Ind. Eng. Chem. Res. 2003, 42, 5697-5701
5697
RESEARCH NOTES Mass Transport in Cross-Corrugated Membranes and the Influence of TiO2 for Separation Processes Keith Scott† and Justo Lobato*,‡ School of Chemical Engineering and Advanced Materials, University of Newcastle upon Tyne, Merz Court NE1 7RU, U.K., and Faculty of Chemistry, Department of Chemical Engineering, University of Castilla-La Mancha, Campus Universitario s/n, 13004 Ciudad Real, Spain
This study was carried out to improve our knowledge on the effect of cross-corrugated membranes as turbulence promoters and on the influence of solid (TiO2) in the fluid on mass transport behavior in cross-corrugated membrane systems. The electrochemical limiting-current technique has been employed to determine mass-transfer coefficients. The influence of cross-corrugated flow channels and the orientation of flow to the angle of corrugation (0°, 45°, and 90°) on the mass-transfer coefficient are reported. The effect of TiO2 and viscosity on the mass transport has been investigated using different percentages of TiO2, from 0.025% to 0.1%, and two values of viscosity, 1.0 × 10-3 and 1.9 × 10-3 kg m-1 s-1 (Sc ) 1483 and 4997, respectively). It was observed that, as the viscosity increases, the mass transport coefficient decreases. The presence of TiO2 implies slightly decreased values of the mass-transfer coefficient. The mass-transfer correlation showed that, at low values of Reynolds number (values of the Reynolds number in the range of 100-1400), laminar flow conditions do not exist. 1. Introduction The measurement of a limiting-current diffusioncontrolled process provides a versatile and accurate technique for the determination of mass- and heattransfer rates and the investigation of certain hydrodynamic phenomena.1 Various systems have been suggested. Typically, the cathodic reduction of ferricyanide ions to ferrocyanide ions at an inert electrode has been chosen:
Fe(CN)6-3 + e- f Fe(CN)6-4
(1)
The reverse reaction may again proceed at the anode, so that again the bulk concentration of the electro-active species remains unchanged. The method has been applied in a wide variety of geometric and hydrodynamic situations.2-4 The technique has been used for measuring the masstransfer rate between a fluid and a solid surface in different electrochemical units, such as electrochemical reactors3 or a water-oil full pipe for corrosion studies.5,6 This work reports experimental results obtained for a hydrodynamic study of cross-corrugated surfaces with different angles of flow to the direction of the corrugation (0°, 45°, and 90°) used as turbulence promoters, studying the influence on the mass transport to the electrode with electrochemical techniques.7 The data * To whom correspondence should be addressed. Tel.: +34 926 29 53 00. Fax: +34 926 29 53 18. E-mail: Justo.Lobato@ uclm.es;
[email protected]. † University of Newcastle upon Tyne. ‡ University of Castilla-La Mancha.
presented here represent the first step in the design and characterization of the application of cross-corrugated membrane modules for microfiltration, ultrafiltration, and other membrane separations and are the continuance of previous works.8,9 This work shows the influence of TiO2 on the mass transport rate using different percentages of TiO2, from 0.025% to 0.1%, to know how the presence of insoluble solids would affect mass transport in membrane separations. Experiments were also carried out with different viscosities to study the influence of the Schmidt number. Correlations relating the Reynolds, Schmidt, and Sherwood numbers for the cross-corrugated module were established. 2. Experimental Section In this work, as has been mentioned above, reaction (1) has been chosen because of the large limiting-current plateau and the unchanging nature of the electrode surface geometry. Maintaining conditions conducive to electrolyte stability is vital with this system, and thus light and dissolved oxygen were excluded from the system. The mass-transfer coefficient, k, is determined from the limiting-current density iL using
k ) iL/zFCb
(2)
A cell fabricated from acrylic was used to emulate the cross-flow membrane unit with “membrane simulants” constructed of Perspex plates as shown in Figure 1, giving visibility through the unit. Two corrugated sheets, 67 mm × 35 mm, were used and placed at 90°
10.1021/ie030374b CCC: $25.00 © 2003 American Chemical Society Published on Web 09/25/2003
5698 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003
Figure 1. (a) Scheme of the electrolytic cell and corrugated membranes (nonscale). (b) Angles between the corrugation and the flow direction, for example, 0° and 90°.
