ontario, June 1988.
Mechanism of Extraction and Band Broadening in Solvent Extraction-Flow Injection Analysis Charles A. Lucy a n d Frederick F. Cantwell*
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
Studles were performed In an aqueous/chlorofonn segmented flow stream. The absorbance of each chloroform segment was measured as it passed through an on-tube photometer located at varlous dlstances along the Teflon extraction tube. Band broadenlng, studled by InJectlng iodine Into a single chloroform segment, Is Intermediate In magnitude between that predicted by uslng a mlxing chamber model and that predicted by assumlng only dlffuslonal mixing between the segments and the wettlngjilm of chloroform on the tube wail. Extraction from aqueous Into chloroform segments was studled by generating Iodine within a single aqueous segment uslng the “Iodine clock” reactlon. Application of a “successlvereaction” model to the axial extraction from the front of the aqueous segment reveals that, In straight tubes, solute extracts at the same rate per unit area across ail of the Interface, at both the segment ends and slde.
Studies of liquid-liquid segmented flow streams have established that extraction occurs across the interface at both the ends (axial extraction) and the side (radial extraction) of the aqueous segments (1-3). Experimental techniques that measure the total concentration of solute extracted as a function of time ( I , 2) permit a determination of the overall extraction rate constant, h a , which is the s u m of the products of the axial (@& and radial mass transfer coefficients
(ad)
0003-2700/69/0361-0107$0 1.50/0
times the respective ratios of interfacial area and segment volume (2)
Here ad is the combined interfacial area of the segment ends, asidsis the interfacial area of the side of the cylindrical aqueous segment, and V,, is the volume of the aqueous segment. In this work we consider only the practical analytical situation in which, at equilibrium, the solute is quantitatively extracted into the organic phase. While previous studies have permitted measurement of how,they have not addressed the relative magnitudes of the axial and radial extraction rates. In the present work this question is probed by using a solvent extraction-flow injection analysis (SE-FIA) system employing on-tube photometric detection and single segment injection. On-tube detectors have been used in studies of band broadening in air-water (4-6) and liquid-liquid (7)segmented flow, as well as in a routine fluorescence SE-FIA instrument (3). In an on-tube photometric detector the absorbance due to solute in individual segments is measured as the segments pass through the section of extraction tube in the detector. It is observed that solute in an aqueous segment extracts into the organic segment just ahead of it, as well as into the organic segment behind it. Once in the organic phase, the solute is dispersed backward (band broadened) into trailing 0 1969 American Chemlcal Society
