Contents
List of Figures vii
List of Tables xi
Preface xiii
Chapter 1 Information Entropy 1
1.1 Introduction 1
1.2 History and expectation 1
1.3 Information 5
1.4 Amount of information 6
1.5 Average amount of information before reporting the result 7
1.6 Information entropy based on continuous variable 11
1.7 Probability density distribution function for the maximum information
entropy 12
1.8 Sensitiveness of human experience for quantity and information entropy 18
1.9 Summary 20
Chapter 2 Mixing Phenomena 21
2.1 Introduction 21
2.2 Index for evaluation of mixing performance 23
2.3 Evaluation of mixing performance based on transition response method 26
2.4 Evaluation of mixing performance based on transition probability of
inner substance 55
2.5 Evaluation of mixing performance of multi-component mixing 67
2.6 Summary 79
Chapter 3 Separation Phenomena 81
3.1 Introduction 81
3.2 Definition of separation efficiency 84
3.3 Summary 93
Chapter 4 Turbulent Phenomena 95
4.1 Introduction 95
4.2 Probability density distribution function for velocity fluctuation 99
4.3 Energy spectrum probability density distribution function 100
4.4 Scale of turbulence and turbulent diffusion 105
4.5 Scale-up 108
vi Contents
4.6 Energy spectrum density distribution function of non-Newtonian liquid 118
4.7 Summary 123
Chapter 5 Particle Size Distribution 125
5.1 Introduction 125
5.2 Particle size probability density distribution function (PSD function) 126
5.3 Eddy size distribution in a turbulent flow 131
5.4 Summary 142
Chapter 6 Anxiety/Expectation 143
6.1 Introduction 143
6.2 Safety and anxiety 145
6.3 Evaluation index of anxiety/expectation 146
6.4 Utilization method and usefulness of newly defined degree of anxiety 151
6.5 Decision-making regarding daily insignificant matters 163
6.6 Summary 165
References 167
Epilogue 171
Index 173
List of Figures
Chapter 1
1.1 Probability density distribution for the maximum amount of entropy. 13
1.2 Change of sense of human experience for quantity. 19
1.3 Aha! Thought. 20
Chapter 2
2.1 Typical transient response methods. 26
2.2 Impulse response method in a flow system. 28
2.3 RTD curve of perfect mixing flow. 31
2.4 (a) SPMV model in a flow system. (b) RTD curves in SPMV model in a
flow system. (c) Mixing capacity change with number of tanks in SPMV
model in a flow system. 32
2.5 (a) Stirred vessel of a flow system. (b) Four sets of positions of inlet and
outlet of a flow system. (c) Mixing capacity change with impeller
rotational speed for four sets of positions of inlet and outlet of a flow
system. 35
2.6 Definition diagram for batch system-I. 38
2.7 (a) Stirred vessel of a batch system and imaginary partition of vessel. (b)
Three types of impeller. (c) Relationship between mixedness and real
time of FBDT impeller in a stirred vessel. (d) Relationship between
mixedness and dimensionless time of FBDT in a stirred vessel. (e)
Relationship between mixedness and dimensionless time of FBT and 45
PBT in a stirred vessel. 41
2.8 (a) Aerated stirred vessel and imaginary partition of vessel. (b)
Relationship between mixedness and dimensionless time in an aerated
stirred vessel 48
2.9 (a,b) Concentration distribution of tracer in a cross-section through axis
in a circular pipe (left-hand side dotted lines in both figures are pipe axis,
left-hand side figure is center injection, right-hand side figure is wall ring
injection; z: axial position, r: radial position, rw: pipe radius, U0: pipe
center average velocity, Um: cross average velocity). (c) Mixedness
change in axial direction in a circular pipe. 51
2.10 (a) Bubble column and imaginary partition of column. (b) Relationship
between mixedness and real time in a bubble column. (c) Relationship
between mixedness and dimensionless time based on the contact time of
bubble and liquid in a bubble column. 53
2.11 Definition diagram for batch system-II. 55
viii List of Figures
2.12 Local mixing capacity map in case of FBDT impeller and 45 PBT
impeller in a stirred vessel (lines are contours of height at intervals of 0.02). 63
2.13 Mixedness change with time when tracer is injected from 10-region in
case of FBDT impeller and 45 PBT impeller in a stirred vessel. 64
2.14 (a,b) The degree of dispersion of the tracer particles at down flow region
is shown by number of dots. (a) Vertical cross-section, (b) Horizontal
cross-section. (c) Local mixing capacities and turbulent diffusivity in a
circular pipe. 66
2.15 Definition diagram for multi-component mixing in a stirred vessel. 68
2.16 (a) Initial setting of five components in a stirred vessel. (b) Mixedness
change with time of five-component mixing in case of FBDT impeller
and 45 PBT impeller in a stirred vessel. 73
2.17 Mixing in a crystallizer considering continuous phase (upper left-hand:
imaginary regions partitioned; the others: local size distribution of
dispersion particle and mixedness). 76
2.18 Solid–liquid mixing in a stirred vessel. 78
Chapter 3
3.1 Feed, product, and residuum in case of binary component in a separation
equipment. 83
3.2 Definition diagram for separation process. 85
3.3 (a) Comparison of new efficiency curves and Newton efficiency curves.