to each other. The corrugations were 1 mm deep and 2 mm wide, and the shape was triangular. An EG&G Princeton Applied Research VersaStat was used to conduct the electrochemical reaction using linear sweep voltammetry. The data were logged using EG&G model 270 Research Electrochemistry Software. In this study, the electrolyte composition was 0.3 M Na2CO3, 0.01 M K3Fe(CN)6, and 0.1 M K4Fe(CN)6. A thin nickel cathode, 10 mm × 10 mm, was pressed into one of the membrane plates to take the shape of the corrugations. Figure 2 shows a scanning electron microscopy picture of the electrode, where the flow directions of 0°, 45°, and 90° are indicated. A smooth nickel electrode of 4 times the surface area of the cathode was used as the anode. Because the cathode was smaller and the ferricyanide ion concentration was less than that of ferrocyanide, the process occurring at the cathode controlled the cell current. The back of the cathode was coated with an insulating paint, and an electrical connection was established at the side edge to avoid interference with the flow pattern. Nitrogen was bubbled through the electrolyte to expel dissolved oxygen. At a constant flow rate, a slow linear potential sweep was applied to the cell, and the corresponding currents were measured. Once the cell voltage range at which the limiting-current occurred was identified, the process was repeated for a range of flow rates. The flow between the corrugations was at one of three angles to the nickel-
Figure 2. Details of the angle channels of the corrugated electrodes: (a) 0°; (b) 45°; (c) 90°.
corrugated electrode: (1) at 0° to the corrugation at the electrode, i.e., along the rough of the corrugation, (2) at 45° to the corrugation at the electrode, and (3) at 90° to the corrugation at the electrode, over the ribs of the corrugation. The corrugated membrane plates were crossed as follows: (1) 0° cross with 90°; (2) 90° cross with 0°; (3) 45° cross with 90°; (4) 90° cross with 45 °, where the first angle indicates the angle of the corrugation of the surface in which the electrode was pressed. The mean particle size of TiO2 used was 0.332 µm. Large variations in the Schmidt number, often required for transport studies, are best obtained by modifying the viscosity of the electrolyte, for example, by the addition of glycerin oil to the aqueous electrolyte. With no glycerin, Sc equals 1483, and 25% glycerin yields a Sc value of 4997. 3. Results and Discussion 3.1. Effect of TiO2. Figure 3 shows the variation in the mass-transfer coefficient with the Reynolds numbers for a surface 0° cross-corrugated with 90° and different percentages of TiO2, for both Schmidt numbers studied,
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Figure 3. Mass-transfer coefficients at Reynolds numbers for the system 0° cross-corrugated with 90° and different percentages of TiO2: (a) Schmidt number of 1483; (b) Schmidt number of 4997.
1483 and 4997. It can be seen that the presence of TiO2 in the solution for both Schmidt numbers studied decreased the mass-transfer coefficients. This was due to poor circulation of TiO2 over the corrugated surfaces of the cell and small deposits forming on the cathode. So, the effective area of the cathode for the reduction of ferricyanide was reduced, resulting in a lower limiting current. Consequently, the calculated value of k, using eq 2, became lower with increases in the concentration of TiO2 because of the use of the total area of the cathode in place of the effective area for mass transfer. It is rather difficult to determine the effective area. Similar results were observed when the surfaces were 90° cross-corrugated with 0° (Figure 4). In this case, for a Schmidt number of 1483, the mass-transfer coefficient was found to be almost independent of the concentration of TiO2 particles (Figure 3a). This is due to greater turbulence due to the ribs of the surfaces. Figures 5 and 6 show the variation in the masstransfer coefficient with the Reynolds numbers for a corrugated surface 45° cross-corrugated with 90° and 90° cross-corrugated with 45°, respectively, and different percentages of TiO2, from 0% to 0.1%, of solid for the Schmidt numbers studied, 1483 and 4997. In this configuration, there was a small decrease in the masstransfer coefficient when TiO2 was present. It was reported9 that the turbulence created by the system of a cross-corrugated plate of 90° with 45° was the best of all of the systems studied; therefore, the deposition of
Figure 4. Mass-transfer coefficients at Reynolds numbers for the system 90° cross-corrugated with 0° and different percentages of TiO2: (a) Schmidt number of 1483; (b) Schmidt number of 4997.
