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TitleThermal Food Processing
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Table of Contents
                            Cover
Engineering Aspects of Thermal Food Processing
	ISBN 9781420058581
	Contents
	Series Preface
	Preface
	Series Editor
	Editor
	Contributors
Part I: Fundamentals and New Processes
	Chapter 1: Principles of Thermal Processing: Sterilization
		1.1 Introduction
		1.2 Kinetics of Thermal Processing
			1.2.1 Microbial Destruction
			1.2.2 Kinetics of Food Quality Destruction
		1.3 Process Determination
			1.3.1 Heat Penetration F- and J-Factors
			1.3.2 Criteria for Adequacy of Processing F- and C-Values
		1.4 Optimization of Sterilization and Cooking
		1.5 Establishing Safe Criteria Heat-Processed Foods
		References
	Chapter 2: Principles of Thermal Processing: Pasteurization
		2.1 Introduction
		2.2 Food Pasteurization Fundamentals
			2.2.1 Historical Background and Definitions of Food Pasteurization
				2.2.1.1 Classical Definition of Food Pasteurization
				2.2.1.2 Modern Definition of Food Pasteurization
			2.2.2 Desirable and Undesirable Changes in Foods with the Application of Heat: Quality Optimization of the Process
			2.2.3 Equations for Process Design and Assessment
				2.2.3.1 Bigelow or First-Order Kinetic Models
				2.2.3.2 Nonlinear Survival Curves
				2.2.3.3 Process Design and Assessment
		2.3 Heat Resistance of Microbes Targeting the Production of Safe and Stable Foods
			2.3.1 Spores: Heat-Resistant Microbial Forms
			2.3.2 Microbial Heat Resistance in Low-Acid Pasteurized Chilled Foods (pH > 4.6)
				2.3.2.1 Psychrotrophic Strains of Clostridium botulinum
				2.3.2.2 Other Pathogenic Spore-Forming Bacteria
				2.3.2.3 Non-Spore-Forming Psychrotrophic Pathogens
			2.3.3 Microbial and Endogenous Enzymes Heat Resistance in High-Acid and Acidified Foods (pH < 4.6)
				2.3.3.1 Alicyclobacillus acidoterrestris Spores
				2.3.3.2 Fungal Ascospores
				2.3.3.3 Other Spoilage Bacteria and Fungi
				2.3.3.4 Endogenous Enzymes
		2.4 Design of Pasteurization Processes
			2.4.1 Low-Acid Cooked and Refrigerated Foods
				2.4.1.1 Milk Pasteurization
				2.4.1.2 Surface Pasteurization of Eggs and Raw Meats
			2.4.2 Shelf-Stable High-Acid and Acidified Foods
				2.4.2.1 Beer Pasteurization
		References
	Chapter 3: Aseptic Processing of Liquid Foods Containing Solid Particulates
		3.1 Introduction
		3.2 Fundamentals of Aseptic Processing
			3.2.1 Fundamentals of Heat Transfer
			3.2.2 Flow and Heat Transfer to Liquids in Closed Channels
			3.2.3 Heat Transfer to Particulates
			3.2.4 Heat Transfer Within Particulates
			3.2.5 Residence Time Distribution in Particulate Flows
		3.3 Fundamentals of Safety and Quality
			3.3.1 Kinetics of Safety and Quality Factors
			3.3.2 Validation of Aseptic Lines
		3.4 Aseptic Equipment
			3.4.1 Raw Materials Storage and Handling
			3.4.2 Cook Vessels
			3.4.3 Heating Stage
			3.4.4 Holding Tube
			3.4.5 Cooling Stage
			3.4.6 Aseptic Tanks
			3.4.7 Filler Operation and Pack Decontamination
			3.4.8 Final Product Handling and Storage
			3.4.9 Pumps and Back-Pressure
		3.5 Concluding Remarks
		Acknowledgments
		List of Symbols
		References
