Depulsing System for Positive Displacement Pumps Kent K. Stewart Nutrient Composition Laboratory, Nutrition Institute, Agricultural Research Service, United States Department of Agriculture, Beltsville, Maryland 20705
a packed column. We have combined the ideas of these three groups and have developed a simple, inexpensive depulsing system using a flow resistance network with a needle valve as the flow restrictor and pressure gauges as the mechanical ballast (Figure 1). The depulsing system works by restricting the liquid flow from the pump with the metering valve such that the pressure on pressure gauge No. 1is 5C-100 psi greater than the operating pressure (pressure gauge No. 2). When the flow is thus restricted, the pressure surges, generated by the forward stroke of the positive displacement pump, are mechanically damped by the diaphragm in gauge No. 1. Pressure surges of 50 to 100 psi a t pressure gauge No. 1 are damped to surges of 2-10 psi at pressure gauge No. 2. This system was easily constructed from commercially available parts. The 1/4-28 N F thread tubing adapters are used with standard Teflon tubing 0.063-in. (1/16-in.)0.d. X 0.028-in, i.d. (AWG 22). The tees, 0.031-in. bore and 1/4-28 N F thread parts were made of Kel-F. The 21/2-in.diameter stainless steel pressure gauges were adapted for direct fit to the 1/4-28 fittings. The metering valve was a Nupro SS2MGD double pattern fine metering valve or a Nupro SS-1SG single pattern fine metering valve adapted to f i t the 1/4-28 fittings at each end. Milton Roy Mini pumps models DK and CK have been used successfully with this system. This depulsing system has been used with low pressure (5-500 psi) chromatographic and continuous flow analytical systems at flow rates of 2G-500 mL/h. It is readily adaptable to different operating pressures and different flow rates. Its cost is approximately $300, not including the pump. It has a small liquid volume which permits a rapid change of solutions. When, occasionally, particulate matter plugs the metering valve, the valve is easily cleaned by opening the needle valve for a short time. The system has been in use for over 6 months and has been adopted as the standard method for depulsing positive displacement pumps in this laboratory. The depulsing system would probably also work a t higher pressures (up t o 5000 psi) if the Teflon tubing were replaced by stainless steel tubing.
The quantitative determination of chemical and biochemical compounds in continuous flowing streams requires the precise, accurate, pulseless delivery of the reagents involved in the analysis. This is a requirement for liquid chromatography systems with post-column chemistry as first described for the amino acid analyzer of Spackman, Stein, and Moore ( I ) as well as for the continuous flow analyzers first described by Skeggs ( 2 ) . At operating pressures of 50 psi or lower, delivery of reagents can be accomplished by a variety of means such as peristalic pumps, constant pressure reservoirs, and syringe pumps. At higher pressures, other pumps must be used ( 3 ) such as high pressure syringe pumps, pressure regulated pumps, gas amplifier pumps, gas displacement pumps ( 4 ) ,and a variety of reciprocating, positive displacement pumps with one or more heads and with or without sinusodal drive. Most of these pumps deliver liquid at a very precise rate and even flow, but are expensive. The simple, relatively inexpensive reciprocating positive displacement pumps also deliver liquid very precisely, but introduce pressure spikes into the analytical system. When two or more reagents are delivered in parallel with these pumps, the pressure spikes cause a non-uniform mixing of reagents and reduce the accuracy and precision of the analysis. A number of devices have been designed t o attenuate these pressure spikes. Pressurized gas ballast has been used with fairly good results; however, start-up time tends t o be lengthy and outgassing may be a problem. Freeman and Zielinski (5)designed a flow resistance network depulsing system analogous to a simple RC filter electrical circuit. They used gas ballast combined with a stainless steel tube packed with silica. Mowery and Juvet (6) replaced the packed stainless steel tube with a precision needle valve; permitting the depulsing system to readily operate a t different flow rates and back pressures. The traditional problems associated with gas ballasting are also present in these systems. Careful examination of the ninhydrin pump system of Spackman, Stein, and Moore ( I ) reveals that it is also a flow resistance network; the gas ballast is replaced by a mechanical ballast (the pressure gauge diaphram), and the resistance is
P P E S S U R E ?LUGE N o I
A
\
" Q E S S J R E ;4UGE
No.2
*dETEQIhG V A L V E
y-\ A
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Figure 1. Depulsed positive displacement pump system ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
2125
ACKNOWLEDGMENT
(4) B. L. Karger and L. V. Berry, Anal. Chem., 44, 93-99 (1972). (5) D. H. Freeman and W. L. Zielinski, Natl. Bur. Stand. (U.S.), Tech. Note, 589, 3-18 (1971). (6) R . A. Mowery, Jr., and R. S. Juvet, Jr., J. Chromatogr. Sci., 12. 687-695 (1974).
