Some Complex Phenomena in Fluid and Solid Mechanics

Auteur

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.

Texte du rabat

This book is a tribute to Professor Abdelhak Ambari and brings together ten chapters written by colleagues who were fortunate enough to work with him.

The contributions presented in this book cover the research themes in which Abdelhak Ambari was interested, and to which he made valuable experimental and theoretical contributions. For example: rheology of complex fluids and polymers; hydrodynamic interactions; flows at low Reynolds numbers; characterization of porous media; hydrodynamic instabilities and solid mechanics; electrochemical metrology.

Some Complex Phenomena in Fluid and Solid Mechanics is aimed at a wide community of readers wishing to delve deeper into these scientific themes: since it is oriented toward the world of research, it will be a valuable tool for doctoral students and beyond. The book also provides undergraduate and graduate students with a good introduction to the techniques and approaches developed in fundamental and applied research in the fields of fluid mechanics, solid mechanics and instrumentation.

Contenu

Preface xi
Abdelghani SAOUAB, Stéphane CHAMPMARTIN and Jaafar Khalid NACIRI

Chapter 1 Kinetics of Microphase Separation in Interpenetrating Polymer Gels 1
Mabrouk BENHAMOU

1.1 Introduction 1

1.2 Static study of microphase separation 3

1.3 Kinetic study of microphase separation 5

1.4 Discussion 9

1.5 References 11

Chapter 2 Physics of Hydrodynamic Interactions 15
Stéphane CHAMPMARTIN

2.1 Introduction 15

2.2 Equations of low Reynolds number fluid mechanics 18

2.3 Resistance matrix 21

2.4 Sphere in hydrodynamic interaction in a cylindrical tube 22

2.5 Pair of spheres in hydrodynamic interaction 30

2.6 Conclusion 34

2.7 References 34

Chapter 3 Stokes Flows - Applications to Creeping Flows Around Obstacles and to Flows in Porous Media 37
Mustapha HELLOU, Mohammed Khaled BOURBATACHEand Franck LOMINÉ

3.1 Introduction 37

3.2 Several solutions to the Stokes equation in two-dimensional flow 39

3.3 Application to flows around obstacles 44

3.4 Application to the calculation of the permeability of periodical porous media 56

3.5 Conclusion 63

3.6 References 64

Chapter 4 The Yield Stress Method for the Characterization of Pore Size Distribution of Porous Media: Progress Review 67
Antonio RODRIGUEZ DE CASTRO, Azita AHMADI-SENICHAULTand Abdelaziz OMARI

4.1 Introduction 67

4.2 Yield stress method 70

4.3 Experimental validation of YSM method 74

4.4 Physical significance of the pore size characterized by YSM 80

4.5 Extension of YSM to rough fractures 84

4.6 Conclusion 90

4.7 References 90

Chapter 5 Instabilities and Transition to Turbulence in the Couette-Taylor Flow of a Shear-thinning Viscoelastic Liquid 95
Noureddine LATRACHE, Fayçal KELAI, Olivier CRUMEYROLLEand Innocent MUTABAZI

5.1 Introduction 95

5.2 Experimental set-up and physicochemical characterization of the polymer 99

5.3 Results 101

5.4 Conclusion 117

5.5 References 118

Chapter 6 Application of the WKB Method to the Study of Flow Stability Generated by Low-frequency Modulation of Boundary Conditions 121
Saïd ANISS and Mouh ASSOUL

6.1 Introduction 122

6.2 Application of WKB method for studying the effect of low-frequency phase modulation of temperature on the convection threshold of a fluid layer 127

6.3 Application of the WKB method to the study of pulsed flow stability generated by in-phase low-frequency oscillation, in Taylor-Couette geometry 138

6.4 Conclusion 145

6.5 References 145

Chapter 7 Multiplicity of Convective Flows in a Horizontal Annular Layer 151
Abdelkader MOJTABI and Marie-Catherine CHARRIER-MOJTABI

7.1 Introduction 151

7.2 Mathematical formulation 158

7.3 Various analytical solutions obtained in natural convection 159

7.4. Analytical solution of the convective flow for small annular spaces 160

7.5. Linear stability analysis of the analytically obtained single-cell flow 162

7.6 Conclusion 168

7.7 References 170

Chapter 8 Instability Modeling in Structural Mechanics: Buckling and Wrinkling 173
Noureddine DAMIL and Michel POTIER-FERRY

8.1 Introduction 173

8.2 Classical multi-scale asymptotic approach to instabilities 176

8.3 Another multiple scale method for modeling instabilities: Fourier series with slowly varying coefficients 180

8.4 Various macroscopic models used to describe the formation of instability patterns 185

8.5 A 2D Fourier double scale analysis of global-local instability interaction in sandwich structures 194

8.6 A reduced model based on the multiple scale method in the case of a wrinkling with variable orientation 199

8.7 Conclusion 207

8.8 References 207

Chapter 9 Electrochemical Methods for the Study of Wall Transfer Phenomena 213
Claude DESLOUIS, Bernard TRIBOLLET, Abdellah ARHALIASSand Jack LEGRAND

9.1 Introduction 213

9.2 Principles and definitions 215

9.3 Results in Newtonian fluids 218

9.4 Electrochemical measurements in non-Newtonian media 231

9.5 Conclusion 244

9.6 References 244

Chapter 10 Simulation of the Resin Infusion Process using the Multilayer Approach: An Industrial Case Application 251
Raounak LOUDAD, Abdelghani SAOUAB and Pierre BEAUCHENE

10.1 Introduction 251

10.2 Mathematical modeling 254

10.3 Numerical approach 255

10.4 Analytical modeling of 1D VARI 257

10.5 Model validation 260

10.6 Industrial application 269

10.7 Conclusion 274

10.8 References 275

List of Authors 279

Index 283