	Chapter 4: Ohmic and Microwave Heating
		4.1 Introduction
		4.2 Ohmic Heating
			4.2.1 Ohmic Heater Design
			4.2.2 Electrical Conductivity of Foods
			4.2.3 Effect on Microorganisms
			4.2.4 Sterilization Applications
				4.2.4.1 Continuous Sterilization
				4.2.4.2 In-Package Sterilization
			4.2.5 Electrolytic Effects
			4.2.6 Other Applications
		4.3 Microwave Heating of Foods
			4.3.1 Heating Mechanisms of Foods
			4.3.2 Dielectric Properties of Foods
			4.3.3 Applications in the Food Industry
			4.3.4 Concluding Remarks
		References
	Chapter 5: High-Pressure Thermal Processes: Thermal and Fluid Dynamic Modeling Principles
		5.1 Introduction
		5.2 Modeling System and Sources of Variability
			5.2.1 Components and Materials in a Typical High-Pressure Sterilization System
				5.2.1.1 Components of a High-Pressure Vessel
				5.2.1.2 Pressure Transmission Fluid
				5.2.1.3 Flexible Container
				5.2.1.4 Food Properties
			5.2.2 Critical Process Variables
				5.2.2.1 Initial Temperature Distribution in the Sample, Fluid, and Vessel before Pressurization
				5.2.2.2 Temperature Distribution during Pressurization
				5.2.2.3 Compression Rate
				5.2.2.4 Selecting Pressure and Holding Time
				5.2.2.5 Decompression Rate
				5.2.2.6 Cooling Time after Decompression
		5.3 Governing Equations Inside the Vessel
			5.3.1 Fundamental Physics during a High-Pressure Process
			5.3.2 High-Pressure Process Equations
				5.3.2.1 Heat Transfer Balance Using Fourier’s Law
				5.3.2.2 Contribution of Fluid Motion to Heat Transfer
				5.3.2.3 Possible Initial and Boundary Conditions of the Computational Domain
				5.3.2.4 Thermal Properties of Foods at High-Temperature High-Pressure Conditions
		5.4 Modeling Approaches for Predicting Temperature Uniformity
			5.4.1 Important Design Assumptions in Developing a Model
				5.4.1.1 Assumptions for the Chamber System
				5.4.1.2 Assumptions for Compression Fluid
				5.4.1.3 Assumptions for Food Packages
				5.4.1.4 Assumptions for Processing Conditions
			5.4.2 Analytical Modeling
			5.4.3 Numerical Modeling
				5.4.3.1 Discretization Methods
				5.4.3.2 Computational Fluid Dynamics
				5.4.3.3 Validation of Numerical Models
			5.4.4 Macroscopic Modeling
			5.4.5 Artificial Neural Network Modeling for Process Control
				5.4.5.1 Neural Network Architecture
				5.4.5.2 Artificial Neural Network Development
		5.5 Comparison between Modeling Approaches
			5.5.1 Vessel Simplifications Required to Establish the Model
			5.5.2 Predicting Temperature and Flow Distribution
			5.5.3 Predicting Time–Temperature Profiles
			5.5.4 Determination of Thermophysical Properties by Fitting Temperature Data
			5.5.5 Incorporation of Thermophysical Properties as Functions of Pressure and Temperature
			5.5.6 Coupling Thermal and Fluid Dynamic Models with Inactivation and Reaction Models
			5.5.7 Inactivation Extent or Reaction Output Distribution Throughout the Vessel or Package
			5.5.8 Models Accounting for Package Shrinkage due to Hydrostatic Compression
			5.5.9 Heat Source: The Compression Heating Model
			5.5.10 Materials and Their Properties in a Multicomponent Model
			5.5.11 Multiple Unit Operations in a Single Model
			5.5.12 Computational Demand and Solver Speed Required
