259
Ind. Eng. Chem. Res. 1991,30, 259-264 Q: carrier gas flow rate, m3/s qi: UNIFAC surface area parameter for group i
r; UNIFAC group volume parameter for group i s: floating value of transfer function, s-l V,: volume of gas in the column, m3 V,: volume of liquid in the column, m3 xH2: mole fraction ofHz in the liquid phase y H 2 : mole fraction of Hz in the gas phase ys: activity coefficient of hydrogen y ,*: activity coefficient of hydrogen at infinite dilution in the reference solvent t: root-mean-squareerror 7: mean residence time, s Registry No.
HZ,1333-74-0.
Literature Cited Antunes, C.; Tassios, D. Modified UNIFAC Model for the Prediction of Henry’s Constants. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 457-462. Fahim, M. A.; Wakao, N. Parameter Estimation from Tracer Response Measurements. Chem. Eng. J . 1982,25, 1-8. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria using UNIFAC; Elsevier: Amsterdam, 1977.
Hartounian, H.; Allen, D. T. Group Contribution Methods for Coal-Derived Liquids. Fuel 1988, 67, 1609-1614. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, A. On the Combinatorial Part of the UNIFAC and UNIQUAC Models. Can. J. Chem. Eng. 1980,58, 253-258. Mousa, A. H. N. Prediction of Henry’s Constant by Gas Chromatography. J . Chem. Eng. Jpn. 1984, 17, 206-208. Sander, B. 0.;Jorgensen, S. S.;Rasmussen, P. Gas Solubility Calculations. I. UNIFAC. Fluid Phase Equilib. 1983,11,105-125. Wilhelm, E. Precision Methods for the Determination of the Solubility of Gases in Liquids. CRC Crit. Rev. Anal. Chem. 1985,16 (2), 129-175.
Wilhelm, E. Dilute Solutions of Gases in Liquids. Fluid Phase Equilib. 1986, 27, 233-261. Wilhelm, E.; Battino, R. Thermodynamic Functions of the Solubilities of Gases in Liquids at 25 OC. Chem. Rev. 1973, 73, 1-9. Ying, H.; Yingnian, X.; Prausnitz, J. M. Molecular Thermodynamics of Gas Solubility (I) Henry’s Constants of Gases in Nonpolar Solvents. J. Chem. Ind. Eng. 1988, 3, 144-184. Yow, J.; Smith, J. M. Chromatographic Determination of Solubilities of Gases in Liquids. Lat. Am. J . Chem. Eng. Appl. Chem. 1983, 13, 185-197.
Received for review February 26, 1990 Revised manuscript received June 22, 1990 Accepted July 18, 1990
Low-Pressure Nitrogen Suspensions Terry
W.Motes,* Lawrence C.Faulkner, and Charles A. Hodge
Chemical Development Department, National Fertilizer & Environmental Research Center, Tennessee Valley Authority, Muscle Shoals, Alabama 35660-1010
High-analysis low-pressure nitrogen (LPN) suspensions can be produced by sparging gaseous ammonia into a urea-ammonium nitrate (UAN) solution and then adding fluid clay. LPN suspensions contain more inexpensive ammonia nitrogen and have about the same salt-out temperature as lower nitrogen content UAN solutions. LPN suspensions have higher nitrogen concentrations but vapor pressures comparable to low-pressure aqua ammonia solutions, as well as better suspending properties for cold blending with other fertilizer materials. The optimum composition of a 38% nitrogen LPN solution with a salt-out temperature of about 32 O F and a vapor pressure of about 5 lb/(in.2 g) at 104 O F is about 8% ammonia, with the remaining nitrogen being 48% urea nitrogen and 52% ammonium nitrate nitrogen. Different fertilizer grades of two- and three-component blends can be made by using LPN suspensions. Fertilizer blends with higher nitrogen content are most cost effective. Low-pressure aqua ammonia solution and urea-ammonium nitrate (UAN) solution fertilizers are widely used in the United States. Both products can be handled and applied by using conventional application equipment that is generally available to the farmer. Also, both products can be cold blended with other fertilizer materials, such as monoammonium phosphate (MAP) solution or suspension and potassium chloride, to produce custom-formulated NP or NPK fertilizers. However, cold blending with UAN solution or aqua ammonia usually requires addition of a suspending agent, such as attapulgite clay, during the cold-blending operation to keep the KC1 from settling out (Cole et al., 1984). Another disadvantage of these nitrogen solutions is that both must be limited in grade or nitrogen content to attain the desired salt-out temperature or vapor pressure. UAN solution generally contains 32% nitrogen with a specific ratio of urea to ammonium nitrate to control the physical properties of the solution such as the salt-out temperature. The salt-out temperature usually is controlled at about 32 O F . Lowpressure aqua ammonia solutions usually are limited in concentration to about 25% nitrogen so that the vapor pressure does not exceed about 5 1b/(inv2g) at 104 OF. Higher concentrated aqua ammonia solutions would have
