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• W3169893078 abstract "A novel stochastic model is proposed to characterize the adsorption kinetics of pollutants including dyes (direct red 80 and direct blue 1), fluoride ions, and cadmium ions removed by calcium pectinate (Pec-Ca), aluminum xanthanate (Xant-Al), and reed leaves, respectively. The model is based on a transformation over time following the Ornstein–Uhlenbeck stochastic process, which explicitly includes the uncertainty involved in the adsorption process. The model includes stochastic versions of the pseudo-first-order (PFO), pseudo-second-order (PSO), and pseudo- <math xmlns=http://www.w3.org/1998/Math/MathML id=M1><mi>n</mi></math> -order (PNO) models. It also allows the estimation of the adsorption parameters, including the maximum removal capacity ( <math xmlns=http://www.w3.org/1998/Math/MathML id=M2><msub><mrow><mi>q</mi></mrow><mrow><mi>e</mi></mrow></msub></math> ), the adsorption rate constant ( <math xmlns=http://www.w3.org/1998/Math/MathML id=M3><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math> ), the reaction pseudoorder ( <math xmlns=http://www.w3.org/1998/Math/MathML id=M4><mi>n</mi></math> ), and the variability <math xmlns=http://www.w3.org/1998/Math/MathML id=M5><mfenced open=( close=)><mrow><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math> . The model fitted produced <math xmlns=http://www.w3.org/1998/Math/MathML id=M6><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> values similar to those of the nonstochastic versions of the PFO, PSO, and PNO models; however, the obtained values for each parameter indicate that the stochastic model better reproduces the experimental data. The <math xmlns=http://www.w3.org/1998/Math/MathML id=M7><msub><mrow><mi>q</mi></mrow><mrow><mi>e</mi></mrow></msub></math> values of the Pec-Ca-dye, Xant-Al-fluoride, and reed leaf-Cd+2 systems ranged from 2.0 to 9.7, 0.41 to 1.9, and 0.04 and 0.29 mg/g, respectively, whereas the values of <math xmlns=http://www.w3.org/1998/Math/MathML id=M8><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math> ranged from 0.051 to 0.286, 0.743 to 75.73, and 0.756 to 8.861 (mg/g)1-n/min, respectively. These results suggest a variability in the parameters <math xmlns=http://www.w3.org/1998/Math/MathML id=M9><msub><mrow><mi>q</mi></mrow><mrow><mi>e</mi></mrow></msub></math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M10><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math> inherent to the natures of the adsorbate and adsorbent. The obtained <math xmlns=http://www.w3.org/1998/Math/MathML id=M11><mi>n</mi></math> values ranged from 1.13 to 2.02 for the Pec-Ca-dye system, 1.0–3.5 for the Xant-Al-fluoride system, and 1.8–3.8 for the reed leaf-Cd+2 system. These ranges indicate the flexibility of the stochastic model to obtain fractional <math xmlns=http://www.w3.org/1998/Math/MathML id=M12><mi>n</mi></math> values, resulting in high <math xmlns=http://www.w3.org/1998/Math/MathML id=M13><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> values. The variability in each system was evaluated based on <math xmlns=http://www.w3.org/1998/Math/MathML id=M14><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> . The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation." @default.
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• W3169893078 date "2021-05-27" @default.
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• W3169893078 title "A Stochastic Model for Adsorption Kinetics" @default.
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• W3169893078 doi "https://doi.org/10.1155/2021/5522581" @default.
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