A mathematical model for spaghetti cooking with free boundaries
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1.
Università degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, Firenze
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2.
Università degli Studi di Firenze, Dipartimento di Fisica, Via Sansone 1, I-50019, Sesto Fiorentino (FI)
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Received:
01 January 2010
Revised:
01 November 2010
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76S05, 35R35, 45G10.
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We propose a mathematical model for the process of dry pasta cooking with specific reference to spaghetti.
Pasta cooking is a two-stage process: water penetration followed by starch gelatinization. Differently from the approach adopted so far in the
technical literature, our model includes free boundaries: the water penetration front and the gelatinization onset front representing a fast stage
of the corresponding process. Behind the respective fronts water sorption and gelatinization proceed according to some kinetics.
The outer boundary is also moving and unknown as a consequence of swelling. Existence and uniqueness are proved and numerical simulations are presented.
Citation: Antonio Fasano, Mario Primicerio, Andrea Tesi. A mathematical model for spaghetti cooking with free boundaries[J]. Networks and Heterogeneous Media, 2011, 6(1): 37-60. doi: 10.3934/nhm.2011.6.37
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Abstract
We propose a mathematical model for the process of dry pasta cooking with specific reference to spaghetti.
Pasta cooking is a two-stage process: water penetration followed by starch gelatinization. Differently from the approach adopted so far in the
technical literature, our model includes free boundaries: the water penetration front and the gelatinization onset front representing a fast stage
of the corresponding process. Behind the respective fronts water sorption and gelatinization proceed according to some kinetics.
The outer boundary is also moving and unknown as a consequence of swelling. Existence and uniqueness are proved and numerical simulations are presented.
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