Comments on the pressure produced by a soap film meter

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo Pergamon Chemical En#ineerino Science, Vol. 50, No. 15, pp. 2495-2497, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009 2509/95 59.50 + 0.00 0009-2509(95)00053-4 C o m m e n t s on the pressure produced by a soap film meter (Received 14 December 1993) 4PV-A/,~ INTRODUCTION AND PREVIOUS INVESTIGATION Recently, Barigou and Davidson (1993b) reported the measurement of the pressure drop produced by the motion of soap films of detergent-glycerol solution in vertical cylindrical tubes of varying diameter, as in a soapfilm meter. The meter is usually used to measure gas fiowrate because the single film moves up a tube at a rate equal to the gas flowrate. The gas flowrate is found by timing the film between two suitable graduation marks. A very small but finite pressure is required to move the film up the tube. If there are several separate films then a greater pressure is required. Barigou and Davidson measured the total pressure drop AP required to move N films at a velocity U and suggested that these quantities could be related by the equation: AP = N(AP0 + kU). vent 4F~/-B V • signal amplification EXPERIMENTAL ARRANGEMENT Figure 1 shows a schematic representation of the experimental arrangement. The nitrogen gas cylinder supplies three mass flow controllers (MFC) and each M F C output passes to its respective four-port switching valve (4PV). The output from each 4PV is combined and sent to a three-port switching valve (3PV) which either directs the gas into the selected cylindrical tube to move the film or vents the gas to atmosphere. In the latter position the film is stationary and this allows a direct evaluation of the static weight APo. The idea of the switching valve arrangement is to enable the AP for a particular film to be obtained for up to seven different values of U; this requires the switching valve positions to be I I ~ perspex base soap solution chart recorder (1) In this equation, kU is a drag term and AP0 is the pressure produced by the weight of the soap film. Both k and APo are constants which depend upon the tube diameter; k can be calculated from the gradient of the line and AP o obtained from the intercept of the line. Barigou and Davidson show an excellent fit by experiments to eq. (1) over a velocity range from 1 to 120 mm/s. Barigou and Davidson employed tube diameters from 6.2 to 73.4 m m and showed that both k and APo decreased with increasing tube diameter. Also, Nutt and Burley (1989) carried out a similar investigation using two commercial surfactants and show an excellent fit by experiments to eq. (1) over a velocity range from 20 to 100 mm/s. As a preliminary to measuring the pressure produced by soap films as they move through packings of spheres, we have carried out an investigation of the soap film meter using detergent solution as well as a detergent-glycerol solution (to increase the viscosity) to make the films. We have used an improved experimental arrangement and a lower range of gas flowrates and found that the pressure variation is not linear at low gas flowrates. In addition, a chart recorder was incorporated to monitor the dynamic pressure drop as the film moves up the tube. cylindrical ~be ambient pressure Fig. 1. Schematic experimental arrangement. In the diagram, the 3PV switching valve is shown directing the gas flowrate to vent so that the film is stationary. The D P T is a Furness Controls model F C O 40. changed in a particular sequence. The alternative is to use consecutive films at different velocities; however, this is time-consuming and results have shown that the behaviour can vary from film to film. Unlike the apparatus of Barigou and Davidson (1993b), the pressure tapping to the differential pressure transducer (DPT) is located on the carrier gas inlet pipe instead of on the actual cylindrical tube of investigation. The advantage of this location is that the soap film cannot leave any liquid blocking the tapping. The disadvantage of this location is that the measured AP will include a contribution due to the gas pressure drop through the inlet to the tube and so the effective chart recorder baseline will vary with gas flowrate. However, this is only a problem at high gas flowrates, and can be easily compensated. An experimental run consisted of first sending m a n y films up the tube to wet the entire surface with soap solution to prevent the films thinning and breaking. A film was then formed in the perspex base and it moved up through a conical section into the plain cylindrical tube of particular diameter. For the larger diameters, the tube was machined from a perspex block and fitted tightly into the perspex base. For the smaller diameters, a precision glass tube was glued to a small perspex base which fitted tightly into the perspex base. When the film reaches the top of the tube, a bubble simply blows out and breaks and some liquid returns down the tube wall; unlike Barigou and Davidson there was no prong to break the bubble to return the liquid back down the tube. The pressure is recorded by the D P T and chart recorder for the entire time the film spends in the tube. To 2495 2496 Letters to the Editors convert the chart recorder distances into pressure units requires the DPT to be calibrated. The nominal characteristic of the DPT is an output of one volt corresponding to 10 mm water gauge. The exact calibration was found by comparing the pressure drop recorded by the DPT with a manometer. The viscosity of