solvent mixtures are used, the depth of immersion of the capillary of the burner into the test solution appears t o be critical. It is recommended that the emission readings be taken within the time interval of 10 to 15 seconds after initiation of aspiration and that the beaker which contains the test solution be refilled to the original level before a reading is repeated. Of the solvent mixtures tested, 1,4 dioxane-water (1 to 1 by volume) provided the most reproducible flame conditions. Although the enhancement achieved is less than that obtained with acetone-water or methanol-water in similar volume ratios, slight variation in the volume ratio of 1,4-dioxanewater is not as critical. Higher volume ratios of organic solvent to water provide larger enhancements, but the solvent composition is very critical because of the steep slope of the curve showing the emission intensity us. sol-
vent composition; also the consumption of the test solution is very rapid. ACKNOWLEDGMENT
The authors acknowledge the assistance of Helen P. Raaen in the preparation of this paper. LITERATURE CITED
rem, L. H., “SpectrochemicalAnalp. 78, Addison-Wesley, Cambridge, Mass., 1950. (2) Baker, G. L., Johnson, L. H., ANAL. CHEM.26,465 (1954). (3) Curtis, G. W., Knauer, H . E., Hunter, L. E., Am. SOC. Testzng Materials, Spec. Tech. Publ. No. 116, 67 (1951). (4) Dean, J. A., “Flame Photometry,” Chap. 14, McGraw-Hill, New York, 1mn. -I--. (5) Ibid., p. 211. (6) Dean, J. A., Burger, J. C., ANAL. CHEM.27,1052 (1955). (7) Foster, W. H., Jr., Hume, D. N., Ibad., 31,2033 (1959). (8) Gaydon, A . G., “Dissociation Energies
“ks$’
and Spectra of Diatomic Molecules,” 2nd ed., pp. 201-3, Chapman & Hall, London, 1953. (9) Hinsvark, 0. N., Wittmer, S. H., Sell, H. M., ANAL, CHEM.25, 320
(1953). (10) Kelley, M. T., Fisher, D. J., JoneB, H. C., Ibid., 31, 178 (1959). (11) Lundegardh, H., Lantbruks-Hoqskol. Ann. 3, 49 (1936). (12) Mavrodineanu, R., Boiteux, H.,
ILL’AnalyseSpectrale Quantitative z a r la Flamme,” Chap. 14, Masson et le, Paris, 1954. (13) Menis, O., Rains, T. C., ANAL. CHEM.32, 1837 (1960). (14) Shaw, W. M., Ibid., 30, 1682 (1958). (15) Watanabe, H., Kendall, K. K., Jr., A p p l . Spectroscopy 9, 132 (1955).
RECEIVEDfor review May 25, 1961. Accepted August 11, 1961. Taken in part from a portion of a dissertation submitted by J. C. Burger t o the Graduate School of the University of Tennessee in partial fiilfillment of the requirements for the degree of doctor of philosophy. Presented at Pittsburgh conference on Analytical Chemistry and ilpplied Spectroscopy, March 1957.
Quantitative Study of Factors Influencing Sample Flow Rate in Flame Photometry J.
D. WINEFORDNER and
H. W. LATZ
University o f Florida, Gainesville, Flu.
A variation in solution flow rate during flame photometric analysis produces a change not only in metal atom concentration in the flame but also in flame temperature which will result in a change in population of the excited energy levels. Therefore ,it is desirable to know the factors affecting flow rate and the extent of their effect. Flow rates of various liquids through total consumption atomizer burners are studied in relation to viscosity, surface tension, density, temperature, ionic strength, capillary radius, atomizing gas flow, fuel gas flow, and driving force. It was found that flow rate is mainly dependent on viscosity, the driving force, and the capillary dimensions. A smaller effect has been attributed to solution composition that results in slipping and turbulence during flow, Although the main factors affecting flow rate are those used in the Poiseuille equation for capillary flow, obedience to this equation was found only for high viscosity liquids with low flow rates. Sources of error due to variation in solution flow rate are discussed on the basis of this study.
