Abdelghani Saouab is Professor at the Université Le Havre Normandie, France. His research interests include composite materials, bio-composite and the manufacturing processes of composite materials.Stéphane Champmartin is HDR Associate Professor at the École Nationale des Arts et Métiers, Angers, France. His research focuses on complex flows, suspensions and hydrodynamic interactions.Jaafar Khalid Naciri is Professor Emeritus at Faculté des sciences Aïn Chock, Université Hassan II de Casablanca, Morocco. His research interests include fluid mechanics, deformable tubes flows and asymptotic methods in fluid mechanics.

• Preface xiAbdelghani SAOUAB, Stéphane CHAMPMARTIN and Jaafar Khalid NACIRIChapter 1 Kinetics of Microphase Separation in Interpenetrating Polymer Gels 1Mabrouk BENHAMOU1.1 Introduction 11.2 Static study of microphase separation 31.3 Kinetic study of microphase separation 51.4 Discussion 91.5 References 11Chapter 2 Physics of Hydrodynamic Interactions 15Stéphane CHAMPMARTIN2.1 Introduction 152.2 Equations of low Reynolds number fluid mechanics 182.3 Resistance matrix 212.4 Sphere in hydrodynamic interaction in a cylindrical tube 222.5 Pair of spheres in hydrodynamic interaction 302.6 Conclusion 342.7 References 34Chapter 3 Stokes Flows – Applications to Creeping Flows Around Obstacles and to Flows in Porous Media 37Mustapha HELLOU, Mohammed Khaled BOURBATACHEand Franck LOMINÉ3.1 Introduction 373.2 Several solutions to the Stokes equation in two-dimensional flow 393.3 Application to flows around obstacles 443.4 Application to the calculation of the permeability of periodical porous media 563.5 Conclusion 633.6 References 64Chapter 4 The Yield Stress Method for the Characterization of Pore Size Distribution of Porous Media: Progress Review 67Antonio RODRIGUEZ DE CASTRO, Azita AHMADI-SENICHAULTand Abdelaziz OMARI4.1 Introduction 674.2 Yield stress method 704.3 Experimental validation of YSM method 744.4 Physical significance of the pore size characterized by YSM 804.5 Extension of YSM to rough fractures 844.6 Conclusion 904.7 References 90Chapter 5 Instabilities and Transition to Turbulence in the Couette–Taylor Flow of a Shear-thinning Viscoelastic Liquid 95Noureddine LATRACHE, Fayçal KELAI, Olivier CRUMEYROLLEand Innocent MUTABAZI5.1 Introduction 955.2 Experimental set-up and physicochemical characterization of the polymer 995.3 Results 1015.4 Conclusion 1175.5 References 118Chapter 6 Application of the WKB Method to the Study of Flow Stability Generated by Low-frequency Modulation of Boundary Conditions 121Saïd ANISS and Mouh ASSOUL6.1 Introduction 1226.2 Application of WKB method for studying the effect of low-frequency phase modulation of temperature on the convection threshold of a fluid layer 1276.3 Application of the WKB method to the study of pulsed flow stability generated by in-phase low-frequency oscillation, in Taylor–Couette geometry 1386.4 Conclusion 1456.5 References 145Chapter 7 Multiplicity of Convective Flows in a Horizontal Annular Layer 151Abdelkader MOJTABI and Marie-Catherine CHARRIER-MOJTABI7.1 Introduction 1517.2 Mathematical formulation 1587.3 Various analytical solutions obtained in natural convection 1597.4. Analytical solution of the convective flow for small annular spaces 1607.5. Linear stability analysis of the analytically obtained single-cell flow 1627.6 Conclusion 1687.7 References 170Chapter 8 