Non-Linear Mass Transfer and Hydrodynamic Stability
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Table of contents
- Cover
- CONTENTSvii
- PREFACExi
- Introduction1
- LINEAR MASS TRANSFER THEORY1
- 1. Model theories2
- 2. Boundary layer theory4
- 3. Immobile phase boundary5
- 4. Moving phase boundary7
- 6. Counter-current flow10
- References15
- Part 1: Systems with Intensive Interphase Mass Transfer17
- CHAPTER 1.1. SPECIFICS OF THE HYDRODYNAMIC CONDITIONS OF THE INTENSIVE INTERPHASE MASS TRANSFER17
- 1.1.1. Influence of the intensive interphase mass transfer on hydrodynamics17
- 1.1.2. Boundary conditions of the non-linear mass transfer problem19
- CHAPTER 1.2. GAS (LIQUID)-SOLID SYSTEM21
- 1.2.1. Non-linear mass transfer in the boundary layer21
- 1.2.2. Heat transfer in the conditions of non-linear mass transfer29
- 1.2.3. Multicomponent mass transfer33
- 1.2.4. Non-linear mass transfer in the entrance region of a channel37
- CHAPTER 1.3. GAS-LIQUID AND LIQUID-LIQUID SYSTEMS40
- 1.3.1. Non-linear mass transfer in the gas and in the liquid boundary layer40
- 1.3.2. Multicomponent interphase mass transfer in the case of an intensive mass transfer in the gas54
- 1.3.3. Non-linear interphase mass transfer between two liquids59
- CHAPTER 1.4. GAS–FALLING LIQUID FILM SOLID SURFACE SYSTEM64
- 1.4.1. Non-linear interphase mass transfer between the gas and the falling liquid film64
- 1.4.2. Non-linear effects in the case of a multicomponent interphase mass transfer between the gas a76
- CHAPTER 1.5. EFFECTS OF CONCENTRATION AND TEMPERATURE ON THE NON-LINEAR MASS TRANSFER85
- 1.5.1. Concentration effects85
- 1.5.2. Influence of the high concentration on the mass transfer rate91
- 1.5.3. Non-linear mass transfer and Marangoni effect99
- References107
- Part 2: Electrochemical Systems With High Intensity Electric Currents111
- CHAPTER 2.1. FUNDAMENTALS OF THE KINETIC THEORY OF TRANSPORT OF MASS AND CHARGE IN ELECTRIC SYSTEMS111
- 2.1.1. Method of the self-consistent field112
- 2.1.2. Transport of neutral molecules in the self-consistent field of the double electric layer114
- 2.1.3. Method of the local thermodynamic equilibrium116
- CHAPTER 2.2. ANODIC METAL DISSOLUTION IN AN ELECTROLYTE FLOW118
- 2.2.1. Dissolution of surfaces equi-accessible with respect the ionic mass transfer122
- 2.2.2. Ionic mass transfer due to an anodic dissolution complicated with a reaction of complex forma127
- 2.2.3. Comparison between the theoretical predictions and the experimental data132
- 2.2.4. Ionic mass transfer effects on the hydrodynamics during dissolution of a rotating disk electr134
- 2.2.5. Anodic dissolution of metals in concentrated solutions with variable physical properties137
- 2.2.6. Effect of saturation of near-anode layer by electrode reaction products141
- 2.2.7. Electrochemical dissolution of metal inclusions in channels142
- 2.2.8. Dissolution of rectangular channel walls146
- CHAPTER 2.3. ELECTROCHEMICAL RECOVERY OF METALS FROM CONCENTRATED SOLUTIONS157
- 2.3.1. Method for the establishment of the effects of the apparent diffusion coefficient of the salt158
- CHAPTER 2.4. EFFECT OF THE NON-ISOTHERMAL CONDITIONS AND THE GAS EVOLUTION161
- 2.4.1. Non-isothermal effects on potential distributions in an injection flow electrochemical cell161
- 2.4.2. Gas evolution164
- References165
- Part 3: Chemically Reacting Gas-Liquid Systems171
- CHAPTER 3.1. INTERPHASE MASS TRANSFER MECHANISM172
- 3.1.1. Irreversible chemical reactions178
- 3.1.2. Homogenous catalytic reactions184
- 3.1.3. Reversible chemical reactions187
- 3.1.4. Relationships between the chemical and physical equilibriums during absorption191
- CHAPTER 3.2. MACROKINETICS OF THE CHEMICAL TRANSFORMATIONS193