higher vapor pressures, and specialized equipment would be required for storage, handling, and application. Low-pressure nitrogen (LPN) suspensions can be produced by sparging anhydrous ammonia into a UAN solution and adding fluid clay (attapulgite clay dispersed in water). A less dilute fluid clay can be made by using urea to make up to a 16-0-0-30C grade. The addition of ammonia to the UAN solution increases the nitrogen content, making a more concentrated product with a less expensive source of nitrogen, as compared to urea or ammonium nitrate (AN). The addition of ammonia also can maintain the salt-out temperature of the more concentrated product at about the same level as that of the lower grade 32-0-0 UAN solution. Fluid clay is best added after the ammonia because the sparging of a gas into a suspension reduces its viscosity (TVA, 1978). When making blends, the viscosity of a suspension needs to be high enough to keep added components such as KC1 suspended. LPN suspensions also have an advantage compared with aqua ammonia solution or UAN solution because LPN suspensions contain clay, which could eliminate the need for adding clay during cold blending with other fertilizer materials. Tests were conducted by NFERC researchers to evaluate production of LPN suspensions. First, tests were made
This article not subject to U S . Copyright. Published 1991 by the American Chemical Society
260 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 Table I. Storage Properties of UAN Suspension with Added Free Ammonia chemical anal., wt % viscosity a t sample N NH3 clay, wt % storage time, days 80 "F, CP 1 3.04 0.02 2 395 7 474 14 476 28 480 45 474 60 474 2 36.2 5.04 2 284 7 306 14 324 28 380 45 332 60 334 178 2 ~. 3 38.1 8.85 7 188 14 194 28 200 45 214 60 210 "Clear layer (14.3% by volume;
1/2
in.) on bottom. bClear layer (3.3% by volume;
1/8
gel strength, g cm 12.4 14.5" 12.8" 12.8" 13.3" 12.4" 10.4 8.4 8.3 8.7 7.5 8.4 6.7 5.8 5.96 6.2b 5.6* 6.1b
initial vapor pressure, lb/(in.* g) 70 "F 104 "F 0 0
0
4.9
2.1
11.1
in.) on top.
in which various amounts of ammonia were added to a UAN suspension to determine the effect of the added free ammonia on storage properties of a suspension. Then a series of statistically designed tests was conducted to determine the effects of composition on salt-out temperature, vapor pressure, and other physical properties of a LPN solution. Tests also included production and storage evaluations of NP and NPK grades made from LPN suspension, MAP suspension, and KCl.
Effects of Added Free Ammonia on Storage Properties of a Suspension Gaseous ammonia was sparged into a 31-0-0 UAN suspension to produce samples with various levels of free ammonia for evaluation. For the tests, eutectic 31-0-0 UAN suspensions were prepared from prilled urea, prilled ammonium nitrate, water, and fluid clay (30% clay dispersed in water). Three samples were then prepared from each of the UAN suspensions for evaluation. Sample 1 was the base UAN suspension (no ammonia added). Sample 2 had about 5% by weight ammonia added. Sample 3 had about 10% by weight ammonia added. All samples were formulated to contain 2% by weight attapulgite clay after ammonia addition. The resulting nitrogen and free ammonia contents of the samples as well as the viscosity, gel strength, and vapor pressure measurements are given in Table I. The viscosity, gel strength, and vapor pressure were measured initially. Each sample was then divided into 5 glass jars of approximately l-pt volume and sealed for viscosity and gel strength evaluations at the time intervals listed in Table I. The samples were stored at 80 OF. Viscosity measurements were made with a standard Brookfield viscometer. Gel strength measurements were made with a TVA gelometer (TVA, 1976). Vapor pressures were determined at 70 and 104 O F by using the test apparatus shown in Figure 1. To determine the vapor pressure, a 50-mL sample of each suspension was transferred to a 150-mL steel cylinder, which had been purged of air by flushing with ammonia. The sample in the cylinder was allowed to equilibrate overnight at both 70 and 104 O F in a temperature-controlled oven. The vapor pressure then was read directly from a gauge (i0.5lb/in.? mounted on the sample cylinder. Sparging ammonia into the UAN suspensions lowered the initial viscosities and gel strengths of the suspensions.
