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Mathematical model of the bleaching process with chemical kinetics of first and general order

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Abstract

Mathematical modeling of the bleaching process with a chemical reaction and diffusion of bleaching agent into a thin polymeric matrix film by movement through the micropores is studied in the present paper. The model was developed after considering theoretical methods of chemical engineering, the physical operation mechanism of the bleaching process and the main parameters that influence the diffusion mechanism. The efficiency factor for chemical kinetics of first and nth order processes were described using analytical solutions and perturbation methods. For the solution of the dynamic model, two cases of boundary conditions were explored. The first case describes diffusion in a well-stirred medium and the second case describes the situation when the bulk fluid moves slowly and interfacial resistance is present. In the latter case, the difference finite method was used as numerical tool for solving the problem and finding the concentration profile in the direction of the x-axis. Accordingly, experimental measurements were performed to determine the effective diffusion coefficient of bleaching agent in a polymeric matrix.

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Abbreviations

m :

Mass of molecule

ν :

Speed of particles

τ :

Time

J :

Flux

n :

Order of reaction

c :

Concentration of bleaching agent

D :

Diffusion coefficient

k :

Rate constant

x :

Space coordinate

L :

Half length of the solid

Eε :

Porosity

C L :

Concentration of solute in the bulk

φ:

Thiele module

C :

Dimensionless parameter of concentration

X :

Dimensionless parameter of distance

A,B :

Arbitrary constants

r :

Reaction rate of the process

r s :

Ideal reaction rate without diffusion

η :

Efficiency factor

p :

Number of terms in series expansion

ξ :

Parameter that represents distance at the particle surface

ω :

Parameter that represents \(dC/d\xi\)

S :

Surface area of solid

r m :

Rate of mass transfer at the interface

Bi m :

Mass transfer biot number

q :

Number of interior nodes

∆c :

Difference in fluid concentration

δ:

Thickness of the solid

R 2 :

Coefficient of determination

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Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme Project No. LO1303 (MSMT-7778/2014).

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  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01, Zlín, Czech Republic

    Juan Carlos Beltrán-Prieto & Karel Kolomazník

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  1. Juan Carlos Beltrán-Prieto
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  2. Karel Kolomazník
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Correspondence to Juan Carlos Beltrán-Prieto.

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Beltrán-Prieto, J.C., Kolomazník, K. Mathematical model of the bleaching process with chemical kinetics of first and general order. Reac Kinet Mech Cat 123, 485–503 (2018). https://doi.org/10.1007/s11144-017-1338-0

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  • DOI: https://doi.org/10.1007/s11144-017-1338-0

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