Preface

The word "viscoelastic" means the simultaneous existence of viscous and elastic responses of a material. Hence, neither Newton's law (for linear viscous fluids) nor Hooke's law (for pure elastic solids) suffice to explain the mechanical behavior of viscoelastic materials. Strictly speaking all materials are viscoelastic and their particular response depends on the Deborah number, that is to say the ratio between the natural time of the material (relaxation time) and the time scale of the experiment (essay time). Thus, for a given material, if the experiment is slow, the material will appear to be viscous, whereas if the experiment is fast it will appear to be elastic. Many materials exhibit a viscolastic behavior at the observation times and the area is relevant in many fields of study from industrial to technological applications such as concrete technology, geology, polymers and composites, plastics processing, paint flow, hemorheology, cosmetics, adhesives, etc.

In this book, 16 chapters on various viscoelasticity related aspects are compiled. A number of current research projects are outlined as the book is intended to give the readers a wide picture of current research in viscoelasticity balancing between fundamentals and applied knowledge. For this purpose, the chapters are written by experts from the Industry and Academia.

The first part of the book is dedicated to theory and simulation. The first chapter, by Dávalos-Orozco is a review of the theory of linear and nonlinear natural convection of fluid layers between two horizontal walls under an imposed vertical temperature gradient. Chapter 2 by Tsukahara and Kawaguchi deals with the turbulent flow of viscoelastic fluids through complicated geometries such as orifice flows. Next, in chapter 3, Narahari and Hanneken describe a microscopic formulation of fractional theory of viscoelasticity. Finally, in chapter 4, Kejian revisits the die swell problem of viscoelastic polymeric systems.

The second part of the book covers important aspects of viscoelasticity in biological systems. The first chapter by Sasaki highlights the importance of viscoelasticity in the mechanical properties of biological materials. Next, Dahms and coworkers summarize the current techniques used to probe viscoelasticity with special emphasis on the application of Atomic Force Microscopy to microbial cell mechanics. In chapters 7 and 8 Zenzo and Xi and coworkers focus on the viscoelastic properties of human dermis

#### X Preface

and epithelial cells. Last chapter in this section cover aspects related to the blood flow, where Kitawaki proposes a numerical model for the viscoelasticity of arterial walls.

The third part of the book is devoted to the study of the viscoelastic properties of food colloids. Chapter 10 is an attempt to clarify the relationship between the viscoelastic properties of starches, and their mixtures, and texture in real foods. In chapter 11 Ramirez-Wong and coworkers determine the effect of xantham gum on viscoelastic and textural characteristics of masa and tortilla from extruded nixtamalized corn flour. Finally, in chapter 12, stress-relaxation and dynamic tests are performed to evaluate the viscoelastic properties of dough from soft wheat cultivars.

The last part of the book deals with other miscellaneous applications. Tang and Gao perform a micro-rheological study of fully exfoliated organoclay modified thermotropic liquid crystalline polymers (TLCP). Chapter 14 is an attempt to estimate the thermal deformation in laminated printed circuit boards by the application of a layered plate theory that includes energy transport. In the next chapter, chapter 15, Ibrahim and coworkers describe an approach for the dynamic characterization of passive viscoelasticity of a paraplegic's knee joint. This last section finishes with chapter 16, by Hayssam, and describes a nonlinear viscoelastic model to be applied on compressed plastic films for light-weight embankment.

The format of this book is chosen to enable fast dissemination of new research, and to give easy access to readers. The chapters can be read individually.

I would like to express my gratitude to all the contributing authors that have made a reality this book. I wish to thank also InTech staff and their team members for the opportunity to publish this work, in particular, Ana Pantar, Dimitri Jelovcan, Romana Vukelic and Marina Jozipovic for their support which has made my job as editor an easy and satisfying one.

Finally, I gratefully acknowledge financial support by the Ministerio de Ciencia e Innovación (MICINN MAT 2010-15101 project, Spain), by the European Regional Development Fund (ERDF), and by the projects P10-RNM-6630 and P11-FQM-7074 from Junta de Andalucía (Spain).

> **Juan de Vicente** University of Granada Spain

X Preface

and epithelial cells. Last chapter in this section cover aspects related to the blood flow, where Kitawaki proposes a numerical model for the viscoelasticity of arterial walls.