~~~
_
_
~
TEMPERATURE-CONTROLLED OVEN
Figure 1. Test apparatus for vapor pressure measurement.
However, the viscosities and gel strengths of the suspensions did not decrease with storage time, which indicates that the presence of free ammonia had no detrimental effect on the suspending properties of the clay. Also, the decreases in initial viscosities and gel strengths can be attributed to the turbulence or agitation of the suspension by the sparging action (TVA, 1978). For this reason, ammonia will be added to the solution and then clay will be added to make the suspension. This procedure will be used to make LPN suspensions for the remaining tests. Vapor pressures of the samples were higher at the higher level of addition of ammonia and at higher temperature, as would be expected. In general, all samples were in good condition after the 60-day storage period, with the exception of clear layers that formed in samples 1 and 3 as noted in the footnotes in Table I.
Optimum Composition of LPN Solution The best way to make a LPN suspension is to ammoniate a UAN solution, which contains urea and ammonium nitrate in the desired proportions, and then add fluid clay.
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 261 THERMOMETER
ACETONE DRY ICE BATH
Table 11. Experimental Design Data for Low-Pressure Nitrogen Solutions vapor pressure, ammonia, urea N,” salt-out l b / ( i r ~ g) ,~ wt% temp, O F 70 O F 104 O F test wt % 6.5 13.5 6.5 13.5 5.0 15.0 10.0 10.0 10.0 10.0 10.0 10.0
1
2 3 4 5 6
7 8 9 10 11 12
42.9 42.9 57.1 57.1 50.0 50.0 40.0 60.0 50.0 50.0 50.0 50.0
46.0 10.0 57.0 28.0 45.0 9.0 30.0 50.0 23.0 21.0 20.0 20.0
0.0 1.0 0.0 1.2 0.0 1.0 0.0 0.0 0.0 0.0 0.4 0.0
4.2 10.2 3.4 10.1 3.7 10.5 5.7 5.1 7.0 6.2 7.0 6.4
OPercentage of total of urea nitrogen and AN nitrogen. 60
3+ 3
56
a 52 3
MAGNETIC STIRRER
Figure 2. Test apparatus for salt-out temperature measurement.
Fluid clay can be dispersed with mild agitation in a LPN solution a t room temperature with little or no ammonia loss. Tests show that fluid clay acts as a diluent and has no significant effect on salt-out temperature or vapor pressure. Salt-out temperatures are more easily determined on solutions. A series of statistically designed tests was conducted to determine the optimum composition based on salt-out temperature and vapor pressure on a 38% LPN solution containing ammonia, urea, and ammonium nitrate. Twelve tests were made because of the requirements of the central composite experimental design (Deming and Morgan, 1987). Since UAN solution and ammonia are being used, the optimum composition of a 38% LPN solution should have the desirable quantities of each, namely a salt-out temperature similar to UAN-32, which is 32 OF, and a vapor pressure less than or similar to aqua ammonia, which is 5 lb/(in.* g) a t 104 OF. The tests were designed so that the ammonia content ranged from 5% to 15% by weight total solution weight. Of the remaining nitrogen, urea nitrogen ranged from 10% to 90% of the total and ammonium nitrate nitrogen made up the rest. The dependent variables were salt-out temperature and vapor pressures at 70 and 104 OF. Salt-out temperatures were measured by using the apparatus shown in Figure 2. The procedure was to cool the solution slowly and evenly, seeding with urea crystals, while visually observing the sample for any crystal growth. The temperature a t which crystals first appeared was recorded as the salt-out temperature. Vapor pressures were measured by the same method described previously. Contour plots (not shown) were generated for each of the dependent variables. Minimum points for the salt-out temperature and vapor pressures on the response surface of each plot were determined from either canonical or ridge analyses of the data. The minimum values occurred over essentially the entire range of the ammonia percentages (5-15%). However, the minimum values occurred only
8
E 5
48
544
I
40 5
7
9
11
13
15
AMMONIA, WT % OF TOTAL SOLUTION
Figure 3. Contour plot of salt-out temperature versus percent urea nitrogen and percent ammonia.
