Literature Cited
Burchard, J. K., Toor, H. L., J . Phys. Chem. 66,2016 (1962). Carnian, P. C., J . Phys. Chem. 72, 1707 (1968). Dubrovskii, S. M., Afonina, K. V., Zh. Obsch. Khim. 36, 1869
O’Reilly, D. E., Peterson, E. M., J. Chem. Phys. 56, 2262 (1972). Shuck, F. O., Toor, H. L., J . Phys. Chem. 67,540 (1963). Vignes, A., Sabatier, J. P., Trans. Met. SOC.A I M E 245, 1795 (1969).
P. C.CARMAN
(1966).
Harris, K. R., Pua, C. K. N., Dunlop, P. J., J . Phys. Chem. 74, 3518 (1970).
Kett, T. K., Anderson, D. K., J . Phys. Chem. 73, 1268 (1969). Kirkaldy, J. S.,Lane, J. E., Can. J . Phys. 44, 2059 (1966). Mortimer, R. G., Clark, N. H., IND. ENG.CHEM.,FUNDAX 10,
National Chemical Research Laboratory Pretoria, Republic of South Africa
604 (1971).
RECEIVED for review November 27, 1972 ACCEPTED June 22, 1973
O’Reilly, I). E., Peterson, E. M., J . Chem. Phys. 55, 2155 (1971).
A Curious Anomaly in Parametric Pumping Experimental evidence i s presented to illustrate a curious reversed separation effect in a closed, direct thermal mode parametric pump operating at high frequency. A comparison with a theory that predicts such reversals at high frequency shows that simple velocity lag effects cannot explain the current phenomenon.
High-frequenc y operation of liquid parametric pumps has not been exploited to date. X recent theory (Rice, 1973) suggests the possibility that larger separations may occur at higher frequencies owing to resonance effects. Indeed, this theory suggests that a reversed separation may occur. Some recent experiments in our laboratory have produced this curious “reversed separation’J effect in the enrichment of oxalic acid from aqueous solutions on activiated carbon using the closed, direct thermal mode parametric pump. When operating this type of parametric pump in a single solutesolvent system, one usually synchronizes fluid pulsation and heat addition so that the phase difference between these essential driving forces is 0’ or 180’. For example, when fluid motion is upward in a vertical packed column, heat is removed from the bed (for example, by passing cooling water through a jacket surrounding the bed) and this cooling causes solute to be adsorbed and hence retarded. When fluid motion reverses and moves downward, heat is added to the bed, allowing the solute to desorb and be swept downward with the applied fluid motion. It appears obvious that this “bucketbrigade” should cause solute eventually to accumulate in the well-stirred lower reservoir, while solute should be depleted from the upper reservoir. On the other hand, if we heat the bed on upflow and cool it on downflow, one naturally expects the upper reservoir to be eventually enriched in solute, while the lower reservoir is depleted. Quite the opposite occurred in our experiments. I n the former case (cooling during upflow) we observed the upper reservoir vias enriched; in the latter case (heating on upflow) we observed the lower reservoir was enriched. One of the experiments demonstrating this rather odd reversal is presented in Table I. Initially, we thought this curious reversal was caused by velocity lags in the pore structure of the bed, that is the socalled “annular effect” (Richardson, 1929) which occurs when a fluid is pulsed in a tube a t high frequency. This interesting hydrodynamic phenomenon is discussed by Schlicting (1960) where it is demonstrated that the flow along the axis of the tube lags behind that in the layers near the wall. A recent theory to predict ultiniate separations in the parametric pump (Rice, 1973) exploits this interesting velocity effect and 486 Ind.