			5.5.13 Invested Time in Model Development
			5.5.14 Adaptability to System and Process Modifications
		5.6 Concluding Remarks
			5.6.1 Thermophysical Property Determination
			5.6.2 Analytical Modeling
			5.6.3 Numerical Modeling
			5.6.4 Macroscopic Models
			5.6.5 ANN
			5.6.6 Model Validation with Temperature and Microbial Measurements
		Nomenclature
		References
	Chapter 6: High-Pressure Processes: Thermal and Fluid Dynamic Modeling Applications
		6.1 Introduction
		6.2 Example of an Analytical Model for Single-Point Temperature Prediction
			6.2.1 Temperature Profile Prediction
			6.2.2 Thermophysical Properties Prediction
		6.3 Conductive Models Solved by Applying the Finite Difference Method
			6.3.1 Temperature Distribution Prediction
			6.3.2 Enzyme and Microbial Inactivation Prediction
		6.4 Convective Models Solved by Applying Computational Fluid Dynamics
			6.4.1 Prediction of Temperature Uniformity and Velocity Distribution
				6.4.1.1 Influence of Inflow Velocity on Temperature Distribution
				6.4.1.2 Influence of Fluid Viscosity on Temperature Uniformity and Flow
				6.4.1.3 Flow Fields Predicted and Measured Inside a High-Pressure Vessel
				6.4.1.4 Influence of the Vessel Boundaries on Temperature Uniformity
				6.4.1.5 Vessel Boundary for Turbulent Conditions: The Logarithmic Wall Function
				6.4.1.6 Temperature and Flow in Vessels with Packages at Various Scales
				6.4.1.7 Temperature Uniformity in a Pressure Vessel Containing Solid Food Materials
				6.4.1.8 Effect of Adding a Carrier on Temperature Uniformity and Flow
			6.4.2 Coupling of CFD Models with Enzyme and Microbial Inactivation Kinetic Models
				6.4.2.1 Prediction and Quantification of Residual α-Amylase and E. Coli Inactivation
				6.4.2.2 Distribution of C. botulinum Inactivation in a Pilot-Scale Vessel
				6.4.2.3 Timescale Analysis: Influence of Pressure Vessel Size on Temperature Distribution
		6.5 Macroscopic Model to Represent Processing Conditions in an Entire High-Pressure System
		6.6 Application of Artificial Neural Networks for High-Pressure Process Temperature Prediction
		6.7 Comparison of Capabilities of Existing Models
		6.8 Concluding Remarks
		Nomenclature
		References
Part II: Modeling and Simulation
	Chapter 7: Direct Calculation of Survival Ratio and Isothermal Time Equivalent in Heat Preservation Processes
		7.1 Introduction
		7.2 First-Order Inactivation Kinetics
		7.3 Nonlinear Inactivation Kinetics
			7.3.1 Weibullian (‘Power Law’) Survival
			7.3.2 Log Logistic Temperature Dependence of B(T)
			7.3.3 Calculation of the Survival Ratio in Isothermal and Nonisothermal Heat Treatment
				7.3.3.1 Nonisothermal Conditions
				7.3.3.2 Calculation of the Equivalent Time at a Constant Reference Temperature
			7.3.4 Non-Weibullian Inactivation
		7.4 Web Program to Calculate Sterility
			7.4.1 Creating Survival Curves with Model-Generated Data
				7.4.1.1 Examples of the Program’s Performance
				7.4.1.2 Running the Program with Experimental Data
				7.4.1.3 Calculation of the Survival Ratios in Real Time
		7.5 Concluding Remarks
		Acknowledgment
		References
	Chapter 8: New Kinetic Models for Inactivation of Bacterial Spores
		8.1 Introduction
