Letter pubs.acs.org/est
Letter to the Editor Regarding, “Crossing Turbulent Boundaries: Interfacial Flux in Environment Flows”
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mathematical formulas for expressing the flux are different.9 All diffusion processes fall within the chemical potential-type category including spatially averaged effective diffusion processes such as turbulent diffusion. However, the advectivetype processes are fundamentally different. The mathematical form of all advective-type flux formulas is a media velocity− concentration product. In the case of hyporheic flow, it is the product of the water velocity entering the bed and the chemical concentration at the interface plane separating the adjoining media phases. The presence of an advective-type flux equation at any juncture within the so-called mass transport circuit is theoretically incorrect when applying the RM for flux estimation, proposed axiom. Therefore the use of eqs 5 and 6 for the interfacial flux is inappropriate. Previously publications on environmental mass transport present a number of case studies that illustrate this. For example, the derived flux equation was not the RM form for a theoretical case-study that combined the processes: bed-towater column diffusion equation (a chemical potential-type), and particle settling on the water-side (an advective-type).10 The derivation procedure used was a generalized one consistent with the Lewis−Whitman two-film theory11 but reconfigured to include advective-type processes.9 It is termed the “interfacial compartment model” because it is a mass balance on the interfacial plane separating the adjoining media phases. A casestudy of chemical transport from the atmosphere to soil was also investigated.9 Upon adding the particle deposition process (an advective-type) to three chemical potential-type processes on the soil-side yielded a flux equation unlike the algebraic form of the RM formulation. Another case-study of chemical transport from the atmosphere through a vegetation plant canopy involving gas deposition (a chemical potential-type) and particle deposition failed to reproduce the “the electrical resistance analogy” algebraic formula.12 These theoretical studies on the failures of the RM for flux crossing interfacial boundaries support the proposed axiom. The original electrical circuit (Ohm’s) law13 is applied to a macroscopic system, voltage over finite length, whereas Fick’s first law of diffusion is defined for an infinitesimal length. The law (dated 1827) for electric current flux through solids is an electrical motive potential driven process and the origin of the resistance concept. Kirchoff extended it (dated 1845) to electrical currents flowing in parallel and series circuit arrangements. Lewis and Whitman (dated 1924)11 adapted the concept for a chemical potential-driven process to represent and quantify chemical flux across a gas/liquid interface. A chemical potential-driven flux employs a concentration gradient or a difference in concentrations over a finite path length. A kinetic parameter (referred to as a mass-transfer coefficient or
he following are comments regarding the Feature article entitled: “Crossing turbulent boundaries: interfacial flux in environmental flows” authored by Stanley B. Grant and Ivan Marusic.1The authors selected one of the complex environmental interfaces between media compartments on Earth, viz., the sediment/water interface, to address fluxes in environmental flows. The manuscript highlights fluid turbulence in the adjoining boundary layers on either side of the interface as the common thread to understand and quantify chemical transport. The manuscript focuses on the overall chemical transport from the water column to the bed surface and then within the bed (as a sink). It consists of two parts, one concerns water column turbulence and the other is on transport into the underlying sediment bed. Although the first part is informative, we find several theoretical problems with the processes connecting chemical transport across the interface entering the bed and within the bed. Our concern is with regard to the inconsistent applications of mass transport theory and the generalizations offered for other domains of environmental transport. The descriptions of the turbulent mass transport process on the stream side and the hyporheic exchange processes that drive mass transport on the sediment side are correctly described and the appropriate parameters given in Figure 2. The authors use the popular resistance theory and model (RM), which employs the electric circuit analogy combining series and parallel arrangements, for describing the water-to-sediment chemical flux. They use the RM correctly for the three stream side processes as given by eq 5. However, the illustration provided (Figure 2) showing the overall process and the connection between stream side and hyporheic exchange is incorrect. It depicts simultaneous side-by-side transport processes occurring in parallel in which case eq 6 is incorrect. They also offer this as a generalized principle combining mass transfer circuits tailored to a variety of environmental settings and presumably other interfaces. Invoking the resistance theory to model chemical flux and conceptualizing it as a combination of series/parallel equivalent mass transfer circuits is not always appropriate. A parallel arrangement of mass transfer resistors for the overall chemical transport process between water column and sediment bed is at odds with the conventional theory and laboratory or field evidence. It is a series process with diffusion and advective processes coupled. The series theory for bed-towater transport, in either direction, appears in textbooks and journal articles.2−5 Experimental evidence supporting the series process appears in numerous refereed publications and scholarly works.6−8 Although treating the various processes as effectively independent and parallel can result in useful empiricisms, for example ranking the relative magnitude of individual processes, it is theoretically incorrect and potentially inaccurate. A recent publication on the general subject of mass transport in the environment identified 41 significant processes.9 Twentyfour are chemical potential (Gibbs free energy)-type processes and 17 are the of the media advection-type. The respective © 2012 American Chemical Society
Received: January 9, 2012 Accepted: January 13, 2012 Published: January 30, 2012 1293
dx.doi.org/10.1021/es300040t | Environ. Sci. Technol. 2012, 46, 1293−1294
Environmental Science & Technology
Letter
(14) Monteith, J. L.; Unsworth, M. Principles of Environmental Physics, Chapter 3, 2nd Ed.; Butterworth-Heinemann, Linacre House, Jordan Hill: Oxford, U.K., 1999; p 22−23. (15) National Research Council Committee, . The Tropospheric Transport of Pollutants and Other Substances to the Oceans, Chapter 4; National Academy Press: Washington, DC, 1978; p 112−114.