F
LAME photometry is widely used for the rapid and accurate determination of trace quantities of sodium,
potassium, calcium, and magnesium. The accuracy, however, is greatly dependent on a number of experimental variables that influence the photometric response. The ultimate instrumental measurement which is related to the concentration of the salt in the sample of concern depends upon the method of sample introduction into the flame source, the dispersion of sample solution droplets, the evaporation of any water of solvation to produce a dry salt mist, the dissociation of the salt particles t o produce metal atoms and nonmetal atoms, the excitation of the metal atoms by means of the thermal energy of the flame source, and the emission of radiation as the excited metal atoms drop back to a lower level. The spectral response is indeed related to the number of excited metal atoms per unit volume of flame gases and therefore related to the metal atom concentration in the lower (usually the ground) state, which is related to the metal atom concentration in the original sample solution. This relationship is dependent on any equilibria involving the metal atoms in the flame gases, on the self-absorption of the emitted radiation by the cool atomic vapors surrounding the flame, on collisional losses of energy, and on other broadening phenomena. A number of papers (3, 6, 9, 14, 16), theses (1, 8 ) , and books (7, 10, 13) have
considered several of the above-mentioned variables in relation to spectral intensity (actually photometric response). However, in view of the large number and complexity of the variables, it is extremely difficult and usually meaningless to study the effect of one variable on photometric response, since the latter may be dependent on several other variables which are also changing. This paper concerns the quantitative study of the factors affecting one variable-sample introduction into the flame. Changes in sample flow rate into a flame will directly affect the flame photometric response. The most frequent errors in flame photometric analyses probably occur as a result of changes in sample flow rate which are due to changes in sample composition and/or atomizer characteristics. I n this paper the variations of solution properties, atomizer characteristics, and atomizing gas pressure are studied for total consumption atomizers to determine their effect on sample flow rate. The results are analyzed in terms of the effect of each factor on sample flow rate. It is shown that the simple Poiseuille equation for flow or the usual modification of the Poiseuille equation does not accurately or adequately describe the type of flow which occurs in atomizer capillaries used in flame photometry. VOL. 33, NO. 12, NOVEMBER 1961
1727
I0
-
0
CAPILLARY N o 405O(rmallI CAPILLARY N o 4 0 6 0 ( l a r g i l
a
7: 2
0
7 %I . O O c r n t w i r c
00 ernl~poisre
? = 0.60 contipoire
7: 0.32 centipoise 8 -
01 4
8 12 O X Y G E N PRESSURE ( p s i 1
16
1
Figure 1. Pressure differential as a function of oxygen pressure THEORY
General Discussion of Capillary Flow. The sample solution is introduced into a flame using the Beckman total consumption atomizer burner by allowing oxygen t o flow rapidly past the capillary tip. The pressure differential created allows atmospheric pressure to force solution from a sample beaker through the capillary and into the flame, where i t is atomized by the oxygen stream. Thus we are dealing with capillary flow, and the question arises as to whether the Poiseuille equation for capillary flow is applicable. The Poiseuille equation states that the rate of flow, &, is directly proportional to the fourth power of the capillary radius, R, and the driving force, P; and inversely proportional to the liquid coefficient of viscosity, 7, and the capillary length, L.
