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Flow Measurement and Instrumentation 15 (2004) 331–334

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Short communication

Diffusion problems of soap-film flowmeter when measuringvery low-rate gas flow

Jia Guo a,�, Mark J. Heslop b

a School of Chemical Engineering and Pharmacy, Wuhan Institute of Chemical Technology, No. 366, Zhuodaoquan Road, Wuhan,

Hubei 430073, PR Chinab Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK

Received 20 April 2004; received in revised form 21 May 2004; accepted 2 June 2004

1. Introduction

Soap-film flowmeter (also known as soap bubbleflowmeter) was first introduced by Barr for measuringsmall rates of gas flow at the pressure close to ambient[1]. Nowadays, flowmeters of this type are used as gasflow rate calibration standards in various industrialand scientific applications since they are portable,simple, low-cost and can be readily constructed forrapid calibration [2]. The basic principle of this appar-atus is that the gas flow to be calibrated enters the baseof a graduated glass tube, which is vertically mountedon a stand. A soap film is introduced into the streamby squeezing a rubber teat containing soap solution (ordetergent). The characteristics of the film are such thatit provides a thin, well-defined and stable marker as itmoves up the graduated tube with the gas stream. Thetime required for the film to move between two marksis noted and the flow rate can be calculated. Time maybe measured with a stopwatch or, for higher accura-cies, photocells and electronic timing devices [3]. Theelectronic soap-film flowmeters, which are relativelyexpensive but have problems upon repeated use, arecommercially available. For both electronic and stan-dard soap-film flowmeters, the accepted accuracies areabout �1.0%, as reported by the manufacturers.Usually, suppliers of soap-film flowmeters fail to

provide any detailed instruction on how to use thesoap-film flowmeter properly, as they assume the cali-bration procedure is ‘‘standard’’ as a common sense.However, things are not as simple as they might

appear. For example, as noticed when calibrating the

flow rate for helium gas, the time required for the soap

film to pass through a fixed volume is largely depen-

dent on how many bubbles are created as well as the

segment of the tube monitored for measurement. In

this work, problems arising in using a soap-film flow-

meter when measuring very low-rate gas flow (2–20

ml/min) will be addressed. Effects of gas flow rate, type

of gas used, and the number of bubbles (single or mul-

tiple) on the performance of the flowmeter will be

investigated in order to reveal the diffusion problems

involved in soap-film flowmeters.

2. Experimental

Fig. 1 shows a schematic diagram of the experi-

mental set-up for testing soap-film flowmeters. Gas

(nitrogen, helium or air) was supplied by a gas cylinder

and the upstream pressure was set at 3.4 bar (50 psi) by

a pressure regulator. The gas flow rate was adjusted by

a mass flow controller (MFC, Model VCD 1000, POR-

TER Instrument Company Inc.). The gas flow to be

calibrated was introduced into the graduated glass tube

(50 ml volume) of a soap-film flowmeter, and the time

for the soap film moving up through different segments

(0–10 ml, 10–20 ml, 20–30 ml, 30–40 ml, and 40–50 ml,

denoted as SI, SII, SIII, SIV and SV, respectively, in the

later paragraphs) of the tube was noted. A prong at the

exit of the tube was used to burst the soap films and

return the liquid back down the tube wall for lubricat-

ing the motion of the soap films and hence preventing

their rapid collapse. During the runs for confirming

helium diffusion effects, a flexible hose was affixed to

Nomenclature

C gas concentration, kg/m3

D diffusivity or diffusion coefficient, m2/sH partition coefficient, dimensionlessJ mass flux crossing a membrane, kg/m2 sL thickness of a membrane, mM molecular mass, dimensionlessP absolute pressure, atmT absolute temperature, K

Greek letters

DC concentration differenceX collision integralrAB collision diameter, m

332 J. Guo, M.J. Heslop / Flow Measurement and Instrumentation 15 (2004) 331–334

the exit of the tube to increase the helium concen-tration near to the exit of the glass tube.

3. Results and discussion

Time for a single soap bubble to pass through 10 mlsegment of the graduated tube at various openings ofthe MFC, when helium gas is used, is shown in Fig. 2.When the MFC was fully opened (corresponding to themeasured gas flow rate of 60.0 ml/min) or adjusted for4 turns (37.5 ml/min), no matter which segment wasused for measurement, the recorded time for the soapfilm to pass through each segment was constant, i.e.,the calculated gas flow rate was consistent. Further, a4 turn closing was executed for the MFC, which resul-ted in a lower gas flow rate (27.3 ml/min). It wasobserved that it took relatively longer time for a soapbubble to move through the segment closer to the exitof the tube than that required for the former segments,i.e. the soap bubble slowed down. This phenomenonwas more significant when the MFC was set at 12 turnsin order to have a very low gas flow rate (9.1 ml/min).

To check whether the above mentioned observationis due to a non-uniform tube at different sections, twoother gases (air of 9.8 ml/min and nitrogen of 9.9 ml/min) were tested. The experimental results are providedin Fig. 3. It can be seen that, for air, the soap bubblemoved through each segment at a quite constant rateand there was a slight slowdown for nitrogen gas.Therefore, it suggested that the cross-section of thetube was uniform and that the slowdown of the bubblemight be due to some other reasons. One possibleexplanation is that, for highly permeable gas likehelium, the diffusion of gas to the ambient slowed downthe movement of the bubble. As we know, diffusion islargely dependent on the concentration differencebetween the two sides of the film. In order to increasethe gas concentration at the opening end of the tube, along and flexible hose was affixed to the exit of the glass

Fig. 1. Schematic experimental set-up for soap-film flowmeter test.

