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Anal. Chem. 1885, 57,2155-2157
reference cell flow rates were equalized. Unless cells can be perfectly matched and mobile phase velocities can be exactly equal, complete cancellation is not expected. The dc signal is reduced by 23% when the reference cell was inserted in the optical path. Reflection losses at the surfaces of the second cell account for an attenuation of 15%. The remaining 8% is attributed to the change in beam shape and cancellation of the extra focusing caused by the cylindrical sample cell.
LITERATURE CITED (1) (2) (3) (4)
Leach, R. A.; Harris, J. M. J . Chromafogr. 1981, 278, 15-19. Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 54, 1174-1178. Buffett, C. E.; Morris, M. D. Anal. Chem. 1082, 54, 1824-1825. Buffett, C. E.; Morrls, M. D. Anal. Chem. 1983, 55,376-378.
(5) Sepaniak, M. J.; Vargo, J. D.; Kettler, C. N.; Maskarinec, M. P. Anal. Chem. 1984, 56, 1252-1257. (6) Pang, T.-K. J.; Morris, M. D. Anal. Chem. 1984, 56, 1467-1469. (7) Pang, T.-K. J.; Morris, M. D. Appl. Specfrosc. 1985, 39, 90-93. (8) Yang, Y.; Hairrell, R. E. Anal. Chem. 1084, 56,3002-3004. (9) Leach, R. A.; Harris, J. M. Anal. Chlm. Acta 1084, 164, 91-101. (101 Carter. C . A.: Harris. J. M. Anal. Chem. 1984. 56.922-925. iiij Y a n g , ’ ~Anal. . Chem. 1984, 56. 2336-2338. (12) Dovlchi, N. J.: Harris, J. M. Anal. Chem. 1981, 53,689-692. (13) Oda, S.; Sawada, T. Anal. Chem. 1081, 53,471-474. (14) Smith, R. C.; Baker K. S. Appl. Opt. 1081, 20, 177-184. (15) Dovichi, N. J.; Harris, J. M. Anal. Chem. 1080, 52,2338-2342. (16) Yarlv, Amnon, “Introduction to Optical Electronics”, 2nd ed.; Holt, Rinehart and Wlnston: New York, 1976; pp 18-28. (17) Betz, J. M.; Nikelly, J. G. J . Chromafogr. Sci. 1983, 27, 478-479.
RECEIVED for review March 28,1985. Accepted May 6,1985.
Volumetric Dilutor: Design and Testing of a Passive Mixer John R. Wallace* and Russell A. Nye Denver Research Institute, Chemical and Materials Sciences, 2390 South York Street, Denver, Colorado 80208 The dilution of gas samples is an important analytical operation. For example, a stable, concentrated gas standard may be kept in a pressurized bottle and then diluted immediately prior to use to a less stable dilute mixture. Similarly, prior to analysis, saturated gas samples from chemical or petroleum plants may require dilution to lower the dew point below ambient temperatures or to decrease the analyte concentration to within the dynamic range of the analyzer. In many such applications it is necessary to produce a continuously flowing, diluted stream in order to meet the requirements of the analyzers and to prevent sample loss. However, the dynamic dilution of a gas sample is not easily accomplished using typical gas metering equipment. The calibration of rotameters, mass flowmeters, critical orifices, and orifice plates all depend on the composition of the gas, which in the case of process streams is often unknown and variable. In addition, such devices often contain restricting orifices which can easily become clogged and fouled by condensable material or entrained particles, or components which are easily coorroded by reactive gases ( I , 2). One method to avoid such difficulties is to repeatedly inject a fixed volume of the unknown gas into a flowing diluent gas stream. This method is independent of the composition of the unknown gas and can be calibrated against primary gravimetric standards. The principal difficulty with this method, referred to here as volumetric dilution, is that each injection results in a sharp spike in concentration, followed by a period of zero concentration. Thus, a mixing chamber is required downstream from the injection to average the concentration. The difficulty that arises from such a mixing chamber is best illustrated with a specific example: Consider a vqlumetric dilutor consisting of a 10-L mixing chamber into hhich is injected 1.0 mL of sample ten times per minute along with 1.0 L min-l of diluent at a constant rate. In this example the dilution factor is 100, so that if the original sample contains 10% by volume of the analyte, the diluted sample contains an average of lo00 ppmv (parts per million by volume). With each injection, the concentration increases as a step function by 10 ppmv (Le., 1% relative) and then decays exponentially until the next injection (referred to here as “ripple”). If the concentration in the sample suddenly changes, the concentration in the flask responds exponentially with a time constant of 10 min-’. Forty-six minutes are thus required to achieve 99% of the change. This response time can be 0003-2700/85/0357-2 155$01.50/0
shortened by decreasing the volume of the flask, but at the cost of increasing the ripple. Increasing the injection frequency would decrease the ripple but is limited by the longevity of the valve and the pneumatics of injecting the sample. A single mixing chamber thus results in a generally unsatisfactory compromise between ripple, response time, valve longevity, and size. It is thus the purpose of this effort to design a mixing device with improved performance. As shown below, dramatic improvement can be achieved by simply dividing the mixing chamber into a series of subchambers.