the detergent-glycerol solution was measured to be around 6 mNs/m 2 (around 6 times greater than water) using a U-tube viscometer. This compares with the value of 8 mNs/m 2 reported by Barigou and Davidson. The surface tension of both the detergent and detergent-glycerol solutions was measured to be 23 raN/m, by measuring the capillary rise in a 0.5 mm diameter tube. This compares with a value of 35 mN/m reported by Barigou and Davidson. SUMMARY OF EXPERIMENTAL RESULTS We have made many measurements but only two tube sizes were directly comparable with those of Barigou and Davidson. Figures 2 and 3 show the results obtained by Barigou and Davidson together with our results for the 6 and 12 mm diameter tubes, respectively. Our results have an initial curved section at low velocity and a linear section at higher velocity; the gradient for the detergent-glycerol solution is roughly twice that for the detergent solution without glycerol. Comparing the results for the detergent-glycerol solutions with those of Barigou and Davidson shows that the intercepts given by extrapolation of both linear sections (APo) are in close agreement. However, Barigou's and Davidson's results are linear across the entire velocity range whereas ours are not. More important they measured a gradient of about one-sixth of that obtained by •,•08 E3 o6 =E [] o4 0 [] % 4k. 02i 0 5 10 15 20 velocity / mJllimetres per second J E2 Detergent-Glycerolsol.on • Bangou& Da~clson J Fig. 3. Graph showing comparison of results for straight detergent and detergent-glycerol solutions using a 12 mm diameter cylindrical tube. The graph does not show the complete velocity range of Barigou and Davidson which extends up to 120 mm/s. Our solution was slightly less viscous than that of Barigou and Davidson. Note the difference in gradient. liquid addition B it C US. effective baseline for no bubble DESCRIPTION OF FILM PRESSURE RECORD Figure 4 shows a typical pressure record from the chart recorder for a soap film moving through a cylindrical tube. It should be pointed out that the results of Figs 2 and 3 were not obtained from Fig. 4; Fig. 4 was part of an investigation of the effect of film weight. At position A, the film was stationary (valve 3PV was switched to vent). The difference between position A and the baseline corresponds to the film weight AP o. Using a pipette, liquid was injected down the side of the tube. Liquid was retained in the Plateau border and this nearly doubled the film weight. There is a limit to how much APo can be increased; any excess simply drains from the bottom of the Plateau border. However, for nar- 2 8 I I 20 seconds G D ~E t F r " ~ ~ H | effective baseline for no bubble Fig. 4. Typical pressure record for a detergent film moving through a 7 mm glass cylindrical tube. The pressure readings used to plot the points in Figs 2 and 3 were obtained from similar pressure records by simply measuring the relevant chart-recorder distances. In this experiment liquid was added to increase the size of the Plateau border to its maximum. A similar pressure record was used to measure the AP0 values plotted in Fig. 5; the film speed was increased in steps and then stopped to measure the static weight APo. 15 E E A [] a3 ~0. l-n r~ 10 20 30 velocity / millimetres per second ] [ ] Detergentsok~don • Barigou& {~wldllon ~ Detergent-Glycerolsolution ] ~" Exce~ liquid film Fig. 2. Graph showing comparison of results for detergent and detergent-glycerol solutions using a 6 mm diameter cylindrical tube. For our results, the viscosity of the detergent-glycerol solution is approximately six times greater than that of the detergent solution. The graph does not show the complete velocity range reported by Barigou and Davidson, which extends up to 120 mm/s. The results for the "excess liquid film" are taken from Fig. 4 and are for a 7 mm diameter tube using detergent solution. rower tubes (below about 2.5 mm in diameter), there is no limit to how much liquid can be added. For this situation the Plateau borders cover the entire cross-section and there is no central lamella. Our observation of the tube size at which this occurs confirms that of Barigou and Davidson. Next, the 3PV was switched to move the film at 0.6 mm/s; there was a small pressure increase (position C). The difference between this pressure level and the baseline gives the AP which is the sum of the weight and viscous forces. The film was then stopped by switching the 3PV to vent and the pressure decreased to position D; it can be seen that levels D and B are identical and so the film weight has remained constant over the translation. Next, the film speed was increased to 0.6,1.8 and 4.2 mm/s and the pressure increased to levels E, F and G, respectively. However, after a few seconds at the highest flowrate, the pressure was seen to decrease and when the 3PV was switched to stop the film, the final static weight (difference between position H and baseline) was clearly less than the original static weight (difference between level D and baseline). Probably, as the film speed was increased, it Letters to the Editors ~ 08 E ,E~ 0.6 z& ~xEX x x I~ 041 ~ 0.2 a 0 50 100 150 200 250 300 Distance travelled / m m liquid-deficiem film(~l 7 mrn/s • normal film(~1.7 rnm/s • e~ce~-Ik:luid film~1.7 mrnls normal fiimQS.8 mm/$ exceu-liquid fllm(~5.8 m m / i Fig. 5. Graph showing film static weight measured after stopping films moving at one of two different velocities in a 7 mm diameter tube. The "high" velocity is 5.8 mm/s and the "low" velocity is 1.7 mm/s. The maximum residence