		8.2 History of Survivor Curve Model Approaches
		8.3 Scientific Basis for First-Order Kinetic Models
			8.3.1 Normal Log-Linear Survivor Curves
			8.3.2 Non-Log-Linear Survivor Curves
		8.4 Development of Mechanistic Models for Microbial Inactivation
			8.4.1 Normal Log-Linear Survivor Curves
			8.4.2 Non-Log-Linear Survivor Curves
		8.5 Model Validation and Comparison with Others
		8.6 Applications of Mechanistic Models to Thermal Sterilization
		8.7 Application to High Hydrostatic Pressure Sterilization
		8.8 Application to Stabilization by Curing Salts (Spore Injury)
		8.9 Sources of Other Information
		References
	Chapter 9: Modeling Heat Transfer in Thermal Processing: Retort Pouches
		9.1 Introduction
		9.2 Material Developments, Pouch Structure, and Critical Aspects
		9.3 Main Advantages and Disadvantages of Retort Pouches Compared with Metal Cans or Glass Jars
		9.4 Heat Transfer Modeling in Retort Pouches
		9.5 Mathematical Model
		9.6 Heat Transfer Mechanisms
			9.6.1 Governing Equations and Assumptions
			9.6.2 Thermophysical Properties
			9.6.3 Boundary Conditions
		9.7 Applications of Heat Transfer Models in Processing of Foods Packed in Retort Pouches
		9.8 Model Solution and Implementation
		9.9 Combination of Heat Transfer Models with Microbial Inactivation Models
		9.10 Headspace Pressure Modeling and Prediction of Overriding Pressure Profile
			9.10.1 Mathematical and Physicochemical Considerations
		9.11 Future Trends
		References
	Chapter 10: Heat Transfer in Rotary Processing of Canned Liquid/Particle Mixtures
		10.1 Introduction
		10.2 Types of Retort
			10.2.1 Still Retorts
			10.2.2 Agitating Retorts
				10.2.2.1 End-Over-End Mode
				10.2.2.2 Free Axial Mode
				10.2.2.3 Fixed Axial Mode
				10.2.2.4 Shaka System
		10.3 Heat Transfer to Canned Particulate Liquid Foods in Cans: U and hfp
		10.4 Determination of U and hfp
			10.4.1 Theory for U and hfp
			10.4.2 Experimental Procedures with Restricted Particle Motion
			10.4.3 Experimental Procedure Allowing Particle Motion
				10.4.3.1 From Liquid Temperature Only
				10.4.3.2 Indirect Particle Temperature Measurement
				10.4.3.3 Direct Particle Temperature Measurement
				10.4.3.4 Using U and hfp Correlation
		10.5 Factors Affecting Heat Transfer Coefficients
			10.5.1 Rotational Speed
			10.5.2 Fluid Viscosity
			10.5.3 Mode of Rotation
			10.5.4 Particle Concentration
			10.5.5 Particle Size
			10.5.6 Particle Shape
			10.5.7 Particle Density
		10.6 Prediction Models for Heat Transfer Coefficients (U and hfp)
			10.6.1 Dimensionless Correlations
			10.6.2 Artificial Neural Network
			10.6.3 Comparison between ANN and Dimensionless Correlation Models
		10.7 Flow Visualization
		Nomenclature
		Appendix A
			A.1 Liquid with Particulate
			A.2 Liquid without Particulate
		Appendix B
		References
	Chapter 11: Numerical Model for Ohmic Heating of Foods
		11.1 Introduction
		11.2 Ohmic Treatment
		11.3 Governing Laws
			11.3.1 Heat Transfer Model
			11.3.2 Thermophysical Properties
			11.3.3 Electric Field and the Ohm’s Law
			11.3.4 Microbial Lethality Criterion
		11.4 Experimental Setting
		11.5 Numerical Results
		11.6 Conclusions
		References
	Chapter 12: Computational Fluid Dynamics in Thermal Processing
