Mathematical modelling on non-thermal innovative food preservation processes

(1)

Mathematical Modelling on

Non-Thermal Innovative

Food Preservation Processes

(2)

OUTLINE

Introduction

- Non-thermal Processes - Mathematical Modelling

- Experimental Design and Data Analysis

Cases Studies

- Ozone, UV-C, Thermosonication - Red bell pepper / ozone

- Courgette / UV-C

(3)

OUTLINE

Introduction

- Non-thermal Processes

- Mathematical Modelling

Cases Studies

- Courgette / UV-C

(4)

Product preparation

Product processing (steaming, blanching, cooking)

Minimally processed

Packaging and Dispatch

Semi-processed

Semi-processed _processedHighly Highly processed

Further processing

(freezing, canning, preserving)

NON

(5)

Impact on several quality attributes

The problem is... Heating!

NEW

TE

CHN

OLO

GIE

S

NON

(6)

little loss of:

- colour

- flavour

- texture

- nutrients

NON-THERMAL TECHNOLOGIES

…but still retaining the desired shelf-life and safety!

NON

(7)

Pulsed Electric Fields Exposure of food to an intense electric field by means of controlled pulses of high voltage

Ohmic Heating Generation of heat inside the food as a consequence of Joule effect

Radio Frequency Exposure of food to electromagnetic waves in the radio-frequency range

Microwave Exposure of food to controlled microwaves

High Pressure Short-time exposure to extremely high pressure (up to 5000 bar)

NON

(8)

Super Critical CO₂ Contact of food with CO₂ at supercritical pressure

Ozone Exposure of food to ozone

Ultrasonication Exposure of foods to ultrasounds (US)

US + mild temperatures (T) _{thermosonication}

US + pressure (P) _{manosonication}

US + T + P _{manothermosonication}

UV-C Exposure of food to controlled pulses of UV rays

NON

(9)

OUTLINE

Introduction

- Non-thermal Processes

- Mathematical Modelling

Cases Studies

- Courgette / UV-C

(10)

Model

_{mathematical expression}

i=1,2,...,n (number of experimental runs/observations) j=1,2,...,v (number of independent variables)

k=1,2,...,p (number of model parameters)

y

_i

= f(x

_ij

,

θ

_k

) +

ε

_i

MATHEMATICAL MODELLING

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1000 2000 3000 4000 5000 x y

(11)

Modeling

and

Simulation

Makes

it

possible

to:

Gain

more

knowledge

about

the

process

and

the

effects

on

the

product

;

MATHEMATICAL MODELLING

(12)

Modeling

and

Simulation

Makes

it

possible

to:

Gain

more knowledge

more

knowledge

about

the

process

and the

and

the

effects

on

the

product;

product

;

Reduce

the

number

of

experiments

in

the

development

stage

;

MATHEMATICAL MODELLING

(13)

Modeling

and

Simulation

Makes

it

possible

to:

Gain

more knowledge

more

knowledge

about

the

process

and the

and

the

effects

on

the

product;

product

;

Reduce

the

number

of

experiments

in

the

development

stage

stage;

;

Optimize

the

process

with

respect

to

different

parameters

,

such

as

quality

;

MATHEMATICAL MODELLING

(14)

Modeling

and

Simulation

Makes

it

possible

to:

Gain

more knowledge

more

knowledge

about

the

process

and the

and

the

effects

on

the

product;

product

;

Reduce

the

number

of

experiments

in

the

development

stage

stage;

;

Optimize

Optimize the

the

process

with

respect

to

different

parameters

parameters,

,

such

as quality

as

quality

;

Study

the

influence

on

the

product

during

process

disturbances

.

MATHEMATICAL MODELLING

(15)

Models

should

:

predict

the response variable

accurately

MATHEMATICAL MODELLING

(16)

Models

should

:

predict

the response variable

accurately

adequacy

adequacy of the model

MATHEMATICAL MODELLING

(17)

Models

should

:

predict

the response variable

accurately

adequacy

adequacy of the model

parameters

quality

MATHEMATICAL MODELLING

(18)

Processes

Chemical Physical Food Processes Transport phenomena • heat transfer • mass transfer • momentum transfer Reaction kinetics Properties

MATHEMATICAL MODELLING

(19)

Processes

Chemical Modelling Physical Food Processes Transport phenomena • heat transfer • mass transfer • momentum transfer Reaction kinetics Properties mathematical function variables parameters data points Experimental design Regression schemes

MATHEMATICAL MODELLING

(20)

