ITEM METADATA RECORD
Title: multiscale modelling of gas transport in fruit during controlled atmosphere storage
Other Titles: Micro-scale modelling of gas diffusion in pear tissue during long term storage
Authors: Ho, Quang Tri
Issue Date: 19-Dec-2008
Table of Contents: Contents
Acknowledgements iii
Nederlandse samenvatting v
Abstract ix
Contents xiii
Symbols and Abbreviations xix
1 General introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Respiration and postharvest storage technology . . . . . . . . . . 3
1.3 Gas transport routes in fruit tissue . . . . . . . . . . . . . . . . . 6
1.4 CA storage disorders of fruit . . . . . . . . . . . . . . . . . . . . 8
1.5 Modelling of gas exchange . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Objectives and outline of the work . . . . . . . . . . . . . . . . . 14
2 Multiscale modeling of gas transport in plant tissues 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Mass transport fundamentals . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Fickian law of di�usion . . . . . . . . . . . . . . . . . . . 18
2.2.2 Knudsen di�usion . . . . . . . . . . . . . . . . . . . . . . 19
2.2.3 Advection mass transport . . . . . . . . . . . . . . . . . . 19
2.3 Length scales in multiscale modelling . . . . . . . . . . . . . . . . 20
2.4 Multiscale gas transport modeling . . . . . . . . . . . . . . . . . 22
2.4.1 Macroscale approach . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 Microscale approaches . . . . . . . . . . . . . . . . . . . . 25
2.5 Geometrical model . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.1 Macroscale geometry model . . . . . . . . . . . . . . . . . 26
xiii
xiv CONTENTS
2.5.2 Microscale geometry model . . . . . . . . . . . . . . . . . 27
2.6 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Gas di�usion properties 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Fruit material . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Experimental system and procedure . . . . . . . . . . . . 34
3.2.3 Calibration of the optical sensors . . . . . . . . . . . . . . 36
3.2.4 Respiration measurement . . . . . . . . . . . . . . . . . . 38
3.2.5 Continuum model of gas transport and parameter estimation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Respiration measurement on pear tissue disks . . . . . . . 40
3.3.2 Gas di�usion measurement . . . . . . . . . . . . . . . . . 41
3.3.3 O2 and CO2 di�usion in the tissue . . . . . . . . . . . . . 42
3.3.4 Position dependent di�usivity in a fruit . . . . . . . . . . 43
3.3.5 Maturity e�ect and storage condition on gas di�usivities . 44
3.3.6 Temperature e�ect on respiration and gas di�usivity of
tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.1 Gas di�usion measurement . . . . . . . . . . . . . . . . . 49
3.4.2 O2 and CO2 di�usion in the tissue . . . . . . . . . . . . . 50
3.4.3 Position dependent di�usivities in a fruit . . . . . . . . . 51
3.4.4 Maturity e�ect and storage condition on gas di�usivities . 52
3.4.5 Temperature e�ect on respiration and gas di�usivity of
tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Permeation gas transport 55
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Materials and method . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.2 Model of gas transport in pear tissue . . . . . . . . . . . . 57
4.2.3 Measurement of gas transport parameters . . . . . . . . . 58
4.2.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 O2 and N2 di�usivities . . . . . . . . . . . . . . . . . . . . 62
CONTENTS xv
4.3.2 Gas permeation properties . . . . . . . . . . . . . . . . . . 62
4.3.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.1 O2 and N2 di�usivity . . . . . . . . . . . . . . . . . . . . 65
4.4.2 E�ect of gas permeation . . . . . . . . . . . . . . . . . . . 68
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 A macroscale continuum model for metabolic gas exchange 71
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.1 Fruit material . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.2 Respiration models . . . . . . . . . . . . . . . . . . . . . . 74
5.2.3 Permeation-di�usion-reaction model . . . . . . . . . . . . 75
5.2.4 Measurement of tissue respiration . . . . . . . . . . . . . 76
5.2.5 Measurement of gas exchange coe�cients . . . . . . . . . 76
5.2.6 Pear geometry . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.7 Numerical solution . . . . . . . . . . . . . . . . . . . . . . 77
5.2.8 Model validation . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1 Overview of the continuum-model for exchange of metabolic
gasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.2 Respiration of pear tissue . . . . . . . . . . . . . . . . . . 79
5.3.3 Validation of the respiration di�usion model . . . . . . . . 80
5.3.4 E�ect of permeation of the gas exchange in the whole fruit 83
5.3.5 E�ect of geometry on local respiratory gas concentration . 85
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4.1 Permeation-di�usion-reaction model . . . . . . . . . . . . 85
5.4.2 Comparison of intact pear and pear tissue disk respiration 89