Bingham (5) has pointed out a number of ways in which energy is used in creating capillary flow: 1. Overcoming viscous resistance 2. Creating kinetic energy 3. Creating distortion of streamline flow 4. Producing turbulence 5. Producing slipping a t the capillary walls 6. Producing irregularities which arise from temperature changes
Kormally, factors 4, 5, and 6 are made negligible by regulation of flow conditions. The requirements are accurate temperature control, low fluid velocity, and smooth entry and exit of the liquid to prevent turbulence and 1728
a
ANALYTICAL CHEMISTRY
SOLUTION
FLOW
RATE (ml/rninl
Figure 2. Influence of atomizer capillary radius on flow rate a t various solution viscosities
slipping in the tube. The kinetic energy and end effects are sometimes corrected for in accurate viscometry work (2, 11) and the following equation results: rR4P v = - -8QL -
mpQ
8nL
where p is the density of the liquid and m is a capillary constant. The application of this equation to viscosity measurements is satisfactory, providing that experimental conditions are proper, as stated above. If this is not the case, factors 4, 5, and 6 are no longer negligible. The necessity for temperature control is obvious, since liquid viscosity is highly sensitive to temperature variation, as is density. In addition, the use of metal capillaries introduces the possibility of change in capillary dimensions due to temperature variation. The assumption that there is no slip between a flowing fluid and the walls of a capillary tube mas taken for granted by early workers studying capillary flow. Kevertheless it was the subject of much research, and it was shown by Helmholtz that, if slipping actually occurs, R4 in the Poiseuille equation must be replaced by the term (R4
+ 4;
Ra)
where B is the coefficient of sliding friction. The early literature concerning slip was reviewed by Bingham
(4). Later work by Tammann and Hinnuber (16) and Traube and Whang (17) attempted t o establish the existence of slipping, but their conclusions have been questioned on the basis of their experimental methods. Present-day thinking attributes small or negligible effects to slipping where flow is laminar and relatively slow, but its effect in more complicated flow systems with turbulence and high flow velocity is open to speculation. The increase of fluid flow rate eventually results in turbulent flow in which energy is consumed in the production of eddies. For the purposes of this paper i t should be sufficient to point out that turbulent flow exists when the so-called Reynolds number, Re, is exceeded. Re
v
=
Vpd
-
where is the fluid velocity, is the density, 7 is the viscosity coefficient, and d is the capillary diameter. A value of 2000 has been determined esperimentally (12) as the critical number, above which turbulent flow is predominant. It is important to realize, however, that the transition from laminar to turbulent flow is not an abrupt one and that turbulent forces external t o the capillary can be transmitted to the fluid flowing through the capillary. Flame Photometric Conditions. The flow conditions resulting from
I
/ 0
e 0
C 0
/ CAPILLARY N o . 4 0 6 0 (lorpel C A P I L L A R Y N o . 4 0 2 0 (medium1 CAPILLARY N o . 4 0 5 0 (small1 /
/
/
,’6
G L Y C E R O L - WATER
SOLUTIONS
P U R E ORGANIC LIQUIDS
/
1 I : -
C A P I L L A R Y No 4 0 6 0 ( l a r g e )
- -
C A P I L L A R Y No 4 0 5 0 (small1
\
-
C A P I L L A R Y N o . 4 0 2 0 (medium)
6’
/
/
d
I i
I
e
‘\
I
\
0 5 4
Figure 3. flow rate
8
12
OXYGEN
PRESSURE
16
Figure 4.