within a range of 42-55% urea nitrogen (as a percentage of urea nitrogen + AN nitrogen). Therefore, to more accurately predict the effects of these variables, the experimental design was repeated with the urea nitrogen percentage varied only from 40% to 60%. The ammonia percentage still ranged from 5% to 15%. The results are shown in Table 11. Results of the statistical analyses indicate that both the ammonia and urea nitrogen contents of the solutions have a significant effect on the salt-out temperature. Also, both linear and quadratic terms were significant. The crossproduct term was not significant, indicating that there was no synergistic effect between the ammonia and urea nitrogen contents. The salt-out temperature can be related to the ammonia and urea nitrogen contents as follows:
SO = 535.9 - 9.595A - 18.86U + 0.2739A2 + 0.1987U2, r2 = 0.98 (1) where SO is the salt-out temperature, O F , A is the ammonia content, wt %, and U is the urea nitrogen content, wt 9i urea N + AN N. This equation is represented as a contour plot in Figure 3. X represents the minimum point on the curve within the experimental test range. The salt-out temperature a t this point is 6.4 O F and occurs a t an ammonia content of 14.8% and at a urea nitrogen content of 47.2%. The overall minimum (salt-out temperature of 4.5
262 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 Table 111. NPK Blends from LPN Suspension (36.5-0-0,2% Clay) MAP Suspension (10-29.4-0, 2% Clay), and KCl (0-0-62) viscosity storage chemical anal.. wt % time, at 80 O F , nominalgrade N P20, K20 NH3 H20 clay, wt % days settling, vol 70 CP change, % 1.46 0 14-14-14 13.6 14.3 13.4 3.43 4.5 0 1022 7 0 1010 -1.17 14 0 926 -9.39 21 0 -8.41 936 28 0 -12.04 899 0 12-12-12 12.1 12.2 12.4 3.33 18.1 1.25 0 219 7 0 -8.08 202 14 0 -11.59 195 21 0 -6.12 206 28 0 -5.63 207 21.8 12.6 0 0 22-11-0 11.2 4.43 1.75 1007 7 0 -27.01 735 0 14 711 -29.39 0 21 719 -28.60 0 28 676 -32.87 17.8 0 18-9-0 9.4 3.60 28.5 1.34 0 221 7 0 168 -23.98 151 14 0 -31.67 0 21 137 -38.01 117 28 0 -47.06 7.7 3.22 0 16-8-8 15.8 8.3 23.5 1.27 0 223 7 0 -12.56 195 0 14 -17.94 183 0 21 -26.91 163 0 28 -31.39 153 21-7-0 20.7 7.2 25.2 0 3.90 1.50 0 312 7 0 -25.96 231 14 -24.68 0 235 21 0 -26.92 228 28 0 -32.69 210 18-6-0 17.9 6.1 3.36 35.9 1.28 0 0 133 7 99 -25.56 0 14 -27.07 0 97 21 0 96 -27.82 28 0 93 -30.08 21-7-7 20.6 7.2 6.4 3.79 13.9 1.50 0 0 543 7 0 -14.55 464 14 -16.21 0 455 21 0 419 -22.84 28 0 -24.68 409 15-5-5 14.7 5.6 3.17 5.2 38.5 1.07 0 0 72 7 -40.00 0 48 14 -42.02 0 47 21 0 53 -30.40 28 0 44 -48.28
O F ) occurs outside the experimental test range at about 18% ammonia nitrogen and 46.0% urea nitrogen. The regression analysis of the vapor pressures at 70 OF revealed little because most of the values were zero. Vapor pressures had positive values only at the higher levels of ammonia addition, which indicates that urea nitrogen content had no significant effect on the vapor pressure at 70 OF. The regression analysis of the vapor pressures at 104 O F indicated that the urea nitrogen content did not significantly affect the vapor pressure of the solutions but that the ammonia content did. It also revealed that the linear term was highly significant, whereas the quadratic term was not. On the basis of this, a least-squares linear regression was conducted on the data by using the ammonia content as the independent variable. The equation that resulted was as follows: VP = -1.299
+ 0.7924A,
r2 = 0.91
(2)
where V P is the vapor pressure at 104 OF, lb/(in.2 g), and A is the ammonia content, wt % . This equation is shown graphically in Figure 4. Results of this statistically designed test series indicate that the optimum composition for a 38% low-pressure
nitrogen solution with a salt-out temperature of 32 O F and a vapor pressure of 5 lb/(in.2 g) at 104 OF is about 8% ammonia, with the remaining nitrogen being about 48% urea nitrogen and 52% ammonium nitrate nitrogen. Higher ammonia contents lower the solution salt-out temperature but result in higher vapor pressure. Figures 3 and 4 can be used to determine a compromise between these conflicting properties to produce a suitable product based on the season and the area of the country in which the product is to be produced, used, and stored.