Instability Modeling in Structural Mechanics: Buckling and Wrinkling 173Noureddine DAMIL and Michel POTIER-FERRY8.1 Introduction 1738.2 Classical multi-scale asymptotic approach to instabilities 1768.3 Another multiple scale method for modeling instabilities: Fourier series with slowly varying coefficients 1808.4 Various macroscopic models used to describe the formation of instability patterns 1858.5 A 2D Fourier double scale analysis of global-local instability interaction in sandwich structures 1948.6 A reduced model based on the multiple scale method in the case of a wrinkling with variable orientation 1998.7 Conclusion 2078.8 References 207Chapter 9 Electrochemical Methods for the Study of Wall Transfer Phenomena 213Claude DESLOUIS, Bernard TRIBOLLET, Abdellah ARHALIASSand Jack LEGRAND9.1 Introduction 2139.2 Principles and definitions 2159.3 Results in Newtonian fluids 2189.4 Electrochemical measurements in non-Newtonian media 2319.5 Conclusion 2449.6 References 244Chapter 10 Simulation of the Resin Infusion Process using the Multilayer Approach: An Industrial Case Application 251Raounak LOUDAD, Abdelghani SAOUAB and Pierre BEAUCHENE10.1 Introduction 25110.2 Mathematical modeling 25410.3 Numerical approach 25510.4 Analytical modeling of 1D VARI 25710.5 Model validation 26010.6 Industrial application 26910.7 Conclusion 27410.8 References 275List of Authors 279Index 283

Abdelghani Saouab is Professor at the Université Le Havre Normandie, France. His research interests include composite materials, bio-composite and the manufacturing processes of composite materials.Stéphane Champmartin is HDR Associate Professor at the École Nationale des Arts et Métiers, Angers, France. His research focuses on complex flows, suspensions and hydrodynamic interactions.Jaafar Khalid Naciri is Professor Emeritus at Faculté des sciences Aïn Chock, Université Hassan II de Casablanca, Morocco. His research interests include fluid mechanics, deformable tubes flows and asymptotic methods in fluid mechanics.

• Preface xiAbdelghani SAOUAB, Stéphane CHAMPMARTIN and Jaafar Khalid NACIRIChapter 1 Kinetics of Microphase Separation in Interpenetrating Polymer Gels 1Mabrouk BENHAMOU1.1 Introduction 11.2 Static study of microphase separation 31.3 Kinetic study of microphase separation 51.4 Discussion 91.5 References 11Chapter 2 Physics of Hydrodynamic Interactions 15Stéphane CHAMPMARTIN2.1 Introduction 152.2 Equations of low Reynolds number fluid mechanics 182.3 Resistance matrix 212.4 Sphere in hydrodynamic interaction in a cylindrical tube 222.5 Pair of spheres in hydrodynamic interaction 302.6 Conclusion 342.7 References 34Chapter 3 Stokes Flows – Applications to Creeping Flows Around Obstacles and to Flows in Porous Media 37Mustapha HELLOU, Mohammed Khaled BOURBATACHEand Franck LOMINÉ3.1 Introduction 373.2 Several solutions to the Stokes equation in two-dimensional flow 393.3 Application to flows around obstacles 443.4 Application to the calculation of the permeability of periodical porous media 563.5 Conclusion 633.6 References 64Chapter 4 The Yield Stress Method for the Characterization of Pore Size Distribution of Porous Media: Progress Review 67Antonio RODRIGUEZ DE CASTRO, Azita AHMADI-SENICHAULTand Abdelaziz OMARI4.1 Introduction 674.2 Yield stress method 704.3 Experimental validation of YSM method 744.4 Physical significance of the pore size characterized by YSM 804.5 