THEORY Consider a chamber of total volume V divided into N subchambers of equal volume vi = V / N . The sample of mass m is injected instantaneously at time t = 0 into the first chamber along with the diluent (assumed incompressible) at constant volumetric rate Q. The gas mixture flows serially from one chamber to the next. For this arrangement the time evolution of the concentration in the last chamber is described as a function of reduced time, 9 = tQ/V = a t / N (3)
Equation 1 is normalized in the sense that
Equation 1 has a maximum at 0 = 1 - (l/iV), and as N becomes large, it approaches a Gaussian peak with standard deviation l/Wlz. Consider now a series of injections each of mass m occurring with period 6t, or in reduced time with a period 7 = 6tQ/ V. After n + 1 injections, the time can be expressed as 0 = n7 + 8‘, where 9’ is the time since the last injection. Then the concentration is given by summing eq 1,starting with the most recent injection. The result of this summation can be expressed as the variation about the average concentration, (C) = m/rV
where yi = N(0’ + i~). 0 1985 American Chemlcal Soclety
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
T I M E 1 REDUCED U N I T S 1
T I M E I R E D U C E D UNITS)
Flgure 1. Concentration in the last chamber resulting from a single injection at time = 0. The responses shown have been normalized such that the maximum concentration is unity.
Figure 3. Response of a serial diluter to a step change in input concentration. I
I
I
I
I
I
I
I Reduced U n i t s 1
Concentration variation as a function of the period and number of chambers.
Figure 2.
Equation 3 thus serves to calculate the ripple and response time as a function of N and 7. For sufficiently large 0 (e.g., 0 5 5), CN/ ( C ) becomes a periodic function which varies about unity. This ripple, AC, is defined here quantitatively as the difference between the maximum and minimum value of CN/(C) during one period for large values of 0. For smaller values of 0, eq 3 serves to calculate the response of the mixer to a step change in input concentration, say from 0 to 1.0 at time t = 0. Equations 1 through 3 were next used to calculate the expected behavior of a series of chambers. Figure 1 shows the concentration in the last chamber resulting from a single injection at time = 0. As can be seen, the resulting function gradually narrows and approaches a Gaussian shape with increasing N . With increasing N the function also tends to tail less. This means that when eq 3 is applied, the effect of an impulse occurring at t = 0 can be neglected for 0 > 5. Next, eq 3 was employed to calculate the ripple, AC, as a function of N and T. For this purpose CN/ (C) was determined numerically for one period for 0 1 5, and the difference between the largest and smallest value of CN/( C ) was plotted vs. the period, 7 (Figure 2). One might expect intuitively that the ripple should increase as the individual injections become
TIME ( m i n u t e s )
Flgure 4. Experimental response of a five-chamber serial mixer to a
step change in Input Concentration.
more spiked (Figure 1). However, quite the opposite is found. Increasing the number of chambers above one at first decreases the minimum injection frequency needed to achieve a certain minimum AC. Thus, to achieve a ripple of 51% with a single chamber requires T I 0.01. For the same ripple with N = 3, T can be as large as 0.3. For values of N 2 8, ripple gradually increases, as illustrated by the line for N = 19 in Figure 2. Although not shown in the figure, with increasing N ( N > 20) the plots become increasingly vertical and move gradually to the left. For N > 20, a rule of thumb is that AC I1% for T < 1.5/Nl2. In summary, the data in Figure 2 suggest that 5-20 chambers is optimum. Figure 3 shows the response of a serial mixer for a step change in input concentration. The data in this figure were calculated from eq 3 by assuming a step increase in input concentration at r = 0. Strictly speaking, the response is a function of both T and N . However, for values of T less than those shown, the effect of varying T was negligible. As expected, response time shortens with increasing N . Thus, the reduced time for 99% response is 4.6, 3.0, 2.0, and 1.5 for N = 1, 2, 5, and 19, respectively. Increasing N over 19 results in diminishing returns. With larger N , the response
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Anal. Chem. 1985, 57, 2157-2159 gC VALVE WITH 0.25yl INJECTION VOLUME
n
/
VENT
SAMPLE COLUMN, loom*, 6 PLATES CARRIER GAS
m
DILUTED
OILUENT
( I O Ipml
Flgurs 5. Proposed volumetric dilutor capable of dilution factor of IO', instantaneous response, and 0.1 % ripple.
time gradually approaches 1.0.
