scholarly journals The influence of the non-linear diffusion on the mass transfer of a packaging contaminant into foodstuffs

2018 ◽  
Vol 26 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Gheorghe Juncu
Keyword(s):  
Mass Transfer ◽  
Diffusion Coefficient ◽  
Balance Equation ◽  
Mass Balance Equation ◽  
Linear Mass ◽  
Linear Diffusion ◽  
Kirchhoff Transformation ◽  
Mass Transfer Mechanism ◽  
Concentration Variable ◽  
Non Linear

Abstract The unsteady mass transfer of the packaging constituents to a food has been analysed. The diffusion coefficient inside the packaging was considered concentration - variable while the food was considered concentration spatially gradientless. A well-known technique (Kirchhoff transformation) was used to solve the non-linear mass balance equation. The influence of the non-linear diffusion on the mass transfer mechanism and rate was analysed for different values of the partition coefficient and dilution coefficient.

scholarly journals Applications of Non-Linear Diffusion Equations to the Kinetics of Water Vapour Adsorption by Polymeric Fibres

1992 ◽  
Vol 9 (4) ◽  
pp. 269-275
Author(s):  
B.M. Kats ◽  
V.V. Kutarov ◽  
A.A. Chagodar
Keyword(s):  
Diffusion Coefficient ◽  
Water Vapour ◽  
Exponential Dependence ◽  
Linear Diffusion ◽  
Non Linear ◽  
Vapour Adsorption ◽  
Water Vapour Adsorption ◽  
Numeric Experiment ◽  
Kinetics Of ◽  
Sorbate Concentration

In order to describe the kinetics of water vapour adsorption by polymeric fibres, a numeric experiment has been carried out using the framework of a non-linear diffusion model which takes into account the exponential dependence of the diffusion coefficient on the sorbate concentration in the sorbent. The results show a good correlation between theoretical and experimental kinetic curves for polymolecular adsorption. They also confirm the exponential decrease of the diffusion coefficient with an increase in polymolecular filling.

Estimation of the non-linear diffusion coefficient with Marcov Chain Monte Carlo method based on the integral information

2017 ◽  
Vol 27 (3) ◽  
pp. 639-659 ◽  
Author(s):  
Zbigniew Bulinski ◽  
Helcio R.B. Orlande
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Monte Carlo Method ◽  
Real Life ◽  
Diffusion Problem ◽  
Linear Diffusion ◽  
Content Type ◽  
Inverse Approach ◽  
Non Linear ◽  
Correlated Parameters

Purpose This paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information. Design/methodology/approach The Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique. Findings A number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper. Originality/value An original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

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