Dimensional Analysis of Food Processes

Dimensional Analysis of Food Processes

1st Edition - August 1, 2015

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  • Authors: Guillaume Delaplace, Karine Loubière, Fabrice Ducept, Romain Jeantet
  • eBook ISBN: 9780081004876
  • Hardcover ISBN: 9781785480409

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This book deals with the modeling of food processing using dimensional analysis. When coupled to experiments and to the theory of similarity, dimensional analysis is indeed a generic, powerful and rigorous tool making it possible to understand and model complex processes for design, scale-up and /or optimization purposes. This book presents the theoretical basis of dimensional analysis with a step by step detail of the framework for applying dimensional analysis, with chapters respectively dedicated to the extension of dimensional analysis to changing physical properties and to the use of dimensional analysis as a tool for scaling-up processes. It includes several original examples issued from the research works of the authors in the food engineering field, illustrating the conceptual approaches presented and strengthen the teaching of all.

Key Features

  • Discusses popular dimensional analysis for knowledge and scaling-up tools with detailed case studies
  • Emphasises the processes dealing with complex materials of a multiphase nature
  • Introduces the concept of chemical or material similarity and a framework for analysis of the functional forms of the propoerty


Academics, undergraduate and graduate students of food science/food process engineering and food engineering; professionals in food and process engineering

Table of Contents

    • Foreword
    • Introduction
    • 1: Objectives and Value of Dimensional Analysis
      • Abstract
      • 1.1 Grouping dimensional variables in the form of a set of dimensionless numbers with a precise physical sense
      • 1.2 Constructing generic models which can be used on other scales
      • 1.3 Reduce the number of experiments by providing a synthetic and physical view of the phenomena
      • 1.4 A tool for carrying out processes and assisting a reverse engineering approach
    • 2: Dimensional Analysis: Principles and Methodology
      • Abstract
      • 2.1 Terminology and theoretical elements
      • 2.2 From internal measures to the form of a process relationship
      • 2.3 Configuration and operating point of a system
      • 2.4 Guided example 1: power consumption for a Newtonian fluid in a mechanically stirred tank
    • 3: Practical Tools for Undertaking the Dimensional Analysis Process
      • Abstract
      • 3.1 Establishment of the list of relevant physical quantities which influence the target variable
      • 3.2 Choosing the base
      • 3.3 Some techniques for reducing the set of dimensionless numbers (configuration of the system)
    • 4: Dimensional Analysis of Processes Influenced by the Variability of Physical Properties
      • Abstract
      • 4.1 Introduction
      • 4.2 Influence of the material function on the process relationship and material similarity
      • 4.3 Dimensionless material functions: standard non-dimensionalization method and invariance properties
      • 4.4 How to construct the π – space in the case of a process involving a material with a variable physical property
      • 4.5 Guided example 2
    • 5: Dimensional Analysis: A Tool for Addressing Process Scale-up Issues
      • Abstract
      • 5.1 Conditions to satisfy to ensure complete similarity between the two scales: conservation of the operating point
      • 5.2 Guided example 3: cooking a chicken
      • 5.3 Guided example 4: power of a vertical impeller on an industrial scale
      • 5.4 Guided example 5: emulsification process in an agitation tank
      • 5.5 Specific case of a scale change in a process involving a material with a variable physical property (guided example 6)
    • 6: Case Studies
      • Abstract
      • 6.1 Rehydration time for milk powder in a stirred tank
      • 6.2 Continuous foaming by whipping
      • 6.3 Fouling of a plate heat exchanger by a milk protein solution
      • 6.4 Dry mixing of powders: mixing time and power consumption
      • 6.5 Gas–liquid mass transfer in a mechanically stirred tank containing shear-thinning fluids
      • 6.6 Ohmic heating
    • Conclusions
    • Appendices
    • Appendix 1: Shift Relationships between Spaces of Dimensionless Numbers
    • Appendix 2: Physical Meaning of Dimensionless Numbers Commonly Used in Process Engineering
      • A2.1 Internal measures related to the material fluxes
      • A2.2 Internal measures related to the momentum fluxes
      • A2.3 Internal measures related to the energy fluxes
      • A2.4 Other internal measures
    • Appendix 3: The Transitivity Property of the Standard Non-dimensionalization Method and its Consequences on the Mathematical Expression of Reference-Invariant Standard Dimensionless Material Functions (RSDMFs)
      • A3.1 Transitivity of the standard non-dimensionalization method
      • A3.2 Applying the property of transitivity
    • Appendix 4: Cases Where the Analytical Expression of the Material Function Is Known
      • A4.1 Bingham fluid
      • A4.2 Williamson–Cross fluid
    • Appendix 5: Cases Where There Is No Known Analytical Expression of the Material Function
    • Appendix 6: Relevant Choice of the Reference Abscissa for Non-Newtonian Fluids
      • A6.1 Bingham fluid
      • A6.2 Williamson–Cross fluid
      • A6.3 Summary for non-Newtonian fluids
    • Bibliography
    • Index

Product details

  • No. of pages: 356
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2015
  • Published: August 1, 2015
  • Imprint: ISTE Press - Elsevier
  • eBook ISBN: 9780081004876
  • Hardcover ISBN: 9781785480409

About the Authors

Guillaume Delaplace

Affiliations and Expertise

Research Director in the Department of Science and Process Engineering of Agricultural Products at INRA in Lille, France

Karine Loubière

Affiliations and Expertise

CNRS Research Scientist at the University of Toulouse, France.

Fabrice Ducept

Affiliations and Expertise

Assistant Professor, AgroParisTech, France

Romain Jeantet

Affiliations and Expertise

Professor, Agrocampus Ouest, INRA, Rennes, France

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