NPK Blends Several NP and NPK suspensions were prepared and stored at room temperature for 28 days to evaluate the use of LPN suspensions for cold blending with MAP suspension and potassium chloride. For these tests, it was assumed that a LPN suspension would be used in areas of the country where UAN-32 or aqua ammonia is used. Therefore, the LPN suspension used in these tests was prepared to have a salt-out temperature near that of UAN-32 (32 O F ) and a vapor pressure near that of typical aqua ammonia solution (about 5 lb/(in.* g) at 104 OF). By using data from Figures 3 and 4, a 38% nitrogen LPN solution was formulated to contain 8% free ammonia,
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 263 l2
L
/$.'$ '/
&I-
2
VAPOR PRESSURE
-1,299
r2= 0.91
0
+ 0.7294 (% N b )
-I
Table IV. Relative Cost Comparison for NPK Blends' nitrogen source UAN-31: LPN-36: ratio grade $/ton $/ton savings, $/ton 120.15 116.81 3.34 1:1:1 14-14-14 12-12-12 102.99 100.13 2.86 96.42 91.65 4.77 2:l:l 16-8-8 108.65 101.97 6.68 3:l:l 21-7-7 77.61 72.84 4.77 15-5-5 111.28 104.71 6.57 2:l:O 22-11-0 91.04 85.68 5.36 18-9-0 95.10 88.42 6.68 3:l:O 21-7-0 18-6-0 81.52 75.79 5.73 Raw material costs from; Green Markets; McGraw-Hill, Inc.: New York, Sept 1989. 32-0-0 UAN solution ($3.30/unit N), 105.60 $/ton; 10-30-0 MAP suspension (1.5% clay), 130.00 $/ton; 0-0-62 KC1, 120.00 $/ton; 83-0-0 ammonia, 130.00. *Cost estimated from components and ratio of component costs to TVA as of Sept 1989. 31-0-0 UAN suspension (2% clay), 107.56 $/ton; 36-0-0 LPN suspension (2% clay), 113.27 $/ton.