The third part of the book is devoted to the study of the viscoelastic properties of food colloids. Chapter 10 is an attempt to clarify the relationship between the viscoelastic properties of starches, and their mixtures, and texture in real foods. In chapter 11 Ramirez-Wong and coworkers determine the effect of xantham gum on viscoelastic and textural characteristics of masa and tortilla from extruded nixtamalized corn flour. Finally, in chapter 12, stress-relaxation and dynamic tests are performed to evaluate

The last part of the book deals with other miscellaneous applications. Tang and Gao perform a micro-rheological study of fully exfoliated organoclay modified thermotropic liquid crystalline polymers (TLCP). Chapter 14 is an attempt to estimate the thermal deformation in laminated printed circuit boards by the application of a layered plate theory that includes energy transport. In the next chapter, chapter 15, Ibrahim and coworkers describe an approach for the dynamic characterization of passive viscoelasticity of a paraplegic's knee joint. This last section finishes with chapter 16, by Hayssam, and describes a nonlinear viscoelastic model to be applied on

The format of this book is chosen to enable fast dissemination of new research, and to

I would like to express my gratitude to all the contributing authors that have made a reality this book. I wish to thank also InTech staff and their team members for the opportunity to publish this work, in particular, Ana Pantar, Dimitri Jelovcan, Romana Vukelic and Marina Jozipovic for their support which has made my job as editor an

Finally, I gratefully acknowledge financial support by the Ministerio de Ciencia e Innovación (MICINN MAT 2010-15101 project, Spain), by the European Regional Development Fund (ERDF), and by the projects P10-RNM-6630 and P11-FQM-7074

> **Juan de Vicente** University of Granada

> > Spain

the viscoelastic properties of dough from soft wheat cultivars.

compressed plastic films for light-weight embankment.

easy and satisfying one.

from Junta de Andalucía (Spain).

give easy access to readers. The chapters can be read individually.

**Section 1** 

**Theory and Simulations** 

**Section 1** 

**Theory and Simulations** 

**Chapter 0**

**Chapter 1**

**Viscoelastic Natural Convection**

Additional information is available at the end of the chapter

cited.

Heat convection occurs in natural and industrial processes due to the presence of temperature gradients which may appear in any direction with respect to the vertical, which is determined by the direction of gravity. In this case, natural convection is the fluid motion that occurs due to the buoyancy of liquid particles when they have a density difference with respect the surrounding fluid. Here, it is of interest the particular problem of natural convection between two horizontal parallel flat walls. This simple geometry brings about the possibility to understand the fundamental physics of convection. The results obtained from the research of this system may be used as basis to understand others which include, for example, a more complex geometry and a more complex fluid internal structure. Even though it is part of our every day life (it is observed in the atmosphere, in the kitchen, etc.), the theoretical description of natural convection was not done before 1916 when Rayleigh [53] made calculations under the approximation of frictionless walls. Jeffreys [27] was the first to calculate the case including friction in the walls. The linear theory can be found in the monograph by Chandrasekhar [7]. It was believed that the patterns (hexagons) observed in the Bénard convection (see Fig. 1, in Chapter 2 of [7] and the references at the end of the chapter) were the same as those of natural convection between two horizontal walls. However, it has been shown theoretically and experimentally that the preferred patterns are different. It was shown for the first time theoretically by Pearson [45] that convection may occur in the absence of gravity assuming thermocapillary effects at the free surface of a liquid layer subjected to a perpendicular temperature gradient. The patterns seen in the experiments done by Bénard in the year 1900, are in fact only the result of thermocapillarity. The reason why gravity effects were not important is that the thickness of the liquid layer was so small in those experiments that the buoyancy effects can be neglected. As will be shown presently, the Rayleigh number, representative of the buoyancy force in natural convection, depends on the forth power of the thickness of the liquid layer and the Marangoni number, representing thermocapillary effects, depends on the second power of the thickness. This was not realized for more than fifty years, even after the publication of the paper by Pearson (as seen in the monograph by Chandrasekhar). Natural convection may present hexagonal patterns only when non

> ©2012 Dávalos-Orozco, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

L. A. Dávalos-Orozco

**1. Introduction**

http://dx.doi.org/10.5772/49981

#### **Chapter 0 Chapter 1**