		12.1 Introduction
		12.2 Heterogeneity in Thermal Processing: The Need for Distributed Parameter Models
		12.3 Equations Governing the Main Thermal Processes
			12.3.1 Navier–Stokes Equations
				12.3.1.1 Relationship between Shear Stress and Shear Rate
			12.3.2 Heat Transfer Equation
				12.3.2.1 Equation of State
			12.3.3 Turbulence Models
				12.3.3.1 Eddy Viscosity Models
				12.3.3.2 Near-Wall Treatment
				12.3.3.3 Reynolds Stress Model
				12.3.3.4 Large Eddy Simulation and Direct Eddy Simulation
			12.3.4 Equation for Mass Transfer
			12.3.5 Radiation Models
		12.4 Solving the Transport Phenomena: State of the Art in CFD Solutions
			12.4.1 Numerical Discretization
			12.4.2 Generic Equation and Its Numerical Approximation
			12.4.3 Meshing the Problem
			12.4.4 Obtaining a Solution
				12.4.4.1 Algebraic Equation System
				12.4.4.2 Inner Iteration Loop
				12.4.4.3 Outer Iteration Loop
		12.5 Optimizing Conventional Thermal Processes with CFD
			12.5.1 Sterilization and Pasteurization
				12.5.1.1 Canned Foods
				12.5.1.2 Foods in Pouches
				12.5.1.3 Intact Eggs
			12.5.2 Aseptic Processing
				12.5.2.1 Plate Heat Exchangers for Milk Processing
				12.5.2.2 Plate Heat Exchangers for Yoghurt Processing
			12.5.3 Dehydration
				12.5.3.1 Fluidized Bed Drying
				12.5.3.2 Spray Drying
				12.5.3.3 Forced-Convection Drying
			12.5.4 Cooking
				12.5.4.1 Natural Convection Ovens
				12.5.4.2 Forced Convection Ovens
				12.5.4.3 Baking Ovens
				12.5.4.4 Microwave Ovens
		12.6 Modeling Emerging Thermal Technologies with CFD
			12.6.1 High-Pressure Thermal Processing
			12.6.2 Ohmic Heating
		12.7 Challenges Face the Use of CFD in Thermal Process Modeling
			12.7.1 Improving the Efficiency of the Solution Process
			12.7.2 CFD and Controlling Thermal Processing
			12.7.3 Turbulence
			12.7.4 Boundary Conditions
		12.8 Conclusions
		Nomenclature
		References
Part III: Optimization
	Chapter 13: Global Optimization in Thermal Processing
		13.1 Introduction
		13.2 Dynamic Optimization
		13.3 Multimodality: Need of Global Optimization
		13.4 Global Optimization Methods
		13.5 Global Optimization of Nonlinear Dynamic Systems
		13.6 Stochastic Methods for Global Optimization
			13.6.1 Software for Global Optimization
			13.6.2 Dynamic Optimization of Thermal Sterilization
			13.6.3 Dynamic Optimization of Contact Cooking
			13.6.4 Optimal Control of Microwave Heating
		13.7 Conclusions
		References
	Chapter 14: Optimum Design and Operating Conditions of Multiple Effect Evaporators: Tomato Paste
		14.1 Introduction
		14.2 Methodology
			14.2.1 Problem Description
			14.2.2 Product Quality
			14.2.3 Model Development
			14.2.4 Economic Evaluation
			14.2.5 Maximization of NPV and Minimization of Total Cost
		14.3 CASE Studies
			14.3.1 Steady-State Conditions
			14.3.2 Lycopene Retention
			14.3.3 Economic Evaluation
			14.3.4 Optimum Number of Effects
			14.3.5 Optimum Operating Conditions
		14.4 Conclusions
		Nomenclature
		Acknowledgments
		References
	Chapter 15: Optimizing the Thermal Processing of Liquids Containing Solid Particulates
		15.1 Introduction
		15.2 Fundamentals of Thermal Optimization
			15.2.1 Quality Definition and Assessment for Aseptic Products