~
11 13 15 17 AMMONIA, WT % Figure 4. Effect of ammonia on vapor pressure at 104 O F , lb/(in.2 9). 5
7
9
with the remaining nitrogen being 48% urea nitrogen and 52% ammonium nitrate nitrogen (ratio of urea N to AN N of 0.92). A 16-0-0 fluid clay containing 30% by weight attapulgite clay was then prepared and blended with the 38-0-0 LPN solution. The resulting LPN suspension contained 36.5% nitrogen, 2% clay, and 7.4% free ammonia. The vapor pressure of the LPN suspension at room temperature was essentially zero and at 104 "F was 4.7 lb/(in.2 g). When the solution is diluted with fluid clay, the resulting vapor pressure appears to be decreased by the same proportion as the percentage of ammonia. Therefore, Figure 4 can also be used for a suspension made with 38% LPN solution. To prepare the NP and NPK blends, the LPN suspension was blended with MAP suspension (10.0-29.4-0 with 2% clay) and solution-grade KC1 (0-0-62). The materials were added in the following order: water, MAP suspension, LPN suspension, and KC1. The mixture was agitated for 10 min with a mechanical stirrer with a tip speed of about 15 ft/s. No ammonia fumes were detected during preparation of the blends at room temperature. The blends were stored at room temperature for 28 days and evaluated at weekly intervals. The grades produced and results of the storage tests are given in Table 111. All of the blends remained in good condition during the 28-day storage test. There was no settling in any of the samples. The more concentrated samples usually had higher viscosities, and the grades with the higher proportions of KC1 seem to hold their viscosities better. The other grades, as can be seen from Table 111,decreased from 25% to 48%, and most of those had dropped significantly after only 7 days. Overall, the storage properties of these blends produced by using LPN suspension were good. Some of the grades with higher viscosities can be made with LPN solution to achieve a lower viscosity. A 14-14-14 grade was made by using 38% LPN solution for a comparison of that grade made with 36.5% LPN suspension. The initial viscosity was 375 CPas compared with 1022 cP. After 28 days, the viscosity had only dropped about 9% to 340 cP, whereas the sample made with LPN suspension dropped 12% to 899 cP. The 14-14-14 grade made with LPN solution remained in good condition during the 28day storage test.
Economics of Using L P N Suspensions i n NPK Blends Table IV gives a comparison of the relative cost of blends produced with LPN suspension (36% N) and blends produced with 31-0-0 UAN suspension. As shown, the potential savings in using 36-0-0 LPN suspension depend on the nitrogen content of the NP or NPK blend. The savings, however, could be quite significant depending on the grade and quantities used. Process costs for adding ammonia should be minimal and were not estimated for that reason. Conclusions Free ammonia did not have a detrimental effect on the suspending properties of clay when less than 10% by weight ammonia was added to the UAN-31 suspension. However, sparging ammonia into the UAN suspension did lower the initial viscosity. As expected, the vapor pressures of the suspensions with added ammonia increased with an increase in temperature or ammonia content. Results of the experimental design to determine the optimum composition of a 38% LPN solution indicate that both ammonia and urea nitrogen contents have a significant effect on the salt-out temperature. A regression analysis of the vapor pressure data at 104 O F indicated that the urea nitrogen content did not significantly affect the vapor pressure of the LPN solution but that the ammonia content did. Data from this study can be used to determine the optimum composition of a LPN solution for making LPN suspensions depending on the salt-out temperature and vapor pressure requirements in the area or at the time the LPN suspensions are to be produced, used, and stored. Several different ratios and grades to two- and threecomponent blends made with LPN suspension, MAP suspension, and KCl were stored adequately for 28 days. Viscosities, in general, varied with concentration. A LPN suspension can be used instead of standard UAN nitrogens for a more cost-efficient two- or three-component blend. Savings are greater for blends with higher nitrogen content because of cheaper ammonia nitrogen. Literature Cited Cole, C. A.; Achorn, F. P.; Broder, M. F. Low Preseure Suspensions. Tennessee Valley Authority. Presented at the American Chemical Society Meeting, Philadelphia, PA, 1984.
Ind. Eng. Chem. Res. 1991, 30, 264-267
264
Deming, S. N.; Morgan, S. L. Data Handling in Science and Technology; Elsevier Science Publishing Company, Inc.: New York, 1987;Vol. 3, pp. 197-210. TVA. New Developments in Fertilizer Technology. Tennessee Valley Authority ( U S . ) Bul. Y-107,1976.
TVA. New Developments in Fertilizer Technology. Tennessee Valley Authority (U.S.) Bul. Y-136,1978.