conductance) is used with one on either side of the interface. Thus, the Ohm-Kirchoff and the Lewis-Whitman theories are analogous in the mathematical flux formalism. The familiar series/resistance algebraic structure is commonly referred to as Ohm’s Law.13,14 Unfortunately, the algebraic structure is misused, applying it for both potential and advective mass transport processes alike. Instances attributing the atmospheric particle deposition velocity as the reciprocal of a diffusion resistance are a persistent misuse of the Ohms’ Law.15 We agree with the authors that the RM may be a useful framework for conceptualizing complex environmental transport processes. However, based on the foregoing the general vision that mass transfer circuits and the RM can, in principle, be tailored to a variety of environmental settings is not an appropriate conclusion.
Louis Thibodeaux,* Kalliat Valsaraj Danny Reible
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AUTHOR INFORMATION
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REFERENCES
Corresponding Author
*Phone: 225 578 3055; fax: 225 578 1476; e-mail: thibod@lsu. edu. (1) Grant, S. B.; Marusic, I. Crossing turbulent boundaries: Interfacial flux in environmental flows. Environ. Sci. Technol. 2011, 45, 7107− 7113. (2) Boudreaux, B. P. Jorgensen, B. B. The Benthic Boundary LayerTransport Processes and Biogeochemistry; Oxford University Press: Oxford, U.K., 2001; Chapter 14. (3) DiToro, D. M. Sediment Flux Modeling, Chapter 2; John Wiley & Sons, Inc.: New York, 2001; p 27−29. (4) Thibodeaux, L. J. Environmental Chemodynamics, Chapter 5, 2nd Ed.; John Wiley & Sons, New York, 1996; p 323−325. (5) Hondzo, M.; Reyaerts, T.; Donovan, R.; O’Connor, B. L. Universal scale dissolved oxygen distribution at the sediment-water interface: A power law. Limnol. Oceanogr. 2005, 50 (5), 1667−1676. (6) Thibodeaux, L. J.; Bierman, V. J. The bioturbation-process driven chemical release process. Environ. Sci. Technol. 2003, 1, 253A−258A. (7) Erickson, M. J.; Turner, C. L.; Thibodeaux, L. J. Field observation and modeling of dissolved fraction-sediment-water exchange coefficients for PCBs in the Hudson River. Environ. Sci. Technol. 2005, 39, 549−555. (8) Thibodeaux, L. J.; Reible, D. D.; Valsaraj, K. T. Non-particle resuspension chemical transport from streambeds. In Chemicals In The Environment-Fate, Impacts and Remediation, ACS Symposium Series 806, Chapter 7; Lipknick, R. L., Mason, R. P., et al. Eds.; American Chemical Society, Washington, DC, 2003. (9) Thibodeaux, L. J. The flux equations for mass transport processes across interfaces. In Handbook of Chemical Mass Transport in the Environment; Thibodeaux, L. J.; Mackay, D.; Eds.; Francis and Taylor Group, UK. 2011. Chapter 4. (10) Thibodeaux, L. J.; Germano, J. Sediment-water interfaces: Chemical flux at. In Encyclopedia of Sustainability Science and Technology; Myers, R. A., Ed.; Springer Science+Business Media, LLC, 2011; DOI: 10.1007/978-1-4419-0851-3, (Accepted 17 Oct., 2011) . (11) Lewis, W. K.; Whitman, W. G. Principles of gas adsorption. Ind. Eng. Chem. 1924, 16, 1215−1220. (12) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and PhysicsFrom Air Pollution to Climate Change, Chapter 19, Section 19.2; John Wiley & Sons, Inc.: New York, 1998. (13) Campbell, G. S. An Introduction to Environmental Biophysics, Chapter 1, Transport laws; Springer-Verlag: New York, 1977. 1294
dx.doi.org/10.1021/es300040t | Environ. Sci. Technol. 2012, 46, 1293−1294
