Contents
Preface…………………………………………………………………………………………. vii
Editors……………………………………………………………………………………..ix
Contributors………………………………………………………………………xi
1 Introduction to Wicking in Porous Media………………………………..1
Reza Masoodi and Krishna M. Pillai
2 Wettability and Its Role in Wicking…………………………………………………. 13
Jijie Zhou
3 Traditional Theories of Wicking: Capillary Models………………………… 31
Reza Masoodi and Krishna M. Pillai
4 An Introduction to Modeling Flows in Porous Media……………………..55
Krishna M. Pillai and Kamel Hooman
5 Single-Phase Flow (Sharp-Interface) Models for Wicking……………….97
Reza Masoodi and Krishna M. Pillai
6 Modeling Fluid Absorption in Anisotropic Fibrous
Porous Media…………………………………………………………………………………… 131
Hooman Vahedi Tafreshi and Thomas M. Bucher
7 Wicking in Absorbent Swelling Porous Materials…………………………. 161
Vladimir Mirnyy, Volker Clausnitzer, Hans-Jorg G. Diersch,
Rodrigo Rosati, Mattias Schmidt, and Holger Beruda
8 Evaporation and Wicking……………………………………………………………….. 201
Stephanie Veran-Tissoires, Sandrine Geoffroy, Manuel Marcoux,
and Marc Prat
9 Pore-Network Modeling of Wicking:
A Two-Phase Flow Approach………………………………………………………….. 237
Vahid Joekar-Niasar and S. Majid Hassanizadeh
10 A Fractal-Based Approach to Model Wicking…………………………………263
Jianchao Cai, Boming Yu, and Xiangyun Hu
11 Modeling Wicking in Deformable Porous Media Using
Mixture Theory……………………………………………………………………………….. 295
Daniel M. Anderson and Javed I. Siddique
12 Simulating Fluid Wicking into Porous Media with
the Lattice Boltzmann Method……………………………………………………….. 327
Marcel G. Schaap and Mark L. Porter
Preface
Wicking or spontaneous imbibition of liquids into dry porous media is an industrial problem of great relevance—it finds application in a range of fields from textile processing to food processing to the processing of composite materials. A leading consumer product company funded our research on the wicking performance of one of their products over the last decade. These series of projects brought us to the amazing world of wicking and absorbent technology. While working in this area and conducting an exhaustive literature survey, we realized that different mathematical models based on varied flow physics are available for modeling liquid flow in porous materials during wicking. However, there was no book or publication that could present all the different modeling approaches in one volume in order to compare and disseminate the varied approaches. Hence, in 2010, we decided to collect these approaches and present them in the form of a book such that the basic assumptions and mathematical details associated with each of these methodologies are described. This project required about 2 years of hard work to accomplish our dream and publish this book.
The book contains some of the most important methods and philosophies for modeling wicking, from the traditional models to the latest approaches developed during the last few years. Although we tried to be as inclusive as possible, some important developments in the field may have escaped our dragnet. For example, application of the Ising model to predict the migration of moisture in a network of fibers could not be included due to a lack of contributing authors in the area. Similarly, the statistical approach to model wicking after accounting for randomness in porous media could not be included due to a shortage of time. Despite these shortcomings, we hope this book will be useful to our intended users. Although we have tried to be as meticulous and exact as possible in our work, some mistakes and oversights might have slipped in—we apologize for these misses.
In general, the book is intended for graduate students, professors, scientists, and engineers who are engaged in research and development on wicking and absorbency. In particular, the book is aimed at mathematical modelers who want to predict wicking with the help of computer programs—our goal is to provide a sound conceptual framework for learning the science behind different mathematical models, while at the same time being aware of the practical issues of model validation as well as measurement of important properties and parameters associated with various models. The layout of the book is designed to help in this task. Chapter 1 begins with an introduction on wicking, while Chapter 2 introduces the science behind wetting of surfaces. Chapter 3 introduces the reader to the basic derivation of the capillary model, and extension of the model after including gravity, inertia, and other effects. Since many of the recent models treat wicking as a flow-in- porous-media-type problem, Chapter 4 is dedicated to the science of single- and multi-phase flows in porous media, followed by a brief description of the measurement techniques and theoretical models available for the associated porous-media properties. The remaining chapters provide details of the individual models developed for wicking. Chapter 5 describes how the single- phase flow model accompanied by a sharp-front approximation is effective in modeling liquid imbibition into porous wicks. Chapter 6 describes the application of the unsaturated-flow (Richard’s equation) model to predict wicking in anisotropic fibrous media. Chapter 7 discusses the application of the same unsaturated flow approach to model wicking-type liquid movements in absorbent swelling porous materials. Chapter 8 presents an application of the network models to model wicking accompanied by evaporation in porous materials. Chapter 9 explains advanced two-phase flow physics in network models used to study microscopic aspects of the wicking phenomenon.
Chapter 10 describes a fractal-based approach to model wicking in porous media. In Chapter 11, wicking in deformable sponge is predicted after using the mixture theory to set up the governing equations. Finally, the use of the Lattice Boltzmann method to conduct a direct numerical simulation of wicking flows is presented in Chapter 12.
Our special thanks go to the individual authors who contributed chapters in this book—this project would not have been possible without their hardwork, support, and faith in this project. We are sure they will share our happiness and pride in publishing this book. We would like to express our appreciation to CRC Press for providing us with an opportunity to bring this work to fruition. In particular, we would like to thank the resourceful Jonathan Plant, executive editor at CRC Press, who encouraged and helped us at all stages of the project while doing a bit of firefighting for us to keep the project on track. We also thank Amber Donley, project coordinator at CRC Press, for her help. We also thank Syed Mohamad Shajahan, project manager at Techset Composition who oversaw the production of this book. A special thanks is reserved for Michelle Schoenecker and Dr. Marjorie Piechowski for helping us with the editing of our own chapters. We would also like to acknowledge Milad Masoodi’s help in designing the book cover. Finally, we take this opportunity to express our deep appreciation to our families for their understanding and support during the course of this project that required many hours of activity during holidays, evenings, and weekends.