- 3.2.1.Chemosorption in a falling liquid film195
- 3.2.2. Sulphuric acid alkylation process in a film flow reactor198
- 3.2.3. Non-linear mass transfer in a falling liquid film203
- CHAPTER 3.3. EFFECTS OF THE PHYSICAL PARAMETERS207
- 3.3.1. Concentration effects207
- 3.3.2. Temperature effects210
- References223
- Part 4: Non-Stationary Interphase Mass Transfer with Chemical Reactions225
- CHAPTER 4.1. NON-STATIONARY PHYSICAL ABSORPTION227
- 4.1.1. Problem solution230
- 4.1.2. Solutions at short contact times232
- 4.1.3. Interphase mass transfer resistance located in one of the phases233
- 4.1.4. Solution on the line β = 1234
- 4.1.5. Solution in the upper part of X – Y plane235
- 4.1.6. Solution in the lower part of the X – Y plane236
- 4.1.7. Solution in the left part of X – Y plane237
- 4.1.8. Solution in the right part of X – Y plane239
- 4.1.9. Numerical solutions240
- 4.1.10. Approximations of the numerical solutions246
- 4.1.11. Physical absorption249
- 4.1.12. Non-stationary interphase heat transfer252
- 4.1.13. Interphase heat transfer regimes256
- CHAPTER 4.2. NON-STATIONARY TWO-PHASE ABSORPTION COMPLICATED WITH FIRST ORDER CHEMICAL REACTION261
- 4.2.1. Solution in X-Y plane at ε << 1, εβ << 1265
- 4.2.2. Solution in the area with ε >> 1, εβ << 1268
- 4.2.3. Solution at ε >> 1 and εβ >> 1269
- 4.2.4. Solution in the area with ε << 1 , εβ >> 1269
- 4.2.5. Solution at β2 = 1271
- 4.2.6. Common properties of the solutions271
- 4.2.7. Numerical investigation of the two-phase chemosorption in the initial time interval277
- 4.2.8. Numerical investigation of the chemosorption outside the initial interval288
- 4.2.9. Methodology of the chemosorption design290
- CHAPTER 4.3. NON-STATIONARY ABSORPTION WITH SECOND ORDER CHEMICAL REACTION291
- 4.3.1. Mass transfer in the liquid at short contact times294
- 4.3.2. Transformation of the problem of two-phase chemosorption to a two-phase absorption problem wi303
- 4.4.3. Solution with parameters εN <=1, εβN <=1307
- 4.3.4. Solution with parameters εN>=1 and εβN >= 1328
- 4.3.5. Investigations in the fourth quadrant of the plane XN – YN343
- 4.3.6. Investigations in the second quadrant on the plane XN – YN357
- 4.3.7. Analysis of the basis relations of the two-phase absorption367
- 4.3.8. Applications375
- References386
- Part 5: Hydrodynamic Stability in Systems with Intensive Interphase Mass Transfer389
- CHAPTER 5.1. STABILITY THEORY389
- 5.1.1. Evolution equations389
- 5.1.2. Bifurcation theory394
- 5.1.3. Eigenvalue problems398
- CHAPTER 5.2. HYDRODYNAMIC STABILITY399
- 5.2.1. Fundamental equations399
- 5.2.2. Power theory400
- 5.2.3. Linear theory403
- 5.2.4. Stability, bifurcation and turbulence405
- 5.2.5. Stability of parallel flows407
- CHAPTER 5.3 ORR-SOMMERFELD EQUATION407
- 5.3.1. Parallel flows408
- 5.3.2. Almost parallel flows409
- CHAPTER 5.4. LINEAR STABILITY AND NON-LINEAR MASS TRANSFER410
- 5.4.1. Gas (liquid) –solid system410
- 5.4.2. Gas – liquid system424
- 5.4.3. Liquid-liquid system429
- 5.4.4. Gas-liquid film flow systems.435
- 5.4.5. Effect of concentration440
- 5.4.6. Effect of temperature449
- CHAPTER 5.5. MECHANISM AND KINETICS OF THE TRANSPORT PROCESSES IN SYSTEMS WITH INTENSIVE INTERPHASE451
- 5.5.1. Mass and heat transfer kinetics452
- 5.5.2. Linear stability analysis462
- 5.5.3. Comparison with experimental data470
- 5.5.4. Comparative analysis of the absorption and desorption rates472
- References483
- Conclusion487
- INDEX491
Surveyed in this book are the kinetics of non-linear mass transfer and its effects on hydrodynamic stability in systems with intensive interphase mass transfer, in electrochemical systems with high current density and in chemically reacting systems.