			15.2.2 Sterility Calculations in Mixed and Particulate Flows
			15.2.3 HTST Treatments for Heterogeneous Products
		15.3 Aseptic Quality Optimization
			15.3.1 Role of Ingredients
			15.3.2 Raw Material Storage and Handling
			15.3.3 Cook Vessel Operation
			15.3.4 Heating Stage
			15.3.5 Holding Tube
			15.3.6 Cooling Stage
			15.3.7 Aseptic Tank
			15.3.8 Filler Operation and Packaging
			15.3.9 Minimizing Shear Damage
			15.3.10 Minimizing Product Oxidation
		15.4 Aseptic Cost Optimization
			15.4.1 Optimized Ingredient Sourcing
			15.4.2 Factory-Wide Optimization
			15.4.3 Optimal Control Strategies
			15.4.4 Run-Length Extension
		15.5 Future Trends
		15.6 Concluding Remarks
		Acknowledgments
		Nomenclature
		References
	Chapter 16: Optimizing Plant Production in Batch Thermal Processing: Case Study
		16.1 Introduction
		16.2 Methodology
			16.2.1 Materials
			16.2.2 Equipment
			16.2.3 Heat-Penetration Tests for Products under Study
			16.2.4 Methods
				16.2.4.1 Simultaneous Sterilization Characterization
				16.2.4.2 Cubic Splines
				16.2.4.3 Mathematical Formulation for Simultaneous Sterilization
				16.2.4.4 Computational Procedure
				16.2.4.5 Mixed Integer Linear Programming Model
		16.3 Analysis and Discussions
		16.4 Conclusions
		References
Part IV: Online Control and Automation
	Chapter 17: Online Control Strategies: Batch Processing
		17.1 Introduction
		17.2 Methodology
			17.2.1 Task 1: Proportional Correction Strategy Development
			17.2.2 Task 2: Performance Demonstration
			17.2.3 Task 3: Demonstration of Safety Assurance by Complex Optimization Search Routine
			17.2.4 Task 4: Economic and Quality Impact of Online Correction Strategy
			17.2.5 Task 5: Online Correction without Extending Process Time
		17.3 Analysis and Discussions
			17.3.1 Equivalent Lethality Curves
			17.3.2 Performance Demonstration
			17.3.3 Demonstration of Safety Assurance by Complex Search Routine
			17.3.4 Economic and Quality Impact of Online Correction Strategy
			17.3.5 Correction Strategy without Extending Process Time and Preliminary Validation
		17.4 Conclusions
		Nomenclature
		References
	Chapter 18: Plant Automation for Automatic Batch Retort Systems
		18.1 Introduction
		18.2 Automated Batch Retort Systems
			18.2.1 Material Handling System
				18.2.1.1 Preparing the Load for Process
			18.2.2 Retorts and the LOG-TEC™ Momentum Control System
				18.2.2.1 Control Strategies for Critical Control Points
				18.2.2.2 Preparing to Unload
			18.2.3 Basket Tracking System
				18.2.3.1 BTS Host Computer
				18.2.3.2 Critical Control Points for Basket Tracking System
				18.2.3.3 Process Status and Disposition of Deviated Product
				18.2.3.4 Safety Measures against Unloading Unprocessed Product
		18.3 Process Optimization Using Advanced Control Systems
			18.3.1 Modeling Heat Transfer Processes during Thermal Processing
				18.3.1.1 Empirical Methods (Formula Methods)
				18.3.1.2 Numerical Methods
			18.3.2 Online Correction of Process Deviations in Batch Retorts
			18.3.3 Future Trends on Online Correction of Process Deviations in Continuous Retorts
			18.3.4 Additional Regulatory Considerations
		References
                        
