Corso di Laurea Magistrale in Scienze e tecnologie alimentari - STAL

The interaction between mathematics and food is nowadays very broad. The aim of the course is to scratch the surface of this awesome world through several examples and applications, and to focus on the pervasiveness of math in every phase of a food product's life. We provide the theoretical framework and practical background behind mathematical models and their importance to deeply understanding a system and to test the effect of changes through the studying of transport phenomena, food and theoretical rheology appearing in modeling food process, quality and safety. Finally, we provide a way to translate chemical and enzymatic reactions properly into systems of (nonlinear) differential equations as well as for roughly understanding their solutions space.

This course should provide student to deeply understand basic math and physical principles behind food processes.
Below is detailed the main skills the course provided to according to Dublin descriptors.

A brief description of the structure of the course and of the basic tools and devices provided students follows.

Structure of the course 

The course is through several lectures and each lecture essentially splits into a

• theoretical discussion of a particular topic
• detailed application in food science
• problem solving and routine exercises session on a specific topic
  
  

 Tools provided and multi-media

Lectures will be provided  through slides, videos, notes  and other digital supports and will be available for downloading from the e-learning UniTo platform. Attending either lectures or exercises sessions is strongly recommended.

Each student has the possibility to chose a topic among a list of topics provided during the course. The final exam consists in a

• short written report about 5 pages
• an oral PPT-presentation about 10 minutes + 5 minutes discussion (on the chosen topic)

The topic will be chosen by each student among a list of topics provided  at the beginning of the course. 

Detailed program of the course. Each topic will be introduced through concrete examples in food science and technology and a plethora of applications will be provided.

1.  What is a Mathematical Model?
    [1.1] Principles of Mathematical Modeling
    [1.2] Classifications of models deterministic/stochastic and mechanistic/empirical
    [1.3] Stages of models
    [1.4] Dimensional Analysis and Scale: Buckingham Pi theorem
    [1.5] Approximating and Validating Models
2.  Momentum transport and theoretical Food Rheology
    [2.1] Classification of fluid behavior
    [2.2] Newtonian and non-Newtonian fluid
    [2.3] Time-independent models (Power law, Bingham, Herschel-Bulkley, Casson, Maxwell, Kelvin/Voigt models) and beyond
    [2.4] Time-dependent models and visco-elasticity
3.  Energy and mass transport phenomena and conservation laws
    [3.1] Newton's viscosity law and the kinetic viscosity
    [3.2] Fourier heat law and thermal diffusivity
    [3.3] Fick's law and diffusion
    [3.4] Examples of momentum, mass and energy transfer in food systems and the role of boundary conditions
4.  Kinetic Modeling
    [4.1] Simple kinetic and steady states
    [4.2] Michaelis-Menten equation and enzyme kinetics
    [4.3] Arrhenius equation and effect of temperature:
    [4.4] pH effect on kinetic modeling
    [4.5] Cooking food and shelf life
   
   

 

• C. Dym. Principles of Mathematical Modeling 2nd Edition, Academic Press (2004) [ISBN: 9780122265518]
• M.A.J.S. van Boekel, L.M.M. Tijskens. Kinetic modeling.  [DOI:10.1533/9781855736375.1.35], Food process Modelling
• A. Portaluri. Notes on Mathematical modeling and food science a.a. 2020/21

 

Le modalità di svolgimento dell'attività didattica potranno subire variazioni in base alle limitazioni imposte dalla crisi sanitaria in corso. In ogni caso è assicurata la modalità a distanza per tutto l'anno accademico.