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Engineers encounter particles in a variety of systems. The particles are either naturally present or engineered into these systems. In either case these particles often significantly affect the behavior of such systems. This book provides a framework for analyzing these dispersed phase systems and describes how to synthesize the behavior of the population particles and their environment from the behavior of single particles in their local environments. Population balances are of key relevance to a very diverse group of scientists, including astrophysicists, high-energy physicists, geophysicists, colloid chemists, biophysicists, materials scientists, chemical engineers, and meteorologists. Chemical engineers have put population balances to most use, with applications in the areas of crystallization; gas-liquid, liquid-liquid, and solid-liquid dispersions; liquid membrane systems; fluidized bed reactors; aerosol reactors; and microbial cultures. Ramkrishna provides a clear and general treatment of population balances with emphasis on their wide range of applicability. New insight into population balance models incorporating random particle growth, dynamic morphological structure, and complex multivariate formulations with a clear exposition of their mathematical derivation is presented. Population Balances provides the only available treatment of the solution of inverse problems essential for identification of population balance models for breakage and aggregation processes, particle nucleation, growth processes, and more. This book is especially useful for process engineers interested in the simulation and control of particulate systems. Additionally, comprehensive treatment of the stochastic formulation of small systems provides for the modeling of stochastic systems with promising new areas of applications such as the design of sterilization systems and radiation treatment of cancerous tumors. - A clear and general treatment of population balances with emphasis on their wide range of applicability. Thus all processes involving solid-fluid and liquid-liquid dispersions, biological populations, etc. are encompassed - Provides new insight into population balance models incorporating random particle growth, dynamic morphological structure, and complex multivariate formulations with a clear exposition of their mathematical derivation - Presents a wide range of solution techniques, Monte Carlo simulation methods with a lucid exposition of their origin and scope for enhancing computational efficiency - An account of self-similar solutions of population balance equations and their significance to the treatment of data on particulate systems - The only available treatment of the solution of inverse problems essential for identification of population balance models for breakage and aggregation processes, particle nucleation and growth processes and so on - A comprehensive treatment of the stochastic formulation of small systems with several new applications
Crystallization is an important separation and purification process used in industries ranging from bulk commodity chemicals to specialty chemicals and pharmaceuticals. In recent years, a number of environmental applications have also come to rely on crystallization in waste treatment and recycling processes.The authors provide an introduction to the field of newcomers and a reference to those involved in the various aspects of industrial crystallization. It is a complete volume covering all aspects of industrial crystallization, including material related to both fundamentals and applications. This new edition presents detailed material on crystallization of biomolecules, precipitation, impurity-crystal interactions, solubility, and design.Provides an ideal introduction for industrial crystallization newcomers Serves as a worthwhile reference to anyone involved in the fieldCovers all aspects of industrial crystallization in a single, complete volume
Bridging the gap between theory and practice, this text provides the reader with a comprehensive overview of industrial crystallization. Newcomers will learn all of the most important topics in industrial crystallization, from key concepts and basic theory to industrial practices. Topics covered include the characterization of a crystalline product and the basic process design for crystallization, as well as batch crystallization, measurement techniques, and details on precipitation, melt crystallization and polymorphism. Each chapter begins with an introduction explaining the importance of the topic, and is supported by homework problems and worked examples. Real world case studies are also provided, as well as new industry-relevant information, making this is an ideal resource for industry practitioners, students, and researchers in the fields of industrial crystallization, separation processes, particle synthesis, and particle technology.
Dr. R. Peter King covers the field of quantitative modeling of mineral processing equipment and the use of these models to simulate the actual behavior of ore dressing and coal washing as they are configured to work in industrial practice. The material is presented in a pedagogical style that is particularly suitable for readers who wish to learn the wide variety of modeling methods that have evolved in this field. The models vary widely from one unit type to another. As a result each model is described in some detail. Wherever possible model structure is related to the underlying physical processes that govern the behaviour of particulate material in the processing equipment. Predictive models are emphasised throughout so that, when combined, they can be used to simulate the operation of complex mineral processing flowsheets. The development of successful simulation techniques is a major objective of the work that is covered in the text. - Covers all aspects of modeling and simulation - Provides all necessary tools to put the theory into practice
Lattice Boltzmann Modeling for Chemical Engineering, Volume 56 in the Advances in Chemical Engineering series, highlights new advances in the field, with this new volume presenting interesting chapters on Simulations of homogeneous and heