A mathematical model for spaghetti cooking with free boundaries

Antonio Fasano; Mario Primicerio; Andrea Tesi; Antonio Fasano; Mario Primicerio; Andrea Tesi

doi:10.3934/nhm.2011.6.37

Networks and Heterogeneous Media

2011, Volume 6, Issue 1: 37-60. doi: 10.3934/nhm.2011.6.37

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A mathematical model for spaghetti cooking with free boundaries

1.
Università degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, Firenze
2.
Università degli Studi di Firenze, Dipartimento di Fisica, Via Sansone 1, I-50019, Sesto Fiorentino (FI)

Received: 01 January 2010 Revised: 01 November 2010
76S05, 35R35, 45G10.

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.
- Pasta cooking,
- free boundaries,
- nonlinear integral equations
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.

References

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