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58584_half.pdf


ENGINEERING ASPECTS
OF THERMAL FOOD

PROCESSING

� 2008 by Taylor & Francis Group, LLC.

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005x003_B.eps


and application of kinetic models in response to high-pressure sterilization and

stabilization by curing salts.

8.2 HISTORY OF SURVIVOR CURVE MODEL APPROACHES

The history of survivor curve models provides vital information to address current

important problems related to the characteristics observed in semilogarithmic inac-

tivation curves of microbial populations. Basic mathematical models were proposed

very early in the twentieth century (Chick, 1908, 1910). Watson (1908) examined

two main approaches used to study the inactivation of bacterial spores at that time:

mechanistic and vitalistic. He presented Chick’s model mathematically as a fi rst-

order reaction (Chick–Watson equation) describing the exponential decay commonly

observed in microbial survivor curves. This model is the basis of the mechanistic

approach and defi nes the inactivation of bacterial spores as a pseudo fi rst-order

molecular transformation. The temperature dependency of the corresponding rate

constant was found to be appropriately described by the Arrhenius equation.

The vitalistic approach was based on the assumption that the observed exponential

decay could be explained by differences in resistance of the individuals. Watson

noted that in order for this argument to hold, most of the spores would have to be

at the low extreme of resistance, instead of following the normal distribution that

would be expected from natural biological variability. He concluded that the vitalis-

tic approach could not be correct. Kellerer (1987) stated that the vitalistic approach

is naïve and ignores the rigorous stochastic basis for the inactivation transformation

(Maxwell–Boltzman’s distribution of speed of molecules or random radiation “hits”

on DNA) by using the simplistic assumption that the biological variability of the

resistance can explain the observed behavior correctly.

A third option is the approach developed by Aiba and Toda (1965), where the life

span probability of spores was mathematically defi ned and used to develop expres-

sions describing inactivation of single and clumped spores. This analysis postulated

that for a population of spores (Ni in number and ti in life span), the probability
associated with the distribution of life span is



=
κ∏

0

r

! 1

!i
i

N
P

N


(8.1)

where κ is a normalizing factor.
Based on this probability function, Ni could be described as a function of the life

span (ti) provided that the initial number of spores (N0) was large:


( )expi iN tα′= −β′ (8.2)

or, modifying the discrete equation into its continuous form (for large N0):


( )d exp

d

N
t

t
α′− = −β′


(8.3)

Thus, the probabilistic approach led to the same response equation as that of the

mechanistic approach. This revelation leads to several important concepts:
� 2008 by Taylor & Francis Group, LLC.

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1. Arbitrary use of frequency distribution equations, such as the Weibull distri-

bution, is an extensive “jump” in logic that cannot be rigorously justifi ed.

2. Clumping induces a delay that depends on the number of spores per clump,

and can be described using the probabilistic approach. However, clumping

will not lead to increments in the number of survivors such as those induced

by spore activation.

3. The probabilistic approach established a direct relationship between the

average life span and the rate constant used in the mechanistic approach.

Both approaches lead to the same basic mathematical model.

8.3 SCIENTIFIC BASIS FOR FIRST-ORDER KINETIC MODELS

8.3.1 NORMAL LOG-LINEAR SURVIVOR CURVES

The nature of the inactivation transformation can be addressed and explained in terms

of Eyring’s transition-state theory and the Maxwell–Boltzman distribution of the

speed of molecules from molecular thermodynamics. For a given confi guration (i.e.,

mass and degrees of freedom), the fraction of molecules that have enough kinetic

energy to overcome the energetic barrier (i.e., the activation energy) for a transfor-

mation such as inactivation of spores depends mostly on temperature. Therefore, at

a given temperature, the fraction of molecules that will reach the level of energy

required for the transformation (in this case inactivation) to happen is constant.

The fraction of molecules that have enough energy to react will increase with tem-

perature. For instance, if at a given temperature 10% of the molecules have enough

energy for inactivation to occur, the percentage inactivated during a time interval

will remain constant. This explains why the instantaneous rate of inactivation is

proportional to the number of surviving spores present at that moment. This can be

envisioned by random swatting of fl ies by a blind person trapped in a phone booth.

The number of fl ies successfully swatted per unit of time will depend upon (and be pro-

portional to) the number still in fl ight at that moment, and will decrease exponentially

with time, just as with any concentration-dependent (fi rst-order) reaction. Variability

from biological or environmental factors is refl ected by the effect they have on values

of the rate constants. For example, an increase in temperature (speed of molecules)

could be represented by an increase in rate of swatting (speed of fl y swatter).

8.3.2 NON-LOG-LINEAR SURVIVOR CURVES

Activation of dormant spores and the presence of subpopulations with different

resistance give rise to the “shoulders and tails” appearing as deviations from log-

linearity in some survivor curves exhibited by spore-forming bacteria. Models that

include these concepts based on systems analysis of population dynamics were devel-

oped in the late 1980s and early 1990s (Rodriguez et al., 1988, 1992; Sapru et al.,

1992, 1993), and verifi ed experimentally under extreme-case conditions. The cases

of “shoulders” caused by activation of dormant spores as well as that of “biphasic

tailing” (early rapid inactivation of a subpopulation of relatively low heat resistance

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