The modelling of a textile dyeing process utilizing the method of volume averaging

Souza, Antônio Augusto Ulson de; Whitaker, Stephen

doi:10.1590/s0104-66322003000400011

Cited by 12 publications

(1 citation statement)

References 12 publications

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“…(8), and hence describe the drying behaviour of the resulting homogenised medium. Such an approach has been employed by several authors to describe drying behaviour, (de Souza and Whitaker, 2003;Porras et al, 2006). …”

Section: Continuous Phase Equationsmentioning

confidence: 99%

A new model for the drying of droplets containing suspended solids

Handscomb

Kraft

Bayly

2009

Chemical Engineering Science

110

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Section: Continuous Phase Equationsmentioning

confidence: 99%

A new model for the drying of droplets containing suspended solids

Handscomb

Kraft

Bayly

2009

Chemical Engineering Science

110

View full text Add to dashboard Cite

Modelling of the dyeing process of packed cotton threads using reactive dyes

Souza

Silva

2006

Transp Porous Med

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The Method of Volume Averaging is used to model the process of dyeing textile threads on bobbins. This analysis allows one to upscale the relevant information at the micro-scale, composed of the textile fibres of the thread in contact with the dyeing bath fluid, to the macro-scale, consisting of the bobbins of threads inside the equipment. The final mathematical model consists of two equations, one for the fluid phase external to the thread and the other for the fluid phase internal to the thread. In order to solve the partial differential equations obtained in the mathematical model, the authors developed a computation code using the Method of Finite Volumes. This code utilized a system of generalized coordinates to facilitate application of the boundary conditions to different bobbin geometries. The numerical results for the kinetics of dyeing packed cotton threads with reactive dyes are compared to the experimental results obtained in Brazilian textile industries, leading to good agreement between theory and experiment. This demonstrates that the model developed in this paper is able to predict the operational conditions to be used in the textile industries, minimizing the consumption of dyes and other auxiliaries necessary for the dyeing process. 342 S. M. A. Guelli Ulson de Souza et al. Nomenclature a v | γ κ Surface area per unit volume on the micro-scale, [1/m] a v | βσ Surface area per unit volume on the intermediary scale, [1/m] b σ Vector closure variables of the σ -region, [m] b β Vector closure variables of the β-phase, [m] C i Initial concentration of the η-phase, [kg/m 3 ] C Aη Concentration of the η-phase, [kg/m 3 ] C Aσ Concentration of the σ -region, [kg/m 3 ] C Aβ Concentration of the β-phase, [kg/m 3 ] C A Superficial average concentration, [kg/m 3 ] C Aβ Spatial derivation concentration of the β-phase, [kg/m 3 ] C Aσ Spatial derivation concentration of the σ -region, [kg/m 3 ] C A γ Intrinsic average concentration of the γ -phase; [kg/m 3 ] C Aβ β Intrinsic average concentration of the β-phase; [kg/m 3 ] C Aσ σ Intrinsic average concentration of the σ -region; [kg/m 3 ] d 1 Upper internal diameter of the bobbin, [m] d 2 Upper external diameter of the bobbin, [m] d 3 Lower internal diameter of the bobbin, [m] d 4 Lower external diameter of the bobbin, [m] d β Velocity-like coefficient of the β-phase, [m/s] d σ Velocity-like coefficient of the σ -region, [m/s] Deff γ κ Effective diffusivity tensor of the γ -phase, [m 2 /s] D β Molecular diffusivity, [m 2 /s] D σ Diffusivity of the σ -region, [m 2 /s] D * β Total dispersion tensor, [m 2 /s] Deff β βσ Effective diffusivity tensor of the β-phase, [m 2 /s] D Hydrodynamic dispersion, [m 2 /s] h Mass transfer convective coefficient, [m/s] H Height of the bobbin, [m] k r Rate constant for reaction with the fibre, [s −1 ] k h Pseudo-first-order rate constant of hydrolysis, [s −1 ] K eq Equilibrium constant, [m] i Lattice vectors, [m] β Characteristic length for the β-phase, [m] γ Characteristic length for the γ -phase, [m] κ Characteristic length for th...

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Volume Averaging Study of the Capacitive Deionization Process in Homogeneous Porous Media

Gabitto

Tsouris

2015

Transp Porous Med

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The modelling of a textile dyeing process utilizing the method of volume averaging

Cited by 12 publications

References 12 publications

A new model for the drying of droplets containing suspended solids

A new model for the drying of droplets containing suspended solids

Modelling of the dyeing process of packed cotton threads using reactive dyes

Volume Averaging Study of the Capacitive Deionization Process in Homogeneous Porous Media

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