Extension of YSM to rough fractures 844.6 Conclusion 904.7 References 90Chapter 5 Instabilities and Transition to Turbulence in the Couette–Taylor Flow of a Shear-thinning Viscoelastic Liquid 95Noureddine LATRACHE, Fayçal KELAI, Olivier CRUMEYROLLEand Innocent MUTABAZI5.1 Introduction 955.2 Experimental set-up and physicochemical characterization of the polymer 995.3 Results 1015.4 Conclusion 1175.5 References 118Chapter 6 Application of the WKB Method to the Study of Flow Stability Generated by Low-frequency Modulation of Boundary Conditions 121Saïd ANISS and Mouh ASSOUL6.1 Introduction 1226.2 Application of WKB method for studying the effect of low-frequency phase modulation of temperature on the convection threshold of a fluid layer 1276.3 Application of the WKB method to the study of pulsed flow stability generated by in-phase low-frequency oscillation, in Taylor–Couette geometry 1386.4 Conclusion 1456.5 References 145Chapter 7 Multiplicity of Convective Flows in a Horizontal Annular Layer 151Abdelkader MOJTABI and Marie-Catherine CHARRIER-MOJTABI7.1 Introduction 1517.2 Mathematical formulation 1587.3 Various analytical solutions obtained in natural convection 1597.4. Analytical solution of the convective flow for small annular spaces 1607.5. Linear stability analysis of the analytically obtained single-cell flow 1627.6 Conclusion 1687.7 References 170Chapter 8 Instability Modeling in Structural Mechanics: Buckling and Wrinkling 173Noureddine DAMIL and Michel POTIER-FERRY8.1 Introduction 1738.2 Classical multi-scale asymptotic approach to instabilities 1768.3 Another multiple scale method for modeling instabilities: Fourier series with slowly varying coefficients 1808.4 Various macroscopic models used to describe the formation of instability patterns 1858.5 A 2D Fourier double scale analysis of global-local instability interaction in sandwich structures 1948.6 A reduced model based on the multiple scale method in the case of a wrinkling with variable orientation 1998.7 Conclusion 2078.8 References 207Chapter 9 Electrochemical Methods for the Study of Wall Transfer Phenomena 213Claude DESLOUIS, Bernard TRIBOLLET, Abdellah ARHALIASSand Jack LEGRAND9.1 Introduction 2139.2 Principles and definitions 2159.3 Results in Newtonian fluids 2189.4 Electrochemical measurements in non-Newtonian media 2319.5 Conclusion 2449.6 References 244Chapter 10 Simulation of the Resin Infusion Process using the Multilayer Approach: An Industrial Case Application 251Raounak LOUDAD, Abdelghani SAOUAB and Pierre BEAUCHENE10.1 Introduction 25110.2 Mathematical modeling 25410.3 Numerical approach 25510.4 Analytical modeling of 1D VARI 25710.5 Model validation 26010.6 Industrial application 26910.7 Conclusion 27410.8 References 275List of Authors 279Index 283

Abdelghani Saouab is Professor at the Université Le Havre Normandie, France. His research interests include composite materials, bio-composite and the manufacturing processes of composite materials.Stéphane Champmartin is HDR Associate Professor at the École Nationale des Arts et Métiers, Angers, France. His research focuses on complex flows, suspensions and hydrodynamic interactions.Jaafar Khalid Naciri is Professor Emeritus at Faculté des sciences Aïn Chock, Université Hassan II de Casablanca, Morocco. His research interests include fluid mechanics, deformable tubes flows and asymptotic methods in fluid mechanics.