Processes

Optimisation Chemical Modelling Physical Food Processes Control Design Assessment Transport phenomena • heat transfer • mass transfer • momentum transfer Reaction kinetics Properties Criteria Objectives mathematical function variables parameters data points Experimental design Regression schemes

MATHEMATICAL MODELLING

(21)

Processes

Optimisation Safety Chemical Modelling Physical Food Processes Control Design Assessment Transport phenomena • heat transfer • mass transfer • momentum transfer Reaction kinetics Properties Quality Criteria Objectives mathematical function variables parameters data points Experimental design Regression schemes

MATHEMATICAL MODELLING

(22)

Mechanistic models are more complex, but in

general allow accurate predictions

Empirical models are much simple, but usually

are appropriate to limited practical uses

MATHEMATICAL MODELLING

(23)

Mechanistic models are more complex, but in

general allow accurate predictions

Empirical models are much simple, but usually

are appropriate to limited practical uses

Balance of the advantages and disadvantages,

depending on the final purpose.

MATHEMATICAL MODELLING

(24)

Difficulties

in

food

processes

modelling

:

MATHEMATICAL MODELLING

(25)

Difficulties

in

food

processes

modelling

:

_{Dynamic processes}

MATHEMATICAL MODELLING

(26)

Difficulties

in

food

processes

modelling

:

_{Dynamic processes}

_{Complexity and heterogeneity of products}

MATHEMATICAL MODELLING

(27)

Difficulties

in

food

processes

modelling

:

_{Dynamic processes}

_{Complexity and heterogeneity of products}

_{Structural and physicochemical changes}

MATHEMATICAL MODELLING

(28)

Kinetic

Studies

:

Allow the quantification of the extension and rate

of production/consumption of any substance

MATHEMATICAL MODELLING

(29)

Kinetic

Studies

:

Allow the quantification of the extension and rate

of production/consumption of any substance

Safety

MATHEMATICAL MODELLING

(30)

Kinetic

Studies

:

Allow the quantification of the extension and rate

of production/consumption of any substance

Safety

Quality

MATHEMATICAL MODELLING

(31)

Safety

and

Quality

depend on:

Intrinsic factors

Extrinsic factors

MATHEMATICAL MODELLING

(32)

Safety

and

Quality

depend on:

Intrinsic factors

Extrinsic factors

pH

a

_w others

MATHEMATICAL MODELLING

(33)

Safety

and

Quality

depend on:

Intrinsic factors

Extrinsic factors

pH

a

_w others

T

pH

humidity gas concentration others

MATHEMATICAL MODELLING

(34)

OUTLINE

Introduction

- Experimental Design and Data Analysis

Cases Studies

- Courgette / UV-C

(35)

Model

Validation

:

Heuristic sampling

Experimental design

Minimize variance of:

predicted response

parameter estimates

EXPERIMENTAL DESIGN AND

DATA ANALYSIS

(36)

Data

Analysis

:

Regression schemes

Analysis of residuals

(

)

[

]

2 n 1 i k ij i n 1 i 2 i

y

f

x

,

e

SSR

∑

= =

θ

−

=

Least-squares method

EXPERIMENTAL DESIGN AND

DATA ANALYSIS

(37)

OUTLINE

Introduction

Cases Studies

- Ozone, UV-C, Thermosonication

- Red bell pepper / ozone - Courgette / UV-C

(38)

Ozone Exposure of food to ozone

Ultrasonication Exposure of foods to ultrasounds (US)

US + mild temperatures (T) _{thermosonication}

US + pressure (P) _{manosonication}

US + T + P _{manothermosonication}

UV-C Exposure of food to controlled pulses of UV rays

CASE STUDIES

(39)

OZONE

-Gas formed by 3 oxygen atoms -Highly instable

-In nature it is formed by the action of sun UV light (185 nm)

CASE STUDIES

(40)

OZONE

-Commercially:

Ozone generated by

Electrical Discharge

CASE STUDIES

(41)

OZONE

-Powerful antimicrobial agent _{strong oxidant}

-Lethal or inhibitory effect on microorganisms due to its reaction with: - intracellular enzymes

- nucleic material

- membrane components _{destruction of coating of spores and viral}

capsules

CASE STUDIES

(42)

ULTRASOUNDS

- Vibrations similar to sound waves

- Very high frequencies: 18 kHz – 500 MHz _{greater than upper limit of}

human hearing!

- Some animals, such as dogs, dolphins, and bats, have an upper limit

that is greater than that of the human ear and thus can hear ultrasound.