(001
Influence of oxygen pressure on solution
t h e u s e of a t o t a l c o n s u m p t i o n atomizer burner for flame photometric analyses deviate greatly from the conditions necessary for accurate application of the Poiseuille equation. Temperature control to the degree required is impractical. and heating by the flame and the cooling flow of liquid and gas are present as opposing factors. The driving force, P , becomes complex, since it is a function of the flow system itself. Flow rates of both the solution and atomizing gas are rapid and the latter definitely produces tip turbulence in order to accomplish dispersion of the liquid in the flame. Also the entry of solution into the capillary is abrupt. Therefore, it is doubtful that capillary flow in a total consumption atomizer is adequately described by the Poiseuille equation. Because of the extreme conditions, turbulence and perhaps slipping are believed to contribute to the relationship between flow rate and the factors of viscosity, driving force, and capillary dimensions. EXPERIMENTAL
Apparatus. A Beckman KO.9200 flame attachment was used in conjunction with Beckman total consumption atomizer burners. The choice of total consumption-type burners was dictated by their more widespread use in flame photometers as compared to reflux or chambertype atomizers. The Beckman burners used lvew the hydrogen-
oxygen No. 4050 small bore capillary, No. 4020 medium bore capillary, and No. 4060 large bore capillary. Each atomizer burner used differed in tip geometry (spatial and angular relationship of the capillary tip to the oxygen orifice and burner housing). The flow rate of oxygen and hydrogen was measured with two precision-bore rotameters (Ace Glass Co.). The sample flow rates were measured by timing the atomization of known volumes of solution from standard glass cuvettes. Preparation of Solutions and Experimental Measurements. Glycerol-water solutions ranging from 5 t o 40% by weight in 5% increments and ethanol-water solutions ranging from 10 to loo’% in 10% increments were prepared. Sterox AJ (AmicaBurnett Chemical Co.), a nonionic surface active agent, was used t o vary the surface tension of a 10% glycerol solution while maintaining a constant viscosity and density. Viscosities were measured by means of an Ostwald viscometer thermostated a t the desired temperatures. Surface tensions were measured directly with a Du Nuoy tensiometer (Central Scientific Co.). The lengths of the capillaries in the burners were measured directly with the use of calipers. The capillary diameters were measured by three independent methods: insertion of calibrated wires, direct measurement by an optical micrometer] and a flow rate method based on Poiseuille’s equation. An attempt was made to measure P , the driving force, by connecting a mercury manometer to the bottom of the capillary and reading the
10 VISCOSITY
15
2 0
2 5
(cmflpoirer)
Influence of viscosity on solution flow rate pressure differential with the flame both on and off, Procedure. Flow rates were measured a t ambient temperature, and the solution temperatures were recorded to the nearest 0.1” C. just prior t o pipet delivery into the cuvette. Flow times for all solutions run were taken three times in succession, and for deviations greater than 1% the capillary was rinsed thofoughly, wire-cleaned, and rinsed again. Acetone rinses were used for the organics, followed by distilled water, and distilled water only for aqueous solutions. The oxygen and hydrogen flow rates were maintained constant at all times, except when these factors themselves were being investigated. RESULTS
Capillary Geometry Measurements. The capillary radii measured using the flow and optical methods were: No. 4050, 0.121 mm.; No. 4020, 0.174 mm.; and No. 4060,0.222 mm. The wire insertion method gave slightly smaller radii, as expected. The capillary lengths were found to be approximately 5.60 em. for each atomizer. Solution Property Measurements. The solution viscosities a t specific temperatures for the glycerol-water, ethanol-water, and pure organic liquids were taken from viscositytemperature plots constructed from data given by Lange (12). Pressure Differential Measurements. The pressure differential measurements as a function of oxygen pressvre only (no hydrogen flowing) for the three standard burners are VOL 33, NO. 12, NOVEMBER 1961
1729
-
-
c
CAPILLARY
No 4020
0
CAPILLARY
NO 4020-
e
THEORETICAL
--
--
ORGANIC
f'amc
0 ETHANOL
on
ETHANOL
flame off
CURVE
0
GLYCEROL
c
SOLUTIONS
/
3.0
50°/0
-_
CAPILLARY Yo4060
>
50%
___
CAPILLARY N o 4 0 2 0
SOLUTIONS ORGANICS
GLYCEROL
AND
LIQJIDS
(
-
- -CAPILLARY
Wo4050
'\, \
\ \ \ b,
\
I
\
E
>E
-
\ 2.0.
W + 4
U
b L
z
2
I-
; 1.0' 0 In
0
0.
I
,
L
I
2
,3
F L U I D I T Y , I/V
d
(cenlipoisis-')
Figure 5. Flow curve for glycerol solutions and organic liquids
Figure 6.