Figure 5. Mass-transfer coefficients at Reynolds numbers and Schmidt numbers of 1483 and 4997, for the system 45° crosscorrugated with 90°.
TiO2 would be lower and hence the decrease in the mass transport would be lower, as has been observed. 3.2. Correlation of Data. A correlation relating the Reynolds, Sherwood, and Schmidt dimensionless numbers for the cross-corrugated modules, 90° cross-corrugated with 0° and 90° cross-corrugated with 45°, was established.8-13 This work attempted to evaluate the use of cross-corrugated membranes to promote turbulence in regions of relatively low Reynolds numbers and the
5700 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 Table 1. Values of the Constant c, the Exponent a, and the Correlation Coefficient r for a Membrane 90° Cross-Corrugated with 0° and Different Percentages of TiO2 Sc
% TiO2
c
a
r
1483 1483 1483 4997 4997
0 0.05 0.1 0 0.1
0.268 0.223 0.231 0.395 0.593
0.56 0.58 0.58 0.50 0.44
0.998 0.997 0.996 0.999 0.991
Table 2. Values of the Constant c, the Exponent a, and the Correlation Coefficient r for a Membrane 90° Cross-Corrugated with 45° and Different Percentages of TiO2
Figure 6. Mass-transfer coefficients at Reynolds numbers and Schmidt numbers of 1483 and 4997, for the system 90° crosscorrugated with 45°.
Sc
% TiO2
c
a
r
1483 1483 1483 4997 4997
0 0.05 0.1 0 0.1
0.368 0.279 0.359 0.487 0.409
0.57 0.62 0.58 0.52 0.55
0.998 0.960 0.998 0.997 0.998
sponding to a system exhibiting turbulent characteristics:
Sh ) 0.368Re0.58Sc0.333
(5)
Tables 1 and 2 show the results of the correlation for these two systems studied. In all cases, the data fitted a typical equation for turbulent flows. 4. Conclusions
Figure 7. Experimental data and best fit of equations assuming laminar and turbulent conditions, for the system 90° crosscorrugated with 45° and with a Schmidt number of 1483.