times for the high- and low-velocity films are about 50 and 170 s, respectively. deposited liquid on the inside of the tube. One problem concerns where to measure AP for the highest flowrate; after the speed was increased, a plateau in pressure was obtained before the pressure started decreasing. AP was measured from the initial horizontal section before the film weight changed. Figure 5 shows the results of a different experiment where the static weight was measured after stopping a film from one of two speeds; the filled markers correspond to the "low" velocity and the non-filled markers represent the "high" velocity. Films were produced which initially had a Plateau border which was deficient in liquid or had an excess (added by running liquid down the side of the tube). The liquiddeficient films (APo = 0.14 mm water gauge) were produced by moving the films through the perspex base at a sufficiently high velocity that they left liquid on the walls before they were stopped at the bottom of the cylindrical tube. Generally, it can be seen in Fig. 5 that for each velocity there is a steady-state weight and this is greater for the lower film velocity. The distance required to attain the steady state seems to be independent of the film velocity. The behaviour of the films at low velocity is interesting because of the maximum in film weight; the initially deficient film gains excess liquid before shedding some of this liquid as it moves further up the tube. The film weight-distance behaviour is dependent on the amount of liquid on the walls of the tube; if the top of the tube is relatively dry then as the film enters this dry section it deposits liquid leading to a reduction in the film weight. DISCUSSION The results show that the pressure-velocity graph for a soap film is dependent on the amount of liquid in the Plateau border. This in turn is affected by the amount of liquid draining back down the tube. Clearly, a minimum amount of liquid is required on the inside of the tube otherwise the tube would be dry, the Plateau borders would be lost and the bubbles would break. Before our experiments, many films were sent up the tube to wet the initially dry surface. Then, all the pressure measurements were obtained with a single film. The initial curved section of our pressure-velocity graphs indicates a transitional region where the liquid is being redistributed as the speed is increased; in 2497 the linear section (at higher velocity) the size of the Plateau border remains constant. Barigou and Davidson (1993b) sent many films up the tube and there was a prong to break the films and return the liquid down the tube. This technique might maintain the volume of the Plateau border constant when the film speed is increased; this would cause the linear region to extend to zero velocity. This consideration of film weight might explain the difference in bruiting gradients; from Fig. 2 it was seen that the AP contribution due to velocity is greater for a film of lesser weight. The biggest difference between our results and those of Barigou and Davidson is the gradient of the linear portion of the pressure-velocity graph. The gradients of the linear positions of the two lines vary by a factor of six. This is an enormous difference but might be explained by an incorrect velocity scale. Have Barigou and Davidson confused millilitres per second with centimetres per minute? Their maximum velocity (120 mm/s) is very fast indeed. Our tube was about 250 mm long, and allowing for the difficulty in manually forming a single film and taking measurements, a 2 s residence time is very short. Barigou and Davidson did not specify a length for the cylindrical tube, but in a previous paper (1993a) they stated a tube length of 250 mm for a similar experimental arrangement. Comparing our results for the detergent solution and detergent-glycerol solution, it can be seen that the limiting gradient of pressure with velocity is almost twice as high for the detergent-glycerol solution case. The intercepts are almost identical. So, the gradient of the linear section increases with viscosity but six times the viscosity only doubles the gradient. The purpose of this communication has been to show that the behaviour of films in cylindrical tubes is not as simple as it might appear. Care must be taken when representing the film pressure-velocity characteristic as a single line, since the profile can depend upon the initial film weight and on how much liquid is draining down the tube. Results have shown that for certain situations, the film pressure can vary as the film moves up the tube; the film dynamics must be taken into consideration. It would appear that for a particular tube diameter, wall film thickness and film velocity, there is a steady-state film weight (APs). M. J. HESLOP G. MASON* A. PROVATAS: Department of Chemical Engineering Loughborough University of Technology Loughborough, Leicestershire, LEl l 3TU, U.K. REFERENCES Barigou, M. and Davidson, J. F., 1993a, Drainage of a soap film. The 1993 Inst. Chem. Enono Research Event 2, 717-719. Barigou, M. and Davidson, J. F., 1993b, The fluid mechanics of the soap film meter. Chem. Enono Sci. 48, 2587-2597. Nutt, C. W. and Burley, R. W., 1989, The influence of foam rheology in enhanced oil recovery operations, in Foams: Physics, Chemistry and Structure (Edited by A. J. Wilson), pp. 105-147. Springer, Berlin. *Author to whom correspondence should be addressed. tPresent address: School of Chemical Technology, University of South Australia, Pooraka SA5095, Australia.