COMPARISON TO EXPERIMENT A five-section serial mixer was prepared from a 1.5411. stainless steel pipe (51 mm i.d.) capped at each end and containing four equally spaced plates. Each plate w a drilled ~ with two 0.031-in. holes to permit the gas to pass from one chamber to the next but otherwise sealed each chamber. Total internal volume was 677 cm3. Air entered through one cap at a constant flow of 677 cm3min-', and diluted sample exited from the other cap. Gaseous NH3 was injected into a slipstream of the inlet air in 0.10-mL aliquots using a Valco 10-port valve. The diluted NH3 was detected by its UV absorption at 201.6 nm in a 1-cm cell with a Cary 219 spectrophotometer. Constant pressure was maintained in the cell with an external water column.
RESULTS AND DISCUSSION Ripple measurement for this serial mixer was in excellent agreement with theory. For example, for r = 0.2,0.4, and 0.5, AC was < 0.5%,0.9%, and 2.1 %, respectively; these values are essentially identical with those presented in Figure 2. Similar results were obtained with another five-chamber mixer which had been tested earlier. Figure 4 shows the calculated and measured response to a series of injections starting at t = 0. As can be seen, the
actual response is considerably slower than the calculated response. This discrepancy is likely due to incomplete and noninstantaneous mixing in each chamber, a problem which would presumably be solved by a different chamber design. (A previous mixer design demonstrated faster response but slightly poorer ripple.) Nevertheless, the response shown in Figure 4 is at least an order of magnitude faster than a single chamber mixer with the same level of ripple. A series of standards of NH3 in air was prepared covering the range 380 to 3800 ppmv (parts per million by volume) calculated from the injection volume and frequency. The resulting calibration curve appeared entirely linear under visual inspection, supporting the efficacy of this method. Accurate dynamic standards of reactive gases in this concentration range are otherwise difficult to prepare, requiring flowmeters calibrated for the individual gas of interest. In summary, the performance of a mixing volume is improved dramatically by dividing it into a series of equal subvolumes. Five to 20 divisions is optimum in terms of minimizing concentration ripple and response time. Such a serial mixer makes practical the operation of a volumetric gas dilutor based on the periodic injection of a known volume into a constantly flowing diluent. The minimum dilution factor for such an apparatus is determined by the volume of diluent needed to sweep the injection volume and should correspond roughly to 3. On the other hand, a dilution factor of lo7 should be readily achievable by using the device shown in Figure 5. Here a standard gas chromatographic valve injects 0.25 pL of pure gas four times per minute into a carrier gas ffowing at 10 cm3 min-'. Pulses are averaged in a 10-cm3column containing five plates, followed by dilution with 10 L min-l. If the sample is a pure gas, the resulting diluted gas is 0.10 ppmv with a ripple of 0.1%.
LITERATURE CITED (1) Nelson, Gary 0. "ControlledTest Atmospheres"; Ann Arbor Science: Ann Arbor. MI. 1971. (2) "Instruction Manual for Mass Flow Controllers"; 1984, Tylan Corp.: Carson, CA, 1984. (3) Levenspiel, Octave "Chemlcal Reactlon Engineering"; Wlley: New York, 1962; p 282.
RECEIVED for review January 14, 1985. Accepted April 18, 1985. This work was sponsored by the US.Department of Energy under Contract DE-AS20-82LC10845.
Robust, Low Contamination Centrifugal Filter for Trace Analysis J. B. F. Lloyd Home Office Forensic Science Laboratory, Priory House, Gooch Street North, Birmingham B5 SQQ, United Kingdom In the recovery of small liquid volumes from solid materials by filtration or centrifugation a significant portion of liquid may be entrained and lost either in the separated solid or in the filter. Recoveries are much improved by centrifugal microfiltration. Various techniques have been described. For example, for very small samples the filtration may be conducted in adapted capillary tubes (2). For larger samples a separate filter may be supported within a centrifuge tube (2), or a centrifuge tube supporting a second tube the apex of which is pierced and plugged with silica wool (3) can be employed. A convenient device for use with microporous membranes is commercially available from Bioanalytical Systems, Inc. (BAS), West Lafayette, IN (part no. MF-5500). This has been used, for example, in the processing of handswab extracts
for the detection of firearms propellants traces (4) and high explosive traces (5)by high-performance liquid chromatography and, in a modified form, in the determination of organomercury cations (6). In the explosives technique (5) sample contamination can arise from the silicone washer with which the filter is fitted. The contamination interferes only weakly in liquid chromatograms detected electrochemiallyin the reductive mode, but is prominent in the oxidative mode, and interferes considerably in gas chromatograms run with electron capture detection (7). In the latter case the washer was dispensed with, but under this condition there is a possibility of leakage of the filter. Attempts to remove the Contamination by solvent extraction have proved only partially successful. Several other
0003-2700/85/0357-2157$01.50/0Published 1985 by the American Chemical Soclety