Received for review March 26, 1990 Accepted July 19, 1990
Mass-Transfer Correlation for Flow over Cylindrical Microelectrodes David J. Earl, Harlan J. Kragt, Christopher W. Macosko, and H e n r y S . White* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
An annular electrochemical flow cell was designed in which electrolyte flow occurred longitudinally with respect to a cylindrical platinum microelectrode. Convective mass-transfer properties of the annular cell were determined by measurement of faradaic currents corresponding to the masstransfer-limited oxidation of ferrocyanide in water (Sc = 1390) and ferrocene in acetonitrile (Sc = 180). Measurements were made by using electrodes of 25-pm, 127-pm, and 1.0-mm diameter, by using a flow cell of 4%" diameter, and a t flow velocities corresponding to Reynolds numbers between 1and 900. The generalized mass-transfer correlation, based on the electrode diameter, was determined to be Shd = (0.342 f 0.008)Red1/2S~1/3. Introduction Electrochemical measurements based on forced convection have numerous applications in chemical analysis (Bard and Faulkner, 1980) and in hydrodynamic studies (Newman, 1973; Hannatty and Campbell, 1983). The magnitude of a faradaic current i, measured as a function of an applied potential, reflects the average molar flux of electrons to the surface
- 1- - (Ne) nFA which results in oxidation or reduction of an electroactive species. In eq 1, F is the Faraday constant, n is the equivalent number of electrons transferred per mole, and A is the electrode area. The faradaic current is also a measure of the mass-transfer flux of reactant to the surface. For example, the current corresponding to the oxidation of a soluble and chemically stable species, e.g., R + 0 + ne-, can be written as
where (NR) = k,(CRbUlk- C *q, k , is the average masstransfer coefficient, and CRbjkand CRSd are the bulk and surface concentrations of R, respectively. If the electrochemical system is reversible, i.e., if the electron-transfer kinetics at the surface are very rapid, the surface concentrations of 0 and R are described by the Nernst equation, E = Eo'+ (RT/nF) In (COsUrf/CRBU~ ( E O ' is the formal reaction potential), leaving k , as the only unknown parameter in eq 2. A t applied potentials sufficiently positive of E O ' , the surface concentration of the reduced species is driven essentially to zero. Thus, measurement of the faradaic current provides a direct method of obtaining k , for a particular electrode geometry and flow condition. This simple relationship provides an exquisitely simple method for establishing generalized mass-transfer correlations in complex geometrical systems. In this article, a set of electrochemical measurements based on eq 2 is used to establish the generalized masstransfer correlation for an annular flow cell, Figure 1. The key element of the cell is a cylindrical platinum microelectrode (diameter = 25 km, 127 pm, or 1 mm) oriented 0888-5885/91/2630-0264$02.50/0
along the central axis of a long glass tube that serves as the main body of the electrochemical cell. An electrolyte solution containing a soluble electroactive species is pumped through the cell at a specified flow rate, and the resulting current at the Pt wire is measured. Because the electrolyte flow is parallel to the working electrode, the resulting mass-transfer correlation obtained from measurement of current in the laminar flow regime is expected to have a similar form as that for laminar flow over a flat plate Shd = KRed1/zSC'/3 (3) Here, Shd is the Sherwood number (=k,d/Dab), K is an experimentally determined constant, Red is the Reynolds number (=u,,d/u), uav, is the average fluid velocity, u is the kinematic viscosity, Dab is the mass diffusivity of the electroactive species, Sc is the Schmidt number ( = v / o a b ) , and d is the characteristic length. For flow over a flat plate, K = 0.664 and d is the length of the plate. For the concentric annular geometry shown in Figure 1, K is anticipated to be significantly different than that for a flat plate due to (i) the enhanced radial flux of reactive species to the microcylindrical electrode and (ii) the development of the annular flow profile inside the annular cell. Mass-transfer correlations have been established by using cylindrical electrodes (Muller, 1947; Ranz, 1958) where electrolyte flow is orthogonal to the electrode axis. In addition, a theoretical investigation has been made (Sioda, 1989) of tubular flow perpendicular to a cylindrical electrode. However, this report is the first to characterize the configuration where flow through a tube is parallel to a cylindrical microelectrode. Heat-transfer correlations exist for longitudinal flow over a bed of cylinders (Axford, 1965) but, because they are obtained for fully developed mass-transportprofiles over bundles of large diameter rods, do not apply to the cell arrangement of Figure 1. Experimental Section Materials. The body of the cell was constructed from a l-m-long, 0.48-cm-i.d. Pyrex glass tube, Figure 1. The length and diameter of the tube were chosen in order to eliminate entrance and exit flow effects on the flow behavior of the test area at the middle of the cell. The glass cell was modified with ports to allow attachment of a 0 1991 American Chemical Society
