Correspondence Comment on “Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media” In a recent publication, Tufenkji and Elimelech (1) present a correlation for particle collection efficiency in granular media, purportedly to provide a predictive capability that “overcomes the limitation of current approaches” [specifically, those by Yao et al. (2) and Rajagopalan and Tien (3), although the one by Yoshimura (4) was not mentioned] “over a wide range of conditions commonly encountered in natural and engineered systems”. Here, we offer some remarks in order to provide a proper context to better understand and assess the work of Tufenkji and Elimelech (1) and to draw attention to their misunderstandings concerning earlier studies. Improvements over existing correlations can be sought for two reasons: (i) to expand the range of applicability and (ii) to give better prediction. For the type of correlations presented by refs 1 and 3, one begins with an idealized model system (i.e., a porous media model, simplified hydrodynamics, a model dispersion with uniform and identical particles, etc.) for which the deposition rate is calculated. In developing such correlations, one faces two broad issues: (i) First, what level of “accuracy” should one seek or demand in developing correlations for the collector efficiency? One should bear in mind that the level of accuracy that can be demanded from correlations is dictated by the accuracy of experimental collection efficiencies the correlating equations are designed to estimate. (ii) What level of details should one demand from the idealized models used? Any idealized models inevitably differ substantially from the real systems for which the correlation is eventually used. The primary objective of a correlation is to capture the essential physics of the factors that determine the deposition rate. The purpose is not to mimic the model system used exactly. Does generating simulated data from simplified models “exactly” lead to a correlation capable of “predicting” practical situations known for wide variability? The answer, clearly, is “No”. Regarding the work of Tufenkji and Elimelech (1) specifically, we offer the following comments. Accuracy of Experimental Data. The effects of porous media on predicting particle collection have been examined previously; see Tables 4.4.A, 4.4.B, and 7.4 of Tien (ref 5; pp 126-127 and 233). As shown in these tables, under identical conditions η can fluctuate by as much as a factor of 2 or even greater. The same conclusion was also found by Chang and co-workers from simulations based on the Langevin equation (6-8). These results demonstrate unequivocally the limitations in using simple models for predicting particle collection. Therefore, it makes no sense to seek an extremely high level of accuracy between the correlation and the simulated model data. Indeed, because of these considerations, the Rajagopalan and Tien (3) or RT equation did not seek to obtain an “exact” correlation based on complete trajectory equation. Furthermore, for the correlation they obtained, Rajagopalan and Tien (3) chose to round off the exponents of various dimensionless groups to simple ratios instead of using decimal numbers of multiple digits. Doing as Tufenkji and Elimelech (1) did would certainly improve the agreement 5494
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between model calculations and the estimates based on the correlating equationsbut what is the value of such “improvements”? Tufenkji-Elimelech Results. A number of points concerning the comparisons presented by Tufenkji and Elimelech (1) call into question their conclusions. The collector efficiency used by Tufenkji and Elimelech (1) is based on the amount of particles convected through a Happel cell. However, the single-collector efficiency of Tufenkji and Elimelech (1) is based on the amount convected through the projected area of the collector. For a proper comparison, this difference must be considered. Similarly, in comparisons with experimental data, the quantities to be compared must be similarly (and consistently) defined. It is unclear whether Tufenkji and Elimelech (1) fully recognized this fact, as also noted by Nelson (9). Figure 4 in ref 1 gives a comparison of some selected experimental data with predictions from the various correlations. First, it is not clear whether the same data were used in their comparisons. In both panels b and c of Figure 4, the largest ηexp values are about 0.0055. But these data do not appear in Figure 4a. Moreover, when statistical reasons are used to claim better prediction, one should present both the experimental errors and the estimation errors. Under certain conditions, a 10-15% variation in NR can lead to variations of the order of 0.001 or more in η; therefore, significantly reducing the “accuracy” of the statistical fit shown in Figure 4c. Further, in Figure 4b, which compares the RT