(b) S-shaped curve of new efficiency. 91
3.4 Distillation column. 92
Chapter 4
4.1 Velocity fluctuations with time. 96
4.2 Effect of combination of values of  and  on ESD. 104
4.3 Estimated curves based on new ESD function and practical data of ESD. 106
4.4 Velocity-measured region in a stirred vessel. 109
4.5 ESD in impeller discharge flow region in a stirred vessel. 110
4.6 Relationship between average wave number of smallest eddy group and
kinetic viscosity. 110
4.7 (a) Distributions of energy values and (b) distributions of double
correlation values of turbulent fluctuations in impeller discharge flow
region in a stirred vessel. 112
4.8 Evaluation of traditional scale-up rules based on new ESD function. 114
4.9 ESD for air and water flow in a circular pipe (involve the data by authors). 116
4.10 Relationship between pipe diameter and number of eddy groups. 117
4.11 Rheology characteristics of 0.6 wt% aq. CMC sol. 120
4.12 Measured ESD of 0.6 wt% aq. CMC sol. and fitted ESD curve based on
new ESD function. 121
4.13 Velocity-measuring probes based on electrode reaction controlled by
mass transfer rate. 122
List of Figures ix
Chapter 5
5.1 (a) Data of Rosin–Rammler distribution and fitted PSD curve based on
new PSD function. (b) Original PSD curve and realized probability curve
in the case of Rosin–Rammler distribution. (c) Data of log-normal
distribution and fitted PSD curve based on new PSD function. (d) Data
of normal distribution and fitted PSD curve based on new PSD function. 133
5.2 Data of droplet size probability density distribution in liquid–liquid
mixing and fitted PSD curve based on new PSD function. 136
5.3 Flow states controlled by stirring and aeration. 137
5.4 Data of bubble size probability density distribution in an aerated stirred
vessel and fitted PSD curve based on new PSD function. 138
5.5 Data of crystal size probability density distribution and fitted PSD curve
based on new PSD function. 140
5.6 Data of crushed product size probability density distribution and fitted
PSD curve based on new PSD function. 142
Chapter 6
6.1 Information entropy distribution. 147
6.2 Difference between maximum amount of information entropy and
amount of information entropy at arbitrary probability value. 148
6.3 Anxiety/expectation–probability curve. 150
6.4 Difference between objective probability and subjective probability. 151
6.5 Anxiety–probability curve in the case of accident in outdoors. 153
6.6 Priority between two units to improve. 155
6.7 Expectation–probability curve for decision-making to adopt the means to
improve. 157
6.8 Anxiety–probability curve for decision-making to adopt the means to
improve. 158
6.9 Expectation–probability curve of betting for certain condition that gives
reasonable explanation. 162
6.10 Distributions of weight function. 164
6.11 Anxiety–probability curves considering weight function. 164
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List of Tables
Chapter 1
1.1 Relationships among information entropies 11
Chapter 2
2.1 Traditional indices of mixing performance 24
2.2 Transition probability from j-region to i-region of FBDT impeller and
45 PBT impeller 61
2.3 Volume fraction of all components 76
Chapter 3
3.1 Separation of binary component 83
3.2 Quantitative relationship among indices of mixing and separation
performance. 89
3.3 Initial conditions and the sensitivity of new separation efficiency in case
of distillation operation 93
Chapter 4
4.1 Traditional ESD Function 100
4.2 Traditional scale-up rules 111
4.3 Relationship between pipe inner diameter (cm) and number of eddy groups 117
Chapter 5
5.1 Values of curve fitting parameters in new PSD function for typical three
traditional PSDs 132
Chapter 6
6.1 Fourfold pattern and winning results 160
6.2 Percentage of respondents of betting 161

نوشته شده توسط محمد صادق کریمی در جمعه پانزدهم مهر ۱۳۹۰ |

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