Eng. Chem. Fundam., Vol. 12, No. 4, 1973
indeed shows that when u R 2 / 6 ) > 650, a reverse separation should occur. We tested this theoretical prediction in the following way. High-frequency experiments using aqueous oxalic acid were performed in a vertical bed packed with activated carbon (cylindrical in shape with average particle dimensions of 4mm length X 1.5-mm diameter). The jacketed bed was in. i.d. and contained 40 in. of packed length. Well-stirred reservoirs having capacities of 9.5 (upper) and 20 (lower) i n a awere attached to the column ends. Fluid pulsing was accomplished using a lever arm-cam arrangement to produce very nearly (=k20/,) sinusoidal fluid motion. Cooling water a t approximately 25OC was circulated in the jacket surrounding the bed during upflow, while hot water (56OC) was circulated during downflow. Under such conditions, it was expected that a high concentration would prevail in the lower reservoir and a low concentration in the upper reservoir. Operation in this manner was deemed sensible, since if the reverse were true (heating upflow, etc.) a high concentration should prevail in the upper reservoir and density driven flow would be a problem. On observing the reversed separation, we then applied heating on upflow, cooling downflow, and found the lower reservoir was enriched (Table I) showing a t least the curious reversal was consistent, but still unexplained. Details of the experimental work are presented elsewhere (Mackenzie, 1972). We next propose to test the previously mentioned theory. Taking the Schmidt number as 355 and a computed pore hydraulic radius (based on a measured flow void fraction of 0.5) as 0.315 mm, the theory predicts that reverse separation should occur when w > 18 radians/sec or for cycle times less than 0.35 see. This prediction is a factor of 100 off the mark in predicting the current results, where cycle times as long as 210 see produced the curious reversed separation. The possibility that natural convection could have caused the anomaly was tested by the simple expedient of reversing the thermal flux (Le., heating upflow, cooling downflow as in Table I) and still the reversed separation persisted. We concluded some effect other than velocity lag and natural convection caused the reversed separation, such as: (1) abnormal equilibrium isotherm; (2) interparticle thermal and mass diffusion in the radial direction or thermal lag; (3) inter-
Table 1. Concentration History in Parametric Pump with Heating on Upflow, Cooling on Downflow. Time, hr
Upper reservoir oxalic acid concn, g1l.b
Table II. Adsorption Equilibrium Isotherms for Aqueous Oxalic Acid (Mol Wt 126.07) on Activated Carbon.
Lower reservoir oxalic acid concn, g/IP
11.9 11.7 5.75 11.8 12.8 23,75 10.8 14.05 28.5 9.75 14.18 46.5 9.19 15.25 53.5 8.55 14.85 70.5 7.62 15.5 75.5 7.2 15.5 94.5 6.43 16.2 111.5 6.43 16.1 a Interstitial fluid amplitude, 6.6 cm; cycle time, 215 sec; applied temperatures, 56OC/25OC. * Based on 1-ml samples titrated with 0.005 N KMnO,.
0
facial heat and mass resistances between adsorbent particle and moving fluid; (4)intraparticle diffusion and adsorption kinetics; and (5) heat transfer resistances between thermal jacket and packed bed. To check the first of these possibilities, equilibrium isotherms for the oxalic acid-water-activated carbon system were determined in our laboratory a t approximately the parapump operating temperatures of 25 and 55°C. The possibility that higher adsorption occurs a t high temperature than a t low temperature (an abnormal isotherm) was disregarded for the resulting Type I isotherms reported in Table 11. It is one of the salient features of the parametric pump that such a small driving force as is evident in Table I1 could indeed produce the sizable solute separation reported in Table I . We speculate that the effects listed as items 2 and 4 are the most likely candidates to explain the anomaly. At high frequencies, thermal penetration will seriously lag behind velocity. A theory to predict this phase difference can be treated very simply if the axial temperature gradient is small. The current experimental work has shown this to be the case. Five thermocouples spaced uniformly along the axis and mounted to measure the centerline temperature have shown that the axial temperature did not vary by more than 2°C. The general transport equations presented by Baker and Pigford (1971) are considered good descriptions of the parapump process, except t h a t the axial diffusion terms should
55 f 0 . l 0 C
25 xk 0 . l o C Solids composition, mg/g of dry solid
liquid composition, g/l.
1 04 7 8 12 6 20 8 26 1 26 8 24 4 28 1 Supplied by Ajax
0 48
Solids composition, mg/g of dry solid
liquid composition,
s/l.
0 72 6 2
0 64
1 9 4 8 10 4 19 6 6 30 2 0 40 5 6 48 7 Chemicals, Sydney (Batch No. 11218). 1 3 9 16 26 37 45
6 7 6 9 6 8 9
10 19 20 19 19 22
4 2 8
be deleted and replaced with radial diffusion terms in the direct mode of operation. Nomenclature
a,
D R
= = =
total particle surface/particle volume diffusivity hydraulic radius in packed bed, c/a,(l
-
E)
GREEKLETTERS a = bed void fraction outside the adsorbent particles w = frequency literature Cited
Baker, B., Pigford, R. L., IND.ENG.CHEM.,FUNDAM. 10, 283 (1971).
Mackenzie, M., B.E. Thesis, University of Queensland, Australia, 1972.
Rice, R. G., IND. ENG.CHEM., FUNDAM. 12, 406 (1973). Richardson, E. G., Tyler, E., PTOC.Phys. SOC.London
42, 1
(1929).
Schlicting, H., “Boundary Layer Theory,” 4th ed, p 230, McGraw-Hill, New York, N. Y., 1960. RICHARD G. RICE* MALCOLM MACKENZIE
Department of Chemical Engineering University of Queensland St. Lucia, Brisbane, Queensland, Australia
RECEIVED for review December 4, 1972 ACCEPTED June 18, 1972
Ind. Eng. Cham. Fundam., Vol. 12, No. 4, 1973
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