influence of SiO2 on the mass transport of such membranes. The Leveque-type relationship is valid to correlate mass transfer along the surface of the membrane channels under laminar conditions (Re < 2100):8
(
)
dh x
Sh ) C Re × Sc
0.333
(3)
where dh is the equivalent diameter of the channel (4 × area/perimeter), which was used as the characteristic length to calculate the Reynolds and Sherwood numbers, C is a constant that depends on the geometry of the cell, and x is the distance from the leading edge. The following equation, valid for mass-transfer entrance in turbulent channel flow,12 was used to correlate the data assuming turbulent conditions:
Sh ) cReaSc0.333
(4)
where c is a constant. Figure 7 shows, as an example, the correlation of experimental data for a system of 90° cross-corrugated with 45°, a Schmidt number of 1483, without TiO2, and compares this with the theoretical Leveque equation, for laminar flow. It can be concluded that the data do not fit the Leveque equation but fit an equation corre-
Mass transport coefficients have been calculated at the surface of cross-corrugated plates, with different angles of liquid flow. The turbulence created by the system of a plate of 90° cross-corrugated with 45° was greater and hence the most important of all of the systems studied. The study showed that an increase in the viscosity produced a decrease in the mass-transfer coefficient at the same range of Reynolds number. The presence of TiO2 produced a decrease in the mass transport coefficient for a Schmidt number of 4997. For the system formed by the plate of 90° cross-corrugated with 45°, there was no decrease in the mass transport in the presence of TiO2 because of the higher turbulence created by this system. The mass transport correlation showed that the laminar flow regime, normally associated with low Reynolds number, does not represent the conditions in the cross-corrugated module. It is likely that the irregular flow path caused by the membrane corrugation enhanced mass transfer to the extent that turbulent flow conditions become applicable. Nomenclature Cb ) bulk reactant concentration (mol m-3) dh ) equivalent diameter (m) iL ) limiting-current density (A m-2) F ) Faraday’s constant (96 501 C mol-1) k ) mass-transfer coefficient (m s-1) Re ) Reynolds number Sc ) Schmidt number Sh ) Sherwood number x ) distance from the leading edge (m) z ) number of electrons associated with the reaction (in the ferricyanide-ferrocyanide system, it is 1)
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Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5701 (2) Krishma, P. G.; Chakravarty, K.; Ramabrahmam, G.; SubbaRao, D.; Venakateswarlu, P. Ionic Mass Transfer in the Presence of Turbulence Promoters in a Circular Conduct. Int. Commun. Heat Mass Transfer 2001, 28, 499-508. (3) Trinidad, P.; Walsh, F. C.; Gilroy, D. Conversion Expressions for Electrochemical Reactors which Operate under Mass Transport Controlled Reaction Conditions, Part I: Batch Reactor, PFR and CSTRS. Int. J. Eng. 1998, 14, 431-441. (4) Doan, H. D.; Fayed, M. E.; Trass, O. Measurements of Local and Overall Mass-Transfer Coefficients to a Sphere in a Quiescent Liquid using a Limiting Current Technique. Chem. Eng. J. 2001, 81, 53-61. (5) Wang, H.; Hong, T.; Cai, J. Y.; Dewald, H. D.; Jepson, W. P. Enhancement of the Instantaneous Mass-Transfer Coefficient in Large Diameter Pipeline under Water/Oil Flow. J. Electrochem. Soc. 2000, 147, 2552-2555. (6) Wang, H.; Vedapuri, D.; Hong, T.; Cai, J. Y.; Jepson, W. P. Mass-Transfer Coefficient Measurement in Water/Oil/Gas Multiphase Flow. The ASME J. Energy Resour. Technol. 2001, 123, 144-149. (7) Wragg, A. A.; Leontaris, A. A. Mass Transfer Measurements in a Parallel Cell Using The Limiting Current Technique. DECHEMA Monogr. 1991, 123, 345.
(8) Scott, K.; Lobato, J. Mass Transfer Characteristics of CrossCorrugated Membranes. Desalination 2002, 146, 255-258. (9) Scott, K.; Lobato, J. J. Appl. Electrochem. 2002, submitted for publication. (10) Heitzand, E.; Kreysa, G. Principles of Electrochemical Engineering; VCH: Weinheim, Germany, 1986. (11) Selman, J. R.; Tobias, C. W. Measurements of Mass Transfer by the Limiting Current Technique. Adv. Chem Eng. 1978, 10, 211-318. (12) Scott, K.; Lobato, J. Determination of a Mass-Transfer Coefficient Using the Limiting Current Technique. Chem. Educ. 2002, 7, 214-219. (13) Gonza´lez-Garcı´a, J.; Frı´as, A.; Expo´xito, E.; Montiel, V.; Aldaz, A.; Conesa, J. A. Characterization of an Electrochemical Pilot-Plant Filter-Press Reactor by Hydrodynamic and Mass Transport Studies. Ind. Eng. Chem. Res. 2000, 39, 1132-1142.
Received for review April 30, 2003 Revised manuscript received August 12, 2003 Accepted September 3, 2003 IE030374B
