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Gelification and mass transport in a static non-isothermal waxy solution

Published online by Cambridge University Press:  01 February 2009

A. FASANO ,
L. FUSI ,
J. R. OCKENDON  and
M. PRIMICERIO
A. FASANO
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
L. FUSI
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
J. R. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, 24-29 St. Giles, Oxford, OX1 3LB, UK
M. PRIMICERIO
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
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Abstract

We consider a solution of a mono-component oil and wax. The latter is dissolved in the oil if the temperature is above the so-called cloud point (which depends on the concentration) and it segregates in the form of solid crystals if temperature is below the cloud point. As the solid fraction of wax increases, the diffusivity of liquid wax in the oil decreases (gelification), eventually vanishing. We study a one-dimensional model where temperature is initially above the cloud point and then it is lowered to induce diffusion and gelification. We formulate the relevant mathematical problem (a free boundary problem), studying its well-posedness and showing some qualitative results.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 1 , February 2009 , pp. 93 - 122
Copyright
Copyright © Cambridge University Press 2008

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