• Preface xiAbdelghani SAOUAB, Stéphane CHAMPMARTIN and Jaafar Khalid NACIRIChapter 1 Kinetics of Microphase Separation in Interpenetrating Polymer Gels 1Mabrouk BENHAMOU1.1 Introduction 11.2 Static study of microphase separation 31.3 Kinetic study of microphase separation 51.4 Discussion 91.5 References 11Chapter 2 Physics of Hydrodynamic Interactions 15Stéphane CHAMPMARTIN2.1 Introduction 152.2 Equations of low Reynolds number fluid mechanics 182.3 Resistance matrix 212.4 Sphere in hydrodynamic interaction in a cylindrical tube 222.5 Pair of spheres in hydrodynamic interaction 302.6 Conclusion 342.7 References 34Chapter 3 Stokes Flows – Applications to Creeping Flows Around Obstacles and to Flows in Porous Media 37Mustapha HELLOU, Mohammed Khaled BOURBATACHEand Franck LOMINÉ3.1 Introduction 373.2 Several solutions to the Stokes equation in two-dimensional flow 393.3 Application to flows around obstacles 443.4 Application to the calculation of the permeability of periodical porous media 563.5 Conclusion 633.6 References 64Chapter 4 The Yield Stress Method for the Characterization of Pore Size Distribution of Porous Media: Progress Review 67Antonio RODRIGUEZ DE CASTRO, Azita AHMADI-SENICHAULTand Abdelaziz OMARI4.1 Introduction 674.2 Yield stress method 704.3 Experimental validation of YSM method 744.4 Physical significance of the pore size characterized by YSM 804.5 Extension of YSM to rough fractures 844.6 Conclusion 904.7 References 90Chapter 5 Instabilities and Transition to Turbulence in the Couette–Taylor Flow of a Shear-thinning Viscoelastic Liquid 95Noureddine LATRACHE, Fayçal KELAI, Olivier CRUMEYROLLEand Innocent MUTABAZI5.1 Introduction 955.2 Experimental set-up and physicochemical characterization of the polymer 995.3 Results 1015.4 Conclusion 1175.5 References 118Chapter 6 Application of the WKB Method to the Study of Flow Stability Generated by Low-frequency Modulation of Boundary Conditions 121Saïd ANISS and Mouh ASSOUL6.1 Introduction 1226.2 Application of WKB method for studying the effect of low-frequency phase modulation of temperature on the convection threshold of a fluid layer 1276.3 Application of the WKB method to the study of pulsed flow stability generated by in-phase low-frequency oscillation, in Taylor–Couette geometry 1386.4 Conclusion 1456.5 References 145Chapter 7 Multiplicity of Convective Flows in a Horizontal Annular Layer 151Abdelkader MOJTABI and Marie-Catherine CHARRIER-MOJTABI7.1 Introduction 1517.2 Mathematical formulation 1587.3 Various analytical solutions obtained in natural convection 1597.4. Analytical solution of the convective flow for small annular spaces 1607.5. Linear stability analysis of the analytically obtained single-cell flow 1627.6 Conclusion 1687.7 References 170Chapter 8 Instability Modeling in Structural Mechanics: Buckling and Wrinkling 173Noureddine DAMIL and Michel POTIER-FERRY8.1 Introduction 1738.2 Classical multi-scale asymptotic approach to instabilities 1768.3 Another multiple scale method for modeling instabilities: Fourier series with slowly varying coefficients 1808.4 Various macroscopic models used to describe the formation of instability patterns 1858.5 A 2D Fourier double scale analysis of global-local instability interaction in sandwich structures 1948.6 A reduced model based on the multiple scale method in the case of a wrinkling with variable orientation 1998.7 Conclusion 2078.8 References 207Chapter 9 Electrochemical Methods for the Study of Wall Transfer Phenomena 213Claude DESLOUIS, Bernard TRIBOLLET, Abdellah ARHALIASSand Jack LEGRAND9.1 Introduction 2139.2 Principles and definitions 2159.3 Results in Newtonian fluids 2189.4 Electrochemical measurements in non-Newtonian media 2319.5 Conclusion 2449.6 References 244Chapter 10 Simulation of the Resin Infusion Process using the Multilayer Approach: An Industrial Case Application 251Raounak LOUDAD, Abdelghani SAOUAB and Pierre BEAUCHENE10.1 Introduction 25110.2 Mathematical modeling 25410.3 Numerical approach 25510.4 Analytical modeling of 1D VARI 25710.5 Model validation 26010.6 Industrial application 26910.7 Conclusion 27410.8 References 275List of Authors 279Index 283