5.4.3 E�ect of temperature on gas exchange . . . . . . . . . . . 91
5.4.4 E�ect of pear size and storage atmosphere composition on
gas exchange . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6 Microscale mechanisms of gas exchange in fruit tissue 93
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.2 Gas concentration pro�les in intact fruit . . . . . . . . . . 95
6.2.3 Characteristic gas exchange rates in tissue samples . . . . 96
xvi CONTENTS
6.2.4 Construction of a 2-D geometric model of pear cortex tissue 96
6.2.5 Microscale gas exchange model . . . . . . . . . . . . . . . 97
6.2.6 Physical properties and respiration parameters of pores,
cell walls and cells . . . . . . . . . . . . . . . . . . . . . . 100
6.2.7 In silico study of gas exchange . . . . . . . . . . . . . . . 101
6.2.8 Apparent di�usivity of pear cortex tissue . . . . . . . . . 101
6.2.9 Macroscale continuum model . . . . . . . . . . . . . . . . 103
6.2.10 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . 103
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.3.1 Microscale gas exchange . . . . . . . . . . . . . . . . . . . 104
6.3.2 Apparent O2 and CO2 di�usivity . . . . . . . . . . . . . . 104
6.3.3 Gas concentration gradients in pear fruit . . . . . . . . . 106
6.3.4 Sensitivity of gas exchange to microscale features . . . . . 110
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.4.1 Microscale model vs. macroscale model . . . . . . . . . . 110
6.4.2 Importance of the cell wall . . . . . . . . . . . . . . . . . 112
6.4.3 Transport of CO2 in the intracellular compartments . . . 112
6.4.4 Biological variation of apparent di�usivities . . . . . . . . 113
6.4.5 Anoxia and core disorders in bulky plant organs . . . . . 113
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7 3-D Microscale modelling of gas di�usion in fruit tissue 117
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . 118
7.2.1 Tissue microstructure . . . . . . . . . . . . . . . . . . . . 118
7.2.2 Microscale gas exchange model . . . . . . . . . . . . . . . 119
7.2.3 Numerical solution . . . . . . . . . . . . . . . . . . . . . . 119
7.2.4 Physical properties and respiration parameters of the microscale
model . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.5 Continuum model and apparent di�usivity . . . . . . . . 122
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3.1 Gas concentration pro�le . . . . . . . . . . . . . . . . . . 123
7.3.2 O2 transport in di�erent types of pear tissue . . . . . . . 124
7.3.3 Flux of gas transport through the tissue . . . . . . . . . . 128
7.3.4 REV and simulated di�usivity in cortex tissue . . . . . . 129
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.4.1 3-D microscale model versus 2-D model . . . . . . . . . . 130
7.4.2 Gas di�usion at di�erent types of tissue . . . . . . . . . . 130
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
CONTENTS xvii
8 Multiscale modelling of gas exchange 133
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2.2 Macroscale model . . . . . . . . . . . . . . . . . . . . . . 135
8.2.3 Microscale model . . . . . . . . . . . . . . . . . . . . . . . 136
8.2.4 Localisation . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.2.5 Numerical solution . . . . . . . . . . . . . . . . . . . . . . 137
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.3.1 Gas transport properties and respiration kinetics parameters
of fruit tissue . . . . . . . . . . . . . . . . . . . . . . 137
8.3.2 Multiscale modeling of gas transport of pear in relation
to storage conditions . . . . . . . . . . . . . . . . . . . . . 139
8.3.3 E�ect of fruit ripening on internal gas concentration . . . 142
8.3.4 CO2 concentration in pear fruit . . . . . . . . . . . . . . . 143
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.4.1 E�ect of CO2 on the risk of browning disorder . . . . . . 146
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
9 General conclusions and future work 149
9.1 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A 155
A.1 Sensitivity analysis and optimization of the measurement set-up . 155
A.2 Relative bias of gas di�usivity . . . . . . . . . . . . . . . . . . . . 156
A.3 Total coe�cient of variation . . . . . . . . . . . . . . . . . . . . . 157
B 159
B.1 Numerical scheme for the permeation-di�usion-reaction model . . 159
C 161
C.1 Sample preparation for microscopic image . . . . . . . . . . . . . 161
C.2 CO2 species in the liquid phase . . . . . . . . . . . . . . . . . . . 161
C.3 CO2 transport model in cell including the vacuole . . . . . . . . 162
C.3.1 Model of CO2 transport with cell including the vacuole
(CIV model) . . . . . . . . . . . . . . . . . . . . . . . . . 162
C.3.2 In silico simulation of CO2 transport with cell including
the vacuole (CIV model) . . . . . . . . . . . . . . . . . . . 162
xviii Table of Contents
Bibliography 165
List of publications 183
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Division of Mechatronics, Biostatistics and Sensors (MeBioS)

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