Catching gas with droplets : modelling and simulation of a diffusion-reaction process

S. Mourik, van; Y. Gennip, van; M.A. Peletier; A.V. Hlod; V. Shcherbakov; P.H.M.W. Panhuis, in 't; E. Vondenhoff; P. Eendebak; J.B. Berg, van den

Catching gas with droplets : modelling and simulation of a diffusion-reaction process

S. Mourik, van, Y. Gennip, van, M.A. Peletier, A.V. Hlod, V. Shcherbakov, P.H.M.W. Panhuis, in 't, E. Vondenhoff, P. Eendebak, J.B. Berg, van den

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

Abstract

The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial differential equations: a reaction-diffusion equation for the oxygen concentration and a reaction equation for the scavenger concentration. A probabilistic background of this model is given and different methods are used to get information from the model. Homogenization theory is used to describe the influence of the shape of the scavenger droplets on the oxygen flux, an argument using the Fourier number of the foil leads to insight into the dependency on the position of the scavenger and a method via conformal mappings is proposed to find out more about the role of the size of the droplet. Also simulations with Mathematica were done, leading to comparisons between different placements and shapes of the scavenger material in one- and two-dimensional foils.

Original language	English
Title of host publication	Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006)
Editors	E.R. Fledderus, R.W. Hofstad, van der, E. Jochemsz, J. Molenaar, T.J.J. Mussche, M.A. Peletier, G. Prokert
Place of Publication	Eindhoven
Publisher	Technische Universiteit Eindhoven
Pages	69-100
Publication status	Published - 2006

Cite this

Mourik, van, S., Gennip, van, Y., Peletier, M. A., Hlod, A. V., Shcherbakov, V., Panhuis, in 't, P. H. M. W., Vondenhoff, E., Eendebak, P., & Berg, van den, J. B. (2006). Catching gas with droplets : modelling and simulation of a diffusion-reaction process. In E. R. Fledderus, R. W. Hofstad, van der, E. Jochemsz, J. Molenaar, T. J. J. Mussche, M. A. Peletier, & G. Prokert (Eds.), Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006) (pp. 69-100). Technische Universiteit Eindhoven.

Mourik, van, S. ; Gennip, van, Y. ; Peletier, M.A. et al. / Catching gas with droplets : modelling and simulation of a diffusion-reaction process. Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006). editor / E.R. Fledderus ; R.W. Hofstad, van der ; E. Jochemsz ; J. Molenaar ; T.J.J. Mussche ; M.A. Peletier ; G. Prokert. Eindhoven : Technische Universiteit Eindhoven, 2006. pp. 69-100

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title = "Catching gas with droplets : modelling and simulation of a diffusion-reaction process",

abstract = "The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial differential equations: a reaction-diffusion equation for the oxygen concentration and a reaction equation for the scavenger concentration. A probabilistic background of this model is given and different methods are used to get information from the model. Homogenization theory is used to describe the influence of the shape of the scavenger droplets on the oxygen flux, an argument using the Fourier number of the foil leads to insight into the dependency on the position of the scavenger and a method via conformal mappings is proposed to find out more about the role of the size of the droplet. Also simulations with Mathematica were done, leading to comparisons between different placements and shapes of the scavenger material in one- and two-dimensional foils.",

author = "{Mourik, van}, S. and {Gennip, van}, Y. and M.A. Peletier and A.V. Hlod and V. Shcherbakov and {Panhuis, in 't}, P.H.M.W. and E. Vondenhoff and P. Eendebak and {Berg, van den}, J.B.",

year = "2006",

language = "English",

pages = "69--100",

editor = "E.R. Fledderus and {Hofstad, van der}, R.W. and E. Jochemsz and J. Molenaar and T.J.J. Mussche and M.A. Peletier and G. Prokert",

booktitle = "Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006)",

publisher = "Technische Universiteit Eindhoven",

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Mourik, van, S, Gennip, van, Y, Peletier, MA, Hlod, AV, Shcherbakov, V, Panhuis, in 't, PHMW, Vondenhoff, E, Eendebak, P & Berg, van den, JB 2006, Catching gas with droplets : modelling and simulation of a diffusion-reaction process. in ER Fledderus, RW Hofstad, van der, E Jochemsz, J Molenaar, TJJ Mussche, MA Peletier & G Prokert (eds), Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006). Technische Universiteit Eindhoven, Eindhoven, pp. 69-100.

Catching gas with droplets : modelling and simulation of a diffusion-reaction process. / Mourik, van, S.; Gennip, van, Y.; Peletier, M.A. et al.
Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006). ed. / E.R. Fledderus; R.W. Hofstad, van der; E. Jochemsz; J. Molenaar; T.J.J. Mussche; M.A. Peletier; G. Prokert. Eindhoven: Technische Universiteit Eindhoven, 2006. p. 69-100.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

TY - GEN

T1 - Catching gas with droplets : modelling and simulation of a diffusion-reaction process

AU - Mourik, van, S.

AU - Gennip, van, Y.

AU - Peletier, M.A.

AU - Hlod, A.V.

AU - Shcherbakov, V.

AU - Panhuis, in 't, P.H.M.W.

AU - Vondenhoff, E.

AU - Eendebak, P.

AU - Berg, van den, J.B.

PY - 2006

Y1 - 2006

N2 - The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial differential equations: a reaction-diffusion equation for the oxygen concentration and a reaction equation for the scavenger concentration. A probabilistic background of this model is given and different methods are used to get information from the model. Homogenization theory is used to describe the influence of the shape of the scavenger droplets on the oxygen flux, an argument using the Fourier number of the foil leads to insight into the dependency on the position of the scavenger and a method via conformal mappings is proposed to find out more about the role of the size of the droplet. Also simulations with Mathematica were done, leading to comparisons between different placements and shapes of the scavenger material in one- and two-dimensional foils.

AB - The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial differential equations: a reaction-diffusion equation for the oxygen concentration and a reaction equation for the scavenger concentration. A probabilistic background of this model is given and different methods are used to get information from the model. Homogenization theory is used to describe the influence of the shape of the scavenger droplets on the oxygen flux, an argument using the Fourier number of the foil leads to insight into the dependency on the position of the scavenger and a method via conformal mappings is proposed to find out more about the role of the size of the droplet. Also simulations with Mathematica were done, leading to comparisons between different placements and shapes of the scavenger material in one- and two-dimensional foils.

M3 - Conference contribution

SP - 69

EP - 100

BT - Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006)

A2 - Fledderus, E.R.

A2 - Hofstad, van der, R.W.

A2 - Jochemsz, E.

A2 - Molenaar, J.

A2 - Mussche, T.J.J.

A2 - Peletier, M.A.

A2 - Prokert, G.

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -

Mourik, van S, Gennip, van Y, Peletier MA, Hlod AV, Shcherbakov V, Panhuis, in 't PHMW et al. Catching gas with droplets : modelling and simulation of a diffusion-reaction process. In Fledderus ER, Hofstad, van der RW, Jochemsz E, Molenaar J, Mussche TJJ, Peletier MA, Prokert G, editors, Mathematics in Industry (Proceedings 55th European Study Group Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006). Eindhoven: Technische Universiteit Eindhoven. 2006. p. 69-100

Catching gas with droplets : modelling and simulation of a diffusion-reaction process

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