CASE STUDIES

(43)

ULTRASOUNDS

- In a biological medium: production of compression and expansion cycles

_{CAVITATION phenomenon}

- The implosion of gas bubbles _{high temperature}

and high pressure spots

_{Cell disruption} _{cellular death}

CASE STUDIES

(44)

ULTRAVIOLET RADIATION

- Ultraviolet light in the non-ionizing region of the electromagnetic

spectrum, between X-rays (200 nm) and visible light (400 nm)

CASE STUDIES

(45)

UV light can be divided into three regions:

- UVA: 320-400 nm – therapeutic effects (dermatological);

- UVB: 280-320 nm – sun burn and plant damage

- UVC: 100-280 nm – dangerous to life – maximum lethal effect at 254 nm

ULTRAVIOLET RADIATION

CASE STUDIES

(46)

ULTRAVIOLET RADIATION - UVC

Lethal effect (254 nm) due to its destroying action on DNA chains

decreasing or inactivation of vital functions of cells

CASE STUDIES

(47)

Products

Strawberry _{Red bell pepper} Watercress

(48)

Technologies

(49)

SAFETY

water ozone US + 65ºC

-+ QU AL ITY UV-C ultrasounds

QUALITY

UV-C water ozone US + 65ºC

-+ S A F E T Y ultrasounds combined

Compromise: safety + quality

Colour pH Antocianins Vitamin C Texture Microstructure Sensorial analysis

However, the impact depends on: Microorganism / Product

(50)

OUTLINE

Introduction

Cases Studies

- Ozone, UV-C, Thermosonication

- Red bell pepper / ozone

- Courgette / UV-C

(51)

0 1 2 3 4 5 6 0 10 20 30 40 50 60 70

Tempo de tratamento (min)

L o g ( N 0 /N )

Red pepper ozonated Red pepper washed Red bell pepper / Listeria innocua

Ozone

red bell pepper

Kinetc

Kinetc behaviourbehaviour

Ozone

Water

Water / Listeria innocua

-3,5 -3,0 -2,5 -2,0 -1,5 -1,0 -0,5 0,0 0 2 4 6 8 10 12 14 16

Tempo de tratamento (min)

L o g ( N /N 0 )

(52)

UV Water Chemicals Ozone US + 65 ºC

-+ Blanching (50 – 85 ºC) 0.5 – 0.8 0.5 – 1.5 0.5 – 2.0 2.5 – 3.0 0.5 – 4.5 4.0 – 5.0

SAFETY (total mesophyls)

No synergetic effects of

ozone with temperature

(53)

OUTLINE

Introduction

Cases Studies

- Courgette / UV-C

(54)

(55)

(56)

0,001 0,01 0,1 1 10 0 20 40 60 80 100 Tim e(s) N /N0 ( (◊◊) ) —_— 11 J/m11 J/m22 ( (_■_■) ) ---- 8 J/m_{8 J/m}22 ( (_○_○) ) ···_··· 5 J/m5 J/m22 total mesophyls at 30 º30 ºCC

(57)

0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 Time (s) C /C 0 0 0.2 0.4 0.6 0.8 1 1.2 0 1000 2000 3000 4000 Time (s) C /C 0

(_◊) heat (_■) heat and UV-C

Effect on Peroxidase ….

Temp. and UV-C

(11 J/m

2

₎

(58)

OUTLINE

Introduction

Cases Studies

- Courgette / UV-C

(59)

Effect on Peroxidase ….

Synergetic effect of

(60)

            −             −                 −       −                 −       −

+

=

t e k t e k R T Tref Ea ref ref T T R Ea ref

e

C

e

C

1 1 2 2 1 1 1 1 02 01

(61)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Time (min) C /C o 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Time (min) C /C o 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Time (min) C /C o 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Time (min) C /C o 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Time (min) C /C o 82.5 ºC 85 ºC 87.5 ºC 90 ºC 92.5 ºC Vitamina C             −                 − −

=

t e k R T T a E

e

C

ref 1 1 ref 0

(62)

          −             − −

=

−

k e t T T R E

e

C

ref 1 1 a ref e 0 e 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 Time (s) a n 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 Time (s) a n 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 Time (s) a n 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 Time (s) a n 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 Time (s) a n Colour a*

(63)

(64)

(65)

CBQF CBQF CBQF

CBQF ---- INTERFACE AINTERFACE AINTERFACE AINTERFACE A4444

State Associated Laboratory State Associated LaboratoryState Associated Laboratory State Associated Laboratory