Abstract
Mercury injection test shows that wallpaper is a porous building material with a complex fractal mass transfer channel. Therefore, fractional Fick’s law is employed to investigate sub-diffusion of 2,2,4 trimethy1-1,3-pentanediol diisobutyrate (TXIB) from wallpaper. In view of the fact that a small amount of TXIB has been released from the wallpaper before the environmental chamber experiment, the non-uniform initial concentration is introduced. Based on fractional Fick’s law, both fractional convective mass transfer equation and fractional mass balance equation have been firstly proposed. Combining the finite difference method and L1 algorithm, the fractional diffusion model is solved numerically. Numerical simulation results show that the present model matches well with the experimental data. Compared with the previous model based on Fick’s law, the present model is in better agreement with experimental data of di-2-ethylhexyl phthalate (DEHP) released from polyvinyl chloride (PVC) flooring. The influence of key parameters on the concentration of TXIB is analyzed graphically. In addition, the absorption amount and absorption rate of TXIB on the environmental bulkhead are numerically simulated for the first time.
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Alexey Z, Peter S (2018) Non-Fickian transport in porous media: always temporally anomalous. Transp Porous Media 124(2):309–323. https://doi.org/10.1007/s11242-018-1066-6
Chang A, Sun HG (2018) Time-space fractional derivative models for CO2 transport in heterogeneous media. Fract Calc Appl Anal 21(1):151–173. https://doi.org/10.1515/fca-2018-0010
Chang A, Sun HG, Zheng CM, Lu BQ, Lu CP (2018) A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs. Physica A 192:371–378. https://doi.org/10.1016/j.physa.2018.02.080
Clausen PA, Hansen V, Gunnarsen L (2004) Emission of di-2-ethylhexyl phthalate from PVC flooring into air and uptake in dust: emission and sorption experiments in FLEC and CLIMPAQ. Environ Sci Technol 38:2531–2537. https://doi.org/10.1021/es0347944
Deng BQ, Kim CN (2004) An analytical model for VOCs emission from dry building materials. Atmos Environ 38:1173–1180. https://doi.org/10.1016/j.atmosenv.2003.11.009
Eriksson AC, Andersen C, Krais AM, Clausen PA, Gudmundsson A, Wierzbicka A, Pagels J (2020) Influence of airborne particles chemical composition on SVOC uptake from PVC flooring-time resolved analysis with aerosol mass spectrometry. Environ Sci Technol 54:85–91. https://doi.org/10.1021/acs.est.9b04159
Fan GT, Xie JC (2018) Common SVOCs in house dust from urban dwellings with schoolchildren in six typical cities of China and associated non-dietary exposure and health risk assessment. Environ Int 120:431–442. https://doi.org/10.1016/j.envint.2018.08.031
Gallon V, Gann PL, Sanchez M, Dematteo C, Bot BL (2020) Emission of VOCs, SVOCs, and mold during the construction process: contribution to indoor air quality and future occupants’ exposure. Indoor Air 30(4):691–710. https://doi.org/10.1111/ina.12647
Johnston CJ, Andersen RK, Toftum J, Nielsen TR (2020) Effect of formaldehyde on ventilation rate and energy demand in Danish home: development of emission models and building performance simulation. Build Simul 12:197–212. https://doi.org/10.1007/s12273-019-0553-1
Kong LY, Mehdi O, Liu B, Li CX, Liu KQ (2019) Multifractal characteristics of MIP-based pore size distribution of 3D-printed powder-based rocks: a study of post-processing effect. Transp Porous Media 139(2):599–618. https://doi.org/10.1007/s11242-018-1152-9
Lim J, Kim S, Kim S, Lee W, Han J, Cha JS (2014) Behavior of VOCs and carbonyl compounds emission from different types of wallpapers in Korea. Int J Environ Res Public Health 11(4):4326–4339. https://doi.org/10.3390/ijerph110404326
Little JC, Hodgson AT, Gadgil AJ (1994) Modeling emissions of volatile organic compounds from new carpets. Atmos Environ 28(2):227–234
Liu F, Anh V, Turner I (2004) Numerical solution of the space fractional Fokker-Planck equation. J Comput Appl Math 166(1):209–219. https://doi.org/10.1016/j.cam.2003.09.028
Liu F, Burrage K (2011) Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Comput Math Appl 62(3):822–833. https://doi.org/10.1016/j.camwa.2011.03.002
Liu FW, Zhuang P, Burrage K (2012) Numerical methods and analysis for a class of fractional advection–dispersion models. Comput Appl Math 64:2990–3007
Liu YF, Zhou XJ, Wang DJ, Song C, Liu JP (2015) A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory. J Hazard 299:685–695. https://doi.org/10.1016/j.jhazmat.2015.08.002
Manoukian A, Buiron D, Temime RB, Wortham H, Quivet E (2016) Measurements of VOC/SVOC emission factors from burning incenses in an environmental test chamber: influence of temperature, relative humidity, and air exchange rate. Environ Sci Pollut Res 23(7):6300–6311. https://doi.org/10.1007/s11356-015-5819-2
Matsumoto M, Hirata KM, Ema M (2008) Potential adverse effects of phthalic acid esters on human health: a review of recent studies on reproduction. Regul Toxicol Pharmacol: RTP 50:37–49. https://doi.org/10.1016/j.yrtph.2007.09.004
