Solid-Liquid Two Phase Flow

Sümer M. Peker, Serife S. Helvaci

• Publisher: Elsevier Science
• Year: 2011
• Print ISBN: 9780444522375
• eBook ISBN: 9780080553412
• Topic: Physical Sciences
• Subtopic: Fluid Mechanics

This book is an undertaking of a pioneering work of uniting three vast fields of interfacial phenomena, rheology and fluid mechanics within the framework of solid-liquid two phase flow. No wonder, much finer books will be written in the future as the visionary aims of many nations in combining molecular chemistry, biology, transport and interfacial phenomena for the fundamental understanding of processes and capabilities of new materials will be achieved. Solid-liquid systems where solid particles with a wide range of physical properties, sizes ranging from nano- to macro- scale and concentrations varying from very dilute to highly concentrated, are suspended in liquids of different rheological behavior flowing in various regimes are taken up in this book. Interactions among solid particles in molecular scale are extended to aggregations in the macro scale and related to settling, flow and rheological behavior of the suspensions in a coherent, sequential manner. The classical concept of solid particles is extended to include nanoparticles, colloids, microorganisms and cellular materials. The flow of these systems is investigated under pressure, electrical, magnetic and chemical driving forces in channels ranging from macro-scale pipes to micro channels. Complementary separation and mixing processes are also taken under consideration with micro- and macro-scale counterparts.- Up-to-date including emerging technologies- Coherent, sequential approach- Wide scope: microorganisms, nanoparticles, polymer solutions, minerals, wastewater sludge, etc- All flow conditions, settling and non-settling particles, non-Newtonian flow, etc- Processes accompanying conveying in channels, such as sedimentation, separation, mixing

1

The Particulate Phase: A Voyage from the Molecule to the Granule

Publisher Summary

Flow behavior of solid–liquid two-phase flow systems depends on the properties of the dispersed solid phase, the continuous liquid phase that suspends the solids, and the interactions between the two phases. This chapter discusses molecular interactions leading up to the formation of solid particle aggregates and surface forces responsible for the stability of suspensions. Molecules of all matter at a temperature above absolute zero possess internal energy expressed as motion in the form of rotation, vibration, and translation, provided there is enough space to permit those motions. Because of the random translatory motion, the molecules frequently collide with each other. The statistical average distance traveled between two collisions is called the mean free path. When the energies of the colliding molecules are not high enough to end-up in a coalition, the original molecules keep colliding with other molecules on their paths, their energies being redistributed after each collision. Furthermore, the same forces that exist between a pair of molecules also exist between a great number of molecules aggregated in the form of a particle. The interactions may be attractive based on electronic distributions (van der Waals) or repulsive due to ionic distributions (double layer repulsions).

Flow behavior of solid–liquid two-phase flow systems depends on the properties of the dispersed solid phase, the continuous liquid phase that suspends the solids and the interactions between the two phases. This chapter is an overview of molecular interactions leading up to the formation of solid particle aggregates and surface forces responsible for the stability of suspensions.

1.1 MOLECULAR INTERACTIONS

Molecules of all matter at a temperature above absolute zero possess internal energy expressed as motion in the form of rotation, vibration, and translation, provided there is enough space to permit these motions. Because of the random translatory motion, the molecules frequently collide with each other. The statistical average distance traveled between two collisions is called the mean free path. When the energies of the colliding molecules are not “high enough” to end-up in a coalition, the original molecules keep colliding with other molecules on their paths, their energies being redistributed after each collision. This random motion, called Brownian motion, is expressed as thermal energy in the terms of k_BT, where k_B is the Boltzmann constant [1.381 × 10⁻²³JK⁻¹] and T, the absolute temperature in [K]. All the molecules would be free and would move randomly within the medium, if thermal energy or internal energy were the only sources of energy the molecules possess. If there is any aggregation or some kind of an order between the molecules, it is due to the attractive forces existing between the molecules. For the attractive forces to be effective, the potential energy they generate should be equal or greater in magnitude than the thermal energy. The thermal energy at 25°C amounts to 1.381 × 10⁻²³ 298 = 4.12 × 1⁻²¹ J, so bonds with energies less than this are bound to break up at 25°C.

All the interactions between atoms and simple molecules are essentially electrostatic in origin. This stems up from the structure of the atom: A positively charged nucleus surrounded by a negatively charged electron cloud. The electron density in between atoms of equal electronegativity, making up a molecule is symmetrical. If there is a deficiency of electrons in this cloud in comparison with a neutral atom or a molecule, the molecule attains a positive charge, called a cation. If, on the other hand, there is a surplus of electrons, the molecule becomes negatively charged and is called an anion. Two similarly charged ions repel and dissimilar ions attract each other. The ionic charge Q of the ionic molecule is the product of the number of missing/surplus electrons, the valence z_i, and the charge of a single electron e in Coulombs, e = 1.602 × 10⁻¹⁹C, Q = z_i e. Due to the symmetry of the electron cloud, the electric field, E, around an ion is considered to have spherical symmetry and to decrease with the square of the radial distance r:

$E=\frac{Q/{\varepsilon }_0{\varepsilon }_{\text{r}}}{4\pi r^2}=\frac{z_{i}e/{\varepsilon }_0{\varepsilon }_{\text{r}}}{4\pi r^2}$ (1.1)

(1.1)

Charge alone does not determine the electric field; the electrical permittivity of vacuum, ε₀ [ε₀ = 8.854 × 10⁻¹² C² J⁻¹m⁻¹], and the relative permittivity with respect to vacuum of...

Table of contents

• Cover image
• Title page
• Table of Contents
• Preface
• List of Contributors
• Chapter 1: The Particulate Phase: A Voyage from the Molecule to the Granule
• Chapter 2: Non-Newtonian Behavior of Solid–Liquid Suspensions
• Chapter 3: Concentrated Suspensions
• Chapter 4: Motion of Particles in Fluids
• Chapter 5: Modeling the Flow of Settling Suspensions
• Chapter 6: Flow of Settling Slurries
• Chapter 7: Mixing in Solid–Liquid Systems
• Chapter 8: Classification and Separation of Solid–Liquid Systems
• Appendix A: Mathematical Operations
• Appendix B: Population Balances
• Appendix C: Tables for Use in Plug Flow in an Annulus
• Index