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**Trends in continuum mechanics of porous media.**
*(English)*
Zbl 1085.74002

Theory and Applications of Transport in Porous Media 18. Dordrecht: Springer (ISBN 1-4020-3143-2/hbk). xii, 279 p. (2005).

Flow through porous media is a subject of research undergoing rapid growth in fluid mechanics and heat transfer. This is quite natural because of its important applications in environmental, geophysical and energy related engineering problems. Prominent applications are the utilization of geothermal energy, the control of pollutant spread in groundwater, the design of nuclear reactors, compact heat exchangers, solar power collectors, heat transfer associated with the deep storage of nuclear waste high performance insulation for buildings, the heat transfer from stored agricultural products that release energy as a result of metabolism of the products, etc. Applications of porous media include also environmental pollution of water resources by toxic synthetic chemical residues, soil mechanics, soil physics, etc.

The purpose of this book is to present the state-of-the-art trends in various fields of the theory of porous media. A brief summary of the book is the following:

The first chapter: Introduction presents practical examples of material systems undergoing external and/or internal loadings which must be studied and described precisely in order to be able to predict the responses of these systems. It also mentions the authors who have contributed to the progress of porous media from the point of mathematical theory concerning mainly the derivation of constitutive equations.

The second and third chapters: Volume fraction concept and kinematics. The chapters describe the volume fraction concept assuming that the porous solid always models a control space and that only the liquids and/or gases contained in the pores can leave the control space (second chapter). There are also given some basic kinematics of porous media widely accepted in the literature (third chapter). Also kinematics of microscopic polar constituents is described and presented. It is mentioned that the additional kinematics quantities introduced in the Cosserat mechanics are, in many cases at present time, not yet accessible and measurable.

Chapters four, five and six: Balance principles, basic inequality (entropy principle) and constitutive theory. It is stated that in the mixture theory and porous medium theory, balance principles – balance of mass, balance of momentum and moment of momentum as well as balance of energy – have to be established for each constituent of all interaction and external agencies. Two forms of entropy inequalities of the mixture body are given in the fifth chapter. The constitutive theory with preliminaries, exploitation of the inequality for ternary and binary capillary porous models, elastic-plastic behavior of the solid skeleton, etc. are presented in chapter six.

Chapter seven: Fundamental effects in gas-and liquid-filled porous solids. The chapter presents the main features of fundamental effects such as uplift, friction, capillarity, effective stresses and phase transitions.

The next two chapters, eight and nine: Poroelasticity and poroelasticity for metallic porous solids. The chapters are devoted to the development of fundamental field equations of poroelasticity, the theory of wave propagation, stress-strain relations, general theorems for saturated porous solids in the rigid ideal-plastic range, etc. The author has shown that, in general, poroelasticity is understood as the pendant to linear elasticity of one-component elastic solid. That means that poroelasticity is devoted exclusively to saturated and/or unsaturated elastic porous solids within the framework of geometrically and physically linear theory with all its consequences.

Chapter ten: Applications in engineering and biomechanics. The chapter describes some applications in soil mechanics (consolidation problem and localization phenomena, phase transitions and chemical engineering and dynamics), chemical engineering (powder compaction and drying processes), building physics (transport of moisture, heat conduction in a fluid-saturated capillary-porous solid), biomechanics, soil physics (agriculture), petroleum industry, material science, local water supplies and plant growth.

The final chapter, eleven: Conclusions and outlook. The chapter presents the main topics treated in this book and the author’s future intention to work at the extension of the theory of porous media to porous solids in small nano-range at the University of Essen, Germany.

In the reviewer’s opinion, this book provides a solid fundamental and comprehensive presentation of the mathematical theory of flow in porous media, pointing out the most important practical applications. It also addresses the theoretical basis for the solution of several problems frequently encountered in the area of flow through porous media and other connected disciplines. The book is recommended to physicists, chemical engineers, biologists, and also to researchers interested in the mathematical theory of flow in porous media and connected topics. I believe that the concepts presented in this book will stimulate new research in porous media both from theoretical and applied point of views.

The purpose of this book is to present the state-of-the-art trends in various fields of the theory of porous media. A brief summary of the book is the following:

The first chapter: Introduction presents practical examples of material systems undergoing external and/or internal loadings which must be studied and described precisely in order to be able to predict the responses of these systems. It also mentions the authors who have contributed to the progress of porous media from the point of mathematical theory concerning mainly the derivation of constitutive equations.

The second and third chapters: Volume fraction concept and kinematics. The chapters describe the volume fraction concept assuming that the porous solid always models a control space and that only the liquids and/or gases contained in the pores can leave the control space (second chapter). There are also given some basic kinematics of porous media widely accepted in the literature (third chapter). Also kinematics of microscopic polar constituents is described and presented. It is mentioned that the additional kinematics quantities introduced in the Cosserat mechanics are, in many cases at present time, not yet accessible and measurable.

Chapters four, five and six: Balance principles, basic inequality (entropy principle) and constitutive theory. It is stated that in the mixture theory and porous medium theory, balance principles – balance of mass, balance of momentum and moment of momentum as well as balance of energy – have to be established for each constituent of all interaction and external agencies. Two forms of entropy inequalities of the mixture body are given in the fifth chapter. The constitutive theory with preliminaries, exploitation of the inequality for ternary and binary capillary porous models, elastic-plastic behavior of the solid skeleton, etc. are presented in chapter six.

Chapter seven: Fundamental effects in gas-and liquid-filled porous solids. The chapter presents the main features of fundamental effects such as uplift, friction, capillarity, effective stresses and phase transitions.

The next two chapters, eight and nine: Poroelasticity and poroelasticity for metallic porous solids. The chapters are devoted to the development of fundamental field equations of poroelasticity, the theory of wave propagation, stress-strain relations, general theorems for saturated porous solids in the rigid ideal-plastic range, etc. The author has shown that, in general, poroelasticity is understood as the pendant to linear elasticity of one-component elastic solid. That means that poroelasticity is devoted exclusively to saturated and/or unsaturated elastic porous solids within the framework of geometrically and physically linear theory with all its consequences.

Chapter ten: Applications in engineering and biomechanics. The chapter describes some applications in soil mechanics (consolidation problem and localization phenomena, phase transitions and chemical engineering and dynamics), chemical engineering (powder compaction and drying processes), building physics (transport of moisture, heat conduction in a fluid-saturated capillary-porous solid), biomechanics, soil physics (agriculture), petroleum industry, material science, local water supplies and plant growth.

The final chapter, eleven: Conclusions and outlook. The chapter presents the main topics treated in this book and the author’s future intention to work at the extension of the theory of porous media to porous solids in small nano-range at the University of Essen, Germany.

In the reviewer’s opinion, this book provides a solid fundamental and comprehensive presentation of the mathematical theory of flow in porous media, pointing out the most important practical applications. It also addresses the theoretical basis for the solution of several problems frequently encountered in the area of flow through porous media and other connected disciplines. The book is recommended to physicists, chemical engineers, biologists, and also to researchers interested in the mathematical theory of flow in porous media and connected topics. I believe that the concepts presented in this book will stimulate new research in porous media both from theoretical and applied point of views.

Reviewer: Ioan Pop (Cluj-Napoca)

### MSC:

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76S05 | Flows in porous media; filtration; seepage |

86A05 | Hydrology, hydrography, oceanography |