equation with data, small changes in certain parameters can easily shift the predictions for ηRT of the four data points on the far right sufficiently to the left thereby improving the predictions. It seems what parameters are chosen and how they are determined could lead to significant differences in the final results. Finally, the Tufenkji and Elimelech (1) correlation applies only in the absence of the double layer forces. It is difficult to envision that there are many natural aquatic systems in which the surfaces of the relevant entities of interest are not charged and dissolved ionic species are not present. On the basis of what is stated above and what we know about the accuracy of the experimental determination of particle collection, the difference between the new correlation and the previous Rajagopalan and Tien (3) equation is hardly significant. In terms of the range of applicability, the Rajagopalan and Tien (3) correlation, at least, is marginally better. Some Other Related Issues. Definition of Efficiencies. Tufenkji and Elimelech (1) used misleading terms such as “single-collector contact efficiency”, “single-collector removal efficiency”, “empirical attachment efficiency”, etc. that are redundant and examples of poor semantic exercises. In general, when an impinging particle contacts a collector, it may bounce off (as in the case of aerosols under certain circumstances). To account for this, the so-called “adhesion probability” has been introduced (see p 209 in ref 5). However, for hydrosol deposition, because of low particle inertia, particle contact inevitably leads to deposition. In particular, the repulsive force barrier does not make it difficult for contacting particles to stick to the collector. Rather, it reduces the extent of arrival of the particle to the collector and therefore reduces deposition. The factor R is the ratio of η in the presence of repulsive interactions to η in the absence of the repulsive barrier and represents the reduction in collection due to repulsive forces. 10.1021/es050309o CCC: $30.25
2005 American Chemical Society Published on Web 06/07/2005
Unfavorable Surface Forces. We are also perplexed by the statement regarding estimating the collector efficiency under unfavorable surface interactions. The various available correlations for R (10-13) were not mentioned, even though one of the authors himself gave a correlation. The suggestion that one should first determine R experimentally and then estimate η from the product of R and η0 utterly makes no sense. Determining R requires the determination of η. If experimental value of η is available, there is no need for any correlations.
Literature Cited (1) Tufenkji, N.; Elimelech, M. Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ. Sci. Technol. 2004, 38, 529536. (2) Yao, K. M.; Habibian, M. T.; O’Melia, C. R. Water and wastewater filtrationsconcepts and applications. Environ. Sci. Technol. 1971, 5, 1105-1112. (3) Rajagopalan, R.; Tien, C. Trajectory analysis of deep-bed filtration with sphere-in-cell porous-media model. AIChE J. 1976, 22, 523-533. (4) Yoshimura, Y. Initial particle collection mechanism in clean deep bed filtration. D.Eng. Dissertation, Kyoto University, Kyoto, Japan, 1980; see also p 234 of ref 5. (5) Tien, C. Granular Filtration of Aerosols and Hydrosols; Butterworth: Stoneham, MA, 1989. (6) Chang, Y. I.; Whang, J. J. Deposition of Brownian particles in the presence of DLVO theory: effect of dimensionless groups. Chem. Eng. Sci. 1998, 53, 3423. (7) Chang, Y. I.; Chern, S. C.; Chern, D. K. Hydrodynamic field effect on Brownian particle deposition in porous media. Sep. Purif. Technol. 2002, 27, 97.
(8) Chang, Y. I.; Du, C. L.; Chen, S. W.; Chen, S. C. Effect of the energy barrier of DLVO theory on the deposition of Brownian particle in porous media using the constricted tube model. Chin. Inst. Chem. Eng. 2004, 35, 65. (9) Nelson, K. E. A Lagrangian method for investigating bacterial transport and adhesionin the colloid filtration theory. Ph.D. Dissertation, University of California, Davis, CA, 2004. (10) Vaidyanathan, R.; Tien, C. Hydrosol deposition in granular beds-An experimental study. Chem. Eng. Commun. 1989, 81, 2. (11) Elimelech, M. Predicting collision efficiencies of colloidal particles in porous media. Water Res. 1992, 26, 1. (12) Bai, R.; Tien, C. A new correlation for the initial filter coefficient under unfavorable surface interactions. J. Colloid Interface Sci. 1996, 179, 631. (13) Bai, R.; Tien, C. Particle deposition under unfavorable surface interactions. J. Colloid Interface Sci. 1999, 218, 448.
Raj Rajagopalan Environmental Science and Engineering Program & Department of Chemical and Biomolecular Engineering National University of Singapore Singapore 117516
Chi Tien* Department of Biomedical and Chemical Engineering Syracuse University Syracuse, New York 13244 ES050309O
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