Conversations with G. R. Beecher and R. F. Doherty, the skillful1 technical assistance of D. J. Higgs, and the art work of Paul Padavano are gratefully acknowledged. LITERATURE CITED (1) D. H. Spackman, W. H. Stein, and S.Moore, Anal. Chem., 30, 1190-1206 ( 1958). (2) L. T. Skeggs, Am. J. Clin. Parhol., 2 8 , 311-322 (1957). (3) L. Berry and B. L. Karger, Anal. Chem., 45, 819A-827A (1973).
RECEIVED for review April 18, 1977. Accepted July 6, 1977. Mention of a trademark of proprietary product does not constitute a guarantee or warranty of the product by the U.S. Department of Agriculture, and does not imply its approval to the exclusion of other products that may also be suitable.
Air Buoyancy Equations for Single-Pan Balances Michael R. Winward,' Earl M. Woolley," and Eliot A. Butler" Department of Chemistty, Brigham Young University, Provo, Utah 84602
Most derivations of the correction for air buoyancy are made considering a two-pan, equal-arm balance that is restored to its zero point of rest. The exact equation for such a balance is
5)(1 F) -1
Mo = Mwts (1 -
-
where Mo is the true mass of the object that is compared to standard weights of mass MMs. The density of air is represented by clair,and the densities of the object and weights by doand d, respectively. Substituting the series expansion of the term [l - (dair/do)]-linto Equation 1 yields
M, = Mwts(1-
")
dWtS /?I \ 2
[1+ daix + d0
1
apply to both types of balances. However, their derivation is based on the implicit assumption that the balance is restored to the null position when a weighing is made. We present a more rigorous derivation to show that Equation 1 is not exact for a single-pan balance except when the beam is a t the null position and we determine the errors that are involved in using that equation. D E R I V A T I O N OF E Q U A T I O N S Figure 1 shows a single-pan balance that has had the pan, weights, and counterpoise removed so that the beam is at equilibrium at the null point. In this figure, a and b represent the centers of mass of the two sides of the beam, cy' is the angle to the center of mass of the left side of the beam from the horizontal plane that passes through the central knife edge, and p' is the corresponding angle to the center of mass of the right side. L, and Lb are the horizontal distances between the central knife edge and the respective centers of mass. Since the sum of the torques about the central knife edge must be zero, we may write
Neglecting all terms that are higher than first order in d h gives
(3) The neglecting of the higher order terms involves an error of approximately 0.0001% if do = 1. For do > 1, the error is smaller. Either Equation 1 or, more commonly, Equation 3 is given in quantitative analysis texts. If in a weighing operation a balance is not restored to its zero point of rest, part of the object's weight is calculated from the deflection of the beam and the sensitivity of the balance. That part of the mass is not subject to the unequal buoyant forces as is the part obtained from the weights on the pan plus the rider. On the equal-arm analytical balance, a maximum of about 3 mg can be determined from the deflection of the beam. Hence, only 3 mg or less of the mass of the object is not subject to unequal buoyant forces. However, on the single-pan balance, the deflection of the beam is used for determining as much as 1 g of the object's weight. Thus, on the single-pan balance a much more significant portion of the object's mass may not be subject to the inequality of buoyant forces., Burg and Veith (1) have pointed out that it is not obvious that the same equation for buoyancy corrections applies to both types of balances. They derived an equation for the single-pan balance and concluded that the same equations did Present address, Union Oil Research Center, Brea, Calif. 2126
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
where M is the mass of, and F, the buoyant force on each respective side of the beam. The acceleration of gravity is represented by g. The term (Mg - F) represents the net downward force acting on the respective sides. (Table I gives a listing of the subscripts used to identify the various masses and forces.) Figure 2 shows the balance with the pan of mass Mp,the weights of mass M I , and the counterpoise, whose mass is M,, replaced on the beam such that the beam is still a t the null position. Let cy be the angle from the horizontal plane to the terminal knife edge and L1 the horizontal distance between the two knife edges. Let @ be the angle from the horizontal plane to the center of mass of the counterpoise and L, be the horizontal distance from this point to the central knife edge. The right hand and left hand torques are equated to give
Figure 3 shows the balance with an object of mass M o placed on the pan and an approximately equivalent mass of weights removed so that the beam is at equilibrium at a position other
