Correspondence/Rebuttal pubs.acs.org/est
Response to Comment on “Predicting the Migration Rate of Dialkyl Organotins from PVC Pipe into Water”
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e thank Li for his interest in our work and thoughtful comments relating to the manuscript by Adams et al.1 That paper reports an attempt to predict the migration rate of alkyl groups dimethyl tin (DMT) and dibutyl tin (DBT) from polyvinyl chloride (PVC) pipe into drinking water using a simple diffusion model. We are pleased to find that, through a scale analysis, Li confirmed our model assumption that the curvature of the pipe can be ignored and that a Cartesian coordinate system is appropriate. Li also simplified our model solution (eq 3 in Li’s correspondence) and pointed out that it is applicable to other situations where chemical pollutants have very small mass diffusivities, including, for example, transport of formaldehyde, volatile organic compounds (VOCs) and semivolatile organic compounds (SVOCs) from indoor materials into air. However, we would like to address some of the limitations inherent in his simplification. The important simplifying assumption is that L/(Dt)1/2 ≫ 1, where D is diffusivity, L is material thickness and t is emission time, but this does not apply under all practical conditions. For example, a typical D value for VOCs in building materials is in the range of 10−11 m2/s to 10−13 m2/s.2,3 Assuming a material thickness of 1−5 mm and an emission time period of hundreds of hours,4 the assumption will not be valid. Moreover, for the case of small D or large L, the emission period t will be long, and thus may also prevent the satisfaction of the simplifying assumption. Furthermore, while our model (eq 7 and 8 in ref 1) was used to predict concentrations for a batch system as used in our experimental study,1 it can also be used for a completely mixed flow-through system, which is more common in real applications, by adjusting the mass balance equation (eq 8). In contrast, Li’s solution combines all equations in the model (eq 1 through 8) and can only be used in closed systems without continuous flow. We therefore appreciate Li’s comments and useful simplification, but we also caution readers to carefully examine the experimental conditions before using the simplified solution.
REFERENCES
(1) Adams, W. A.; Xu, Y.; Little, J. C.; Fristachi, A. F.; Rice, G. E.; Impellitteri, C. A. Predicting the migration rate of dialkyl organotins from PVC pipe into water. Environ. Sci. Technol. 2011, 45 (16), 6902− 6907. (2) Cox, S. S.; Zhao, D. Y.; Little, J. C. Measuring partition and diffusion coefficients for volatile organic compounds in vinyl flooring. Atmos. Environ. 2001, 35 (22), 3823−3830. (3) Xu, Y.; Zhang, Y. P. An improved mass transfer based model for analyzing VOC emissions from building materials. Atmos. Environ. 2003, 37 (18), 2497−2505. (4) Zhang, Y. P.; Luo, X. X.; Wang, X. K.; Qian, K.; Zhao, R. Y. Influence of temperature on formaldehyde emission parameters of dry building materials. Atmos. Environ. 2007, 41 (15), 3203−3216.
Ying Xu†,* John C. Little‡ †
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Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas, United States ‡ Department of Civil & Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States
AUTHOR INFORMATION
Corresponding Author
*Phone: 512-471-6507; e-mail:
[email protected]. Notes
The authors declare no competing financial interest. © 2012 American Chemical Society
Published: February 21, 2012 4252
dx.doi.org/10.1021/es3006628 | Environ. Sci. Technol. 2012, 46, 4252−4252