In Part 1 the non-linear mass transfer as a result of an intensive interphase mass transfer in the gas (liquid)-solid surface, gas-liquid and liquid-liquid systems is considered in the duffusion boundary layer approximation as well as in flat channel taking the longitudinal diffusion into account. The influence of the direction of the intensive interphase mass transfer on heat transfer and multi-component mass transfer is illustrated.
Part 2 discusses non-linear mass transfer in electrochemical systems with high current density using the examples of the anode dissolving of metals in the electrolyte flow and the electro-separation of metals out of concentrated solutions. The theory of the measured electrochemical treatment of metals and alloys, which is a method of wide practical use, has been elaborated on this basis.
In Part 3 the non-linear mass transfer in chemically reacting systems is considered in the cases of: non-linearity of the equations of the chemical reaction's kinetics and intensive interphase mass transfer or thermo-capillary effect due to chemical reactions. On this basis, the mechanisms and the macro-kinetics of the chemical transformations in the gas-liquid systems are discussed.
Part 4 is dedicated to the chemical reaction kinetics in stationary two phase systems at an arbitrary contact time between phases.
In Part 5 the effects of concentration gradients are considered in the approximations of the linear theory of the hydrodynamic stability of almost parallel flows.
In systems with intensive interphase mass transfer, the Marangoni effect could also be observed, beside the effect of non-linear mass transfer. A comparative analysis of both effects is made in this book.
In Part 1 the non-linear mass transfer as a result of an intensive interphase mass transfer in the gas (liquid)-solid surface, gas-liquid and liquid-liquid systems is considered in the duffusion boundary layer approximation as well as in flat channel taking the longitudinal diffusion into account. The influence of the direction of the intensive interphase mass transfer on heat transfer and multi-component mass transfer is illustrated.
Part 2 discusses non-linear mass transfer in electrochemical systems with high current density using the examples of the anode dissolving of metals in the electrolyte flow and the electro-separation of metals out of concentrated solutions. The theory of the measured electrochemical treatment of metals and alloys, which is a method of wide practical use, has been elaborated on this basis.
In Part 3 the non-linear mass transfer in chemically reacting systems is considered in the cases of: non-linearity of the equations of the chemical reaction's kinetics and intensive interphase mass transfer or thermo-capillary effect due to chemical reactions. On this basis, the mechanisms and the macro-kinetics of the chemical transformations in the gas-liquid systems are discussed.
Part 4 is dedicated to the chemical reaction kinetics in stationary two phase systems at an arbitrary contact time between phases.
In Part 5 the effects of concentration gradients are considered in the approximations of the linear theory of the hydrodynamic stability of almost parallel flows.
In systems with intensive interphase mass transfer, the Marangoni effect could also be observed, beside the effect of non-linear mass transfer. A comparative analysis of both effects is made in this book.