A mathematical model for spaghetti cooking with free boundaries

Antonio Fasano; Mario Primicerio; Andrea Tesi

doi:10.3934/nhm.2011.6.37

Article Contents

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

This issue Previous Article Spectral stiff problems in domains surrounded by thin stiff and heavy bands: Local effects for eigenfunctions Next Article On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems

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: December 31, 2009

Revised: October 31, 2010

Published: February 2011

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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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Mathematics Subject Classification: 76S05, 35R35, 45G10.

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