Medium bore atomizer capillary
presented in Figure 1. It was experimentally observed that hydrogen gas flow a t a hydrogen gas pressure of 1.0 p.s.i. decreased the pressure differential due to oxygen flow alone by a small amount. The decrease was within experimental error, however, and did not become larger with increasing hydrogen pressure or with ignition. Flow Rate Measurements. The effect of hydrostatic head in the sample cuvette was shown to be negligible by timing the flow of increasing volumes of the same sample solution. The flow rates for 1.00 and 4.00 ml. of a sample solution (aqueousorganic or pure organic liquid) were identical. The influence of capillary radius on flow rate is presented in Figure 2, in which flow rate a t specific viscosities is plotted as a function of R4. The flow rates of 10% glycerol-water solutions were independent of surface tension over the range of 30 to 73 dynes per sq. cm. The effect of ionic strength was studied by timing the flow of CuClz solutions a t various concentrations. Flow rate was independent of ionic strength below a value of 0.1. Above this value, solution flow rates varied only as a result of viscosity variation. The variation in solution flow rate for each of the three standard atomizer capillaries due to the changing of the 1730
ANALYTICAL CHEMISTRY
2
I
VISCOSITY
atomizing gas (oxygen) pressure is shown in Figure 3. The effect of viscosity on flow was studied over a wide range of viscosities using the glycerol-water, ethanol-water, and pure organic systems previously mentioned. Figure 4 presents the viscosity-flow relationship with points for both the glycerol-water solutions and the organics. The distinction between them should be noted. Even though the organic liquids differ considerably in surface tension and density, it has already been shown from surface tension and hydrostatic head studies that these parameters have no significant influence on solution flow rate. The two curves for the medium bore capillary represent different oxygen pressures but identical oxygen flow rates. A plot of flow rate us. the reciprocal of viscosity (for capillary No. 4020, medium bore) is presented in Figure 5, with the difference between organics and water solutions being shown again. Points have been plotted for solutions atomized into an ignited Oz/Hz flame and for solutions atomized with only oxygen flowing and no flame. A theoretical curve (from Poiseuille's law) is also shown. Similar curves were obtained for the other capillaries. No significant differences in the flow curves resulted when the flame was on or off, except for the large bore capillary which showed a small difference for the low viscosity organics.
(centipoiser)
Flow curves for alcohol solutions
Solutions of alcohol i n u-ater exhibit an increasing viscosity up to a concentration of 50% by weight, and for higher concentrations of ethanol the viscosity decreases. On the basis of the Poiseuille equation, the viscosity-flow curves for these solutions ranging from 10 to 100% ethanol should retrace themselves. This is not the case, as indicated for all three atomizer Capillaries in Figure 6. In Figure 6 the half dots represent the glyccrol-organic curve for the medium bore atomizer capillary (4020). The solutions containing less than 50% ethanol follow the glycerol solution curve, whereas the more concentrated solutions essentially follow the pure organic curve. This same phenomenon was found for all the atomizer capillaries used. DISCUSSION
OF
RESULTS
The pressure differential measurements were carried out to enable the calculation of theoretical flow rates for the various capillaries on the basis of the Poiseuille equation. However, there is no assurance that the values obtained are comparable to the driving force that prevails during atomization of a liquid through the atomizer capillary in question. In addition, the error in measurement amounted to as much as 5y0. The theoretical curve of solution flow rate us. fluidity for the medium bore capillary is illustrated in Figure 5. There is a definite indication that a t the higher viscosities and correspondingly