Matthew P, Joshua F (2021) Measuring gas transport and sorption in large intact geologic specimens via the piezometric method. Transp Porous Media 139:1–20. https://doi.org/10.1007/s11242-021-01627-w
Nelder JA, Mead RA (1965) A simplex method for function minimization. Computer Journal 7:308–313. https://doi.org/10.1093/comjnl/7.4.308
Shao HY, Zhang ZC, Chai JF, Xu G, Tang L, Wu MH (2020) Pollution characteristics and underlying ecological risks of primary semi-volatile organic compounds (SVOCs) in urban watersheds of Shanghai, China. Environ Sci Pollut Res 27(22):27708–27720. https://doi.org/10.1007/s11356-020-08528-3
Shelokar PS, Siarry P, Jayaraman VK, Kulkarni BD (2007) Particle swarm and colony algorithms hybridized for improved continuous optimization. Appl Math Comput 188:129–142. https://doi.org/10.1016/j.amc.2006.09.098
Shinohara N, Mizukoshi A, Uchiyama M, Tanaka H (2019) Emission characteristics of diethylhexyl phthalate (DEHP) from building materials determined using a passive flux sampler and micro-chamber. PLoS One 14(9):e0222557. https://doi.org/10.1371/journal.pone.0222557
Shinohara N, Uchino K (2020) Diethylhexyl phthalate (DEHP) emission to indoor air and transfer to house dust from a PVC sheet. Sci Total Environ 711:134–573. https://doi.org/10.1016/j.scitotenv.2019.134573
Swan SH, Main KM, Liu F, Stewart SL, Kruse RL, Calafat AM (2005) Decrease in anogenital distance among male infants with prenatal phthalate exposure. Environ Health Perspect 113:1056–1061. https://doi.org/10.1289/ehp.8100
Takeuchi SJ, Toshiko TK, Saito I, Hiroyuki K, Kazuo J, Masayuki S, Satoshi K, Hideto J (2018) Differential determination of plasticizers and organophosphorus flame retardants in residential indoor air in Japan. Environ Sci Pollut Res 25(8):7113–7120. https://doi.org/10.1007/s11356-015-4858-z
Wei WJ, Dassonville C, Sivanantham S, Gregoire A, Mercier F (2021) Semivolatile organic compounds in French schools: partitioning between the gas phase, airborne particles and settled dust. Indoor Air 31(1):156–169. https://doi.org/10.1111/ina.12724
Wen ZH, Wang Q, Ren JG, Zhang LY, Yuan YW (2021) Dynamic gas diffusion model of capillary pores in a coal particle based on pore fractal characteristics. Transp Porous Media 140:1–20. https://doi.org/10.1007/s11242-021-01703-1
Wu MH, Yang XX, Xu G, Que CJ, Ma CH, Tang L (2017) Semivolatile organic compounds in surface microlayer and subsurface water of Dianshan Lake, Shanghai, China: implications for accumulation and interrelationship. Environ Sci Pollut Res 24(7):6572–6580. https://doi.org/10.1007/s11356-016-8308-3
Wu YX, Cox SS (2016) A reference method for measuring emissions of SVOCs in small chambers. Build Environ 95:126–132. https://doi.org/10.1016/j.buildenv.2015.08.025
Xiong JY, Cao JP, Zhang YP (2016) Early stage C-history method: rapid and accurate determination of the key SVOC emission or sorption parameters of indoor materials. Build Environ 95:314–321. https://doi.org/10.1016/j.buildenv.2015.09.027
Xu Y, Liu Z, Park J, Clausen PA, Benning JL, Little JC (2012) Measuring and predicting the emission rate of phthalate plasticizer from vinyl flooring in a specially-designed chamber. Environ Sci Technol 46:12534–12541. https://doi.org/10.1021/es302319m
Xu Y, Little JC (2006) Predicting emissions of SVOCs from polymeric materials and their interaction with airborne particles. Environ Sci Technol 40:456–461. https://doi.org/10.1021/es051517j
Yang T, Wang HM, Zhang XK (2020) Characterization of phthalates in sink and source materials: measurement methods and the impact on exposure assessment. J Hazard Mater 396:122–689. https://doi.org/10.1016/j.jhazmat.2020.122689
Yu BM, Lee LJ, Cao HQ (2002) A fractal in-plane permeability model for fabrics. Polym Compos 23(2):201–221. https://doi.org/10.1002/pc.10426
Zhokh AA, Trypolskyi AI, Strizhak PE (2017) An investigation of anomalous time-fractional diffusion of isopropyl alcohol in mesoporous silica. Int J Heat Mass Transf 104:493–502. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.095
Zhou HW, Yang S, Zhang SQ (2018) Conformable derivative approach to anomalous diffusion. Physica A 491:1001–1013. https://doi.org/10.1016/j.physa.2017.09.101
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This research was funded by the National Natural Science Foundation of China (21878018 and 22178022).
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YZ: model building. ML: numerical simulation, experimental operation, writing—original draft. YW: parameter estimation, data analysis. YB: writing—review and editing. All authors read and approved the final manuscript.
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Zhang, Y., Liu, M., Wu, Y. et al. Fractional diffusion model for emission and adsorption prediction of TXIB from wallpaper. Environ Sci Pollut Res 29, 81777–81788 (2022). https://doi.org/10.1007/s11356-022-21436-y
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DOI: https://doi.org/10.1007/s11356-022-21436-y