Fig. 2. Time for single soap bubble to pass through 10 ml segment

of the graduated tube at various openings of the MFC when helium

gas is used.

Fig. 3. Time for single bubble to pass through 10 ml segment of the

graduated tube using different gases.

J. Guo, M.J. Heslop / Flow Measurement and Instrumentation 15 (2004) 331–334 333

tube. Comparison of time for a bubble to pass through10 ml segment of the tube with and without the cappinghose is shown in Fig. 4. After adding the capping hoseto the tube (measured gas flow rate: 10.2 ml/min),which might maintain the equivalent concentrations forhelium at both sides of the soap film, the bubble movedthrough each segment of the tube much more evenlythan without using the capping hose.Normally, a soap film can be considered as an elastic

membrane [4]. Soap film is a sodium salt of a fattyacid, e.g., sodium stearate, C17H35COO

�Na+ with amonomolecular layer of amphipathic ions on the sur-face. The mass flux crossing the soap-film membrane isa function of the following factors [5]:

J ¼ f ðD;H;DC;1=L . . . Þ ð1Þ

where D, H, DC and 1/L are the diffusion coefficient,the partition coefficient, concentration difference, andthe reciprocal of the membrane thickness, respectively.According to the Chapman–Enskog theory of diffu-

sivity for non-polar gas pairs [6]:

D ¼ 1:858� 10�27T3=2

Pr2ABX

1

MAþ 1

MB

� �1=2

ð2Þ

Actually, the diffusivity of helium in air at 293 K is

0:735� 10�4 m2=s, which is much higher than the one

of nitrogen in air (0:197� 10�4 m2=s) at the same tem-perature. H is the partition coefficient, which dependson the chemical structure of the membrane. The termDH is usually known as permeability. Generally, thepermeability of a smaller molecule (for example,helium and hydrogen) is higher than the one of a largermolecule (for example, nitrogen and oxygen). As forconcentration difference (DC), there are two concen-tration gradients involved in the mass transfer processof soap-film flowmeter. The first step of such a process

is the diffusion of gas through the soap film and thenext one is the diffusion of gas from the surrounding ofthe soap film to the ambient via the tube opening.These diffusions would explain the reason why the soapfilm moves slower and slower when approaching theexit of the tube. Moreover, the thickness of soap films(L) varies from 0.2 to 1.5 lm as measured by Lawrenceusing spectroscopic analysis [7]. Barigou and Davidsonalso found that the average thickness of a soap filmwas 0.8 lm by both weighing method and conductancemethod [8]. However, in the soap-film flowmeter, thefilm thickness may increase due to the liquid drainingdown the tube when using multiple bubbles [9].Instead of using a single soap bubble, multiple bub-

bles (2 or 5) were also used in this study. The lowestbubble was used as the indicator for timing. The bub-bles were created as close as possible to reduce thedraining of the liquid, which might change the thick-ness of the later films as mentioned before. Time forsingle or multiple bubbles to pass through 10 ml seg-ment of the graduated tube is shown in Fig. 5. Therewas a slight reduction of diffusion problems using 2bubbles. When 5 bubbles were used, the soap filmmoved much more evenly. This suggested that usingmore bubbles than a single bubble would significantlyimprove the accuracy of measurement.

4. Conclusions

Soap-film flowmeter is widely used for gas flow cali-bration, particularly at very low flow rate applicationssuch as chromatography. However, when calibratinghighly permeable gases like helium and hydrogen, themeasurement accuracy was dependent on the segmentof the tube used. This implies that diffusion of such gasto the ambient slowed down the movement of the soap

Fig. 4. Comparison of time for single bubble to pass through 10 ml

segment of the graduated tube with and without a capping hose.

Fig. 5. Time for single and multiple bubbles to pass through 10 ml

segment of the graduated tube.

334 J. Guo, M.J. Heslop / Flow Measurement and Instrumentation 15 (2004) 331–334

bubble. The closer it was to the exit of the tube was,

the more significant such diffusion effect became. In the

end, extreme cares should be taken when using a soap-

film flowmeter, particularly at a very low flow rate for

high permeable gases. This study suggests that more

than one bubble should be used for measuring very

low-rate gas flows.

References

[1] G. Barr, Journal of Scientific Instrumentation 11 (1934) 321–324.

[2] G.H. Pandya, Simple air flow calibration for gaseous sampling,

Indian Journal of Environmental Health 30 (2) (1989) 168–172.

[3] W.C. Pursley, The calibration of flowmeters, Measurement

þControl 19 (5) (1986) 37–45, (special issue).[4] C. Isenberg, The Science of Soap Films and Soap Bubbles,

TIETO LTD, Clevedon, Avon, 1978.

[5] E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems,

Cambridge University Press, Cambridge, 1997.

[6] A.L. Hines, R.N. Maddox, Mass Transfer: Fundamentals and

Applications, Prentice-Hall, Inc, New Jersey, 1985.

[7] A.S.C. Lawrence, Soap Films: A Study of Molecular Individu-

ality, G. Bell and Sons, Ltd, London, 1929.

[8] M. Barigou, J.F. Davidson, The fluid mechanics of the soap

film meter, Chemical Engineering Science 48 (14) (1993)

2587–2597.

[9] M.J. Heslop, G. Mason, A. Provatas, Comments on the pressure

produced by a soap film meter, Chemical Engineering Science 50

(15) (1995) 2495–2497.