lower flow rates the experimental data are in agreement with the Poiseuille equation within the limits of experimental error. Similar results were also obtained for the large bore capillary, but no comparison iyas made for the small bore capillary, since the method of pressure differential measurement was inadequate in that case. A t an oxygen pressure of approximatrly 10 p s i . for the medium bore as well as the large and small bore burners, the driving force is approximately 70,000 dynes per sq. em. based on the measured pressure differential. I t is not surprising then that no variation in flow rate due t o hydrostatic head or surface tension was observed because of the capillary end effect -Le., the energy required to break the droplets away from the capillary tip. The hydrostatic head can contribute less than 0.7y0 to the driving force a t most, and the surface tension requirements would be less than 0.01%. The effect of these two parameters on capillary length is also found to be negligible when the time required for capillary rise to occur is compared to the flow velocity. Thus the effective length of the capillary is approximately the actual length. The kinetic energy and end effect corrections for the Poiseuille equation Since amount to less than 0.1%. experimental error of flow rate measurements was approximately lyo,it was not necessary to correct for these two minor effects. The results have shown that the flow curves for the different size capillaries do not parallel each other, as would be expected if the flow were a function of the fourth power of the radius as predicted by the Poiscuille equation. From Figure 2, it is apparent that a linear relation between R4 and flow is obtained only with high viscosities (greater than 2 centipoises). Figure 2 indicates deviation from linearity for flow rates greater than 2 ml. per minute when atomizing liquids of viscosities less than 1 cp. This probably indicates the presence of turbulence. The prcsence of turbulence in flow is usually indicated by a Reynolds number (see theory section) larger than 2000. However, the area of transition from laminar to turbulent flow is very hazy and could possibly begin a t much lower valurs. Table I gives Reynolds numbers for several of the liquids investigated, along with corresponding flow rates and velocities. The Reynolds number for the capillary flow of organic liquids of low viscosity is approaching the critical value. Liquids such as acetone, benzene, etc., n-hen atomized from large bore capillaries a t standard pressures, may be in the region of t'urbulence. However, even if the solution flow is not turbulent cvithin the capillary, it is certainly turbulent upon leaving the tip. This is
Table 1.
Reynolds Numbers for Various Liquids
Flow ReynRate, Velocity, old8 Ml./Min. Cm./Sec. No. A. Small Bore Capillary 1.93 73 hcetone 1.20 45 Benzene 0.83 31 570 glycerol 0.40 15 35% glycerol 0.34 13 1-Butanol B. Medium Bore Capillary Acetone 5.66 100 Benzene 3.75 67 54 5% glycerol 3.06 25 357, glycerol 1.39 26 1-Butanol 1.44 C. Large Bore Capillary Acetone
Benzene 5% glycerol 35% dvcerol -" 1-Butanol . I
6.74 4.58 3.36 1.53 1.50
74 50 37 17 17
420 162 73 16 10
880 353 200 38 30 808 329 160 31 24
apparent from the extremely large Reynolds number for oxygen (Re = 33,000) which is flowing rapidly past the capillary tip. It is also possible that turbulence a t the atomizer tip could be transmitted back into the solution flowing through the capillary. Therefore, it is expected that the turbulence which exists in the region of the tip would appreciably influence the flow rate of solutions. It was observed that there is a linear relation between oxygen pressure and pressure differential, as shown in Figure 1. Thus a linear relation between oxygen pressure and solution flow rate is expected if the Poiseuille equation is obeyed. Figure 3 was obtained with a glycerol solution having a viscosity of 1.15 cp. The curves obtained were not linear as shown, and do not extrapolate to zero as expected. Therefore, it is apparent that flow rate is not proportional to the first power of the driving force a t viscosities less than about 1.5 cp. Since the pressure differential is directly proportional to oxygen pressure for all three atomizer capillaries, it is evident that the variations in tip geometry have no appreciable effect on this parameter. However, capillary flow is dependent to a large extent on the mode of solution emergence from the end of the capillary; so it is likely that tip geometry will affect this. Therefore, the tip geometry factor could influence the manner of solution exit and the solution flow rate, but the kind and extent of this effect are not known. The viscosity studies were carried out using constant oxygen and hydrogen flow for all measurements and with the knowledge t h a t other variable parameters such as surface tension and density would have no effect. The experimental points gave extremely
smooth curves in nearly all cases. The curves were reproduced many times a i t h less than 1% variation, except in the case of the medium bore atomizer capillary. The wide variation here (Figure 4) can be best explained on the basis of oxygen orifice clogging. This atomizer required much higher oxygen pressure to attain oxygen flow rates comparable to the other burners. This is evidence of a much smaller oxygen orifice. The resultant clogging necessitated higher oxygen pressures to maintain the same oxygen flow rates, with a resultant increase in velocity through the constricted orifice. This then explains the increased solution flow. The condition could be remedied to some extent by reverse blowing with oxygen coupled with acetone immersion. Even with these precautions and procedures, it was impossible to reproduce the Capillary conditions exactly. This extreme sensitivity of this medium bore atomizer to clogging prevented duplication of data from day to day. The study of flow rates of pure organic liquids (viscosity range of 0.5 to 2.5 cp.) revealed a definite difference in the flow characteristics of organic liquids and water solutions under identical conditions. The variation is illustrated in Figure 4 and is reproducible for all the burner systems used. The same solutions at different temperatures gave points that fall on the same curves. The study of flow indicates that capillary flow rate in total consumption atomizer burners is not governed by the Poiseuille equation over an extended range of viscosity. The product of viscosity, 7 , and solution flow rate, Q, incresses with increasing viscosity despite a constant capillary radius and pressure differential. However, over a limited range of viscosity (variations not greater than 10% from a given value), qQ is constant within experimental error. The constancy of qQ is dependent only on a linear flowfluidity curve. Therefore, the constancy of 7 Q for a series of solutions of different viscosities and for a given atomizer capillary does not necessarily mean the Poiseuille equation is being obeyed. There is only one value of qQ which corresponds to the Poiseuille equation, and this value is dependent only on the radius, R, and the length, L , of the atomizer capillary and the pressure differential, P. This one value of qQ is often approached but seldom attained for atomization of solutions in normal flame photometry. This has been discussed somewhat in length, because other workers have used this as a basis for concluding obedience to the The results Poiseuille equation (7'). given in Figure 5 indicate that only a t high viscosities (greater than 2 cp.) is Poiseuille's law obeyed. The use of organic liquids for flame VOL. 33, NO. 1 2 , NOVEMBER 1961
1731
temperature enhancement is becoming increasingly popular in flame photometric analyses. This entails not only a reduction in viscosity but also a resultant departure from Newtonian flow, which is apparent on the basis of this study. The variation in flow characteristics between water solutions and pure organic liquids is also important and should be discussed. From Figure 4 it is seen that in the region in which the aqueous flow curve separates most greatly from the nonaqueous flow curve, the organic liquids are less dense than water, but the density effect has already been shown to be negligible. The experimental method has been investigated with respect t o pipet delivery of the sample and to minute amounts of sample remaining in the cuvette after aspiration. Both of these have been shown to be negligible. The atomization of organic liquids into a flame results in a more intense or explosive flame, and it was thought that this could be a source of back-pressure which would depress the organic flow rates. However, the flow curves obtained with no flame as shown in Figure 5 exhibited the same variation in organic and water solution curves with only a slight flame effect on both. Therefore, flame effects are not responsible for the variation in flow. One other possible explanation for variation in flow between organics and water solutions is slipping. The slipping occurs between a flowing liquid and a capillary wall, and it is dependent on the coefficient of friction between them. An excellent survey of studies attempting to show the existence or nonexistence and of slipping is given by Bingham (4), later studies have already been discussed (see Theory). Assuming that slipping can occur, this study indicates slipping only a t the higher flow rates, where it would be expected. There is a n increase of flow due t o slipping which would mean the water solutions are more subject to slipping under the conditions employed, since their flows are more rapid. Following this line of reasoning it can be postulated that the organic liquids have a higher affinity for the metal capillary walls and are less subject to slipping. Recent studies on adsorption (18) have indicated that this affinity is dependent on the metal in question and results from electron donation by the organic molecule to the metal surface. Even though existence of slipping under condition of low flow rate and controlled efflux is questionable on the basis of much research, it is possible that slipping exists when flow conditions are extreme, as in this study. Possible further evidence of slipping on a metal (palladium) capillary is given in Figure 6, in which a series of water-ethanol solutions (10 to 100% by 1732
0
ANALYTICAL CHEMISTRY
weight) WRS studied. The results are as expected if these deviations are the result of slipping. SOURCES OF ERROR
IN
FLAME PHOTOMETRY
Variation in sample flow rate due to changes in solution, atomizer, or atomizing gas characteristics result in a corresponding change in meter reading on a flame photometer. The study conducted should be of great aid to analysts who use total consumption atomizer burners (or even chamber-type atomizers, because the basic atomizer is also usually of the total consumption type) in flame emission or absorption spectroscopy for routine analyses, method development research, or basic research. This study should aid an analyst in choosing proper experimental conditions to provide reproducible sample flow rate as well as to predict the variation in sample flow due to a change in solution properties of the sample or changes in the atomizer characteristics or atomizing gas flow. Because the same oxygen and fuel pressures will often give different gas flow rates, it is necessary to use flowmeters in the gas lines to enable reproduction of experimental conditions from day to day, because of the erratic sensitivity and insensitivity of the pressure regulator used to changes in meter pressure readings. For example, a change of “0.1” p.s.i. will often give a large change in gas flow rate, whereas a t other times a change of “0.5” p.s.i. may give no apparent change in gas flow rate. Variation in oxygen flow can occur, even if the oxygen pressure is maintained constant, because of clogging of the oxygen orifice a t the tip of the atomizer burner. A variation in viscosity causes the greatest source of error in flame photometry. A decrease of 1% in viscosity results in a n approximate increase of 1.2% in sample flow rate. This factor becomes all the more important when it is considered that a 2% decrease in viscosity can result from a temperature increase of only 1’ C. Thus if ambient temperature varies 3” C., a maximum error in flow rate of approximately 7% can result. Also, if standard solutions and sample solutions deviate greatly in yiscosity, the error will be substantially increased. Even with accurate control of teniperature, viscosity, and gas pressures, flow rates can still vary. This variation usually occurs after several milliliters of a very viscous liquid or polar organic liquid have been aspirated. This results in a gradual decrease of sample solution flow rate. This decrease is responsible for the gradual downward drift in flame photometer readings that are so often observed on prolonged aspiration (drifts often amount to
readings less than 90% of the initial values). Because water rinsing of the capillary corrected this, it seemed as if the capillary was gradually being reduced in radius because of surface coating. It was found that salt solutions of ionic strength greater than 0.4 required the longest rinsing periods. Acetone, because of its low viscosity, was found t o be a n excellent rinse for organic liquids. A suggested cleaning procedure between determinations would be a 4-ml. acetone rinse followed by a n 8-ml. distilled water rinse. The most direct method of assuring reliable results in flame photometric analyses as far as sample flow rate is concerned is to time directly the flow rates of measured volumes of standards and samples. This simple precaution will assure the operator of a constant flow of solution. In the event that standard solutions and/or sample solutions should vary in flon- rates, it is necessary to adjust the viscosities; if this is not possible, as in many cases, it is necessary to determine the nonlinear fluidity-flow curve for the system. LITERATURE CITED
(1) Al%made, C. T. J., “Flame Photometry, Ph.D. thesis, Cniversity of
Utrooht
“uu”y, 1
1Q5d AVVI.
,”\ 3arr. G.. “MononraDh of Viscometrv.” 1
z.,
Oxford Universit -Prbss, London, 1631. (3) Bernstein, R. S: Ajrican J. Med. Sci. 20, 57 (1956). (4),Bin$am, E. C., “Fluidity and Plasticitv. McGraw-Hill. Kew York, 1922. (5) Bihbham. E. C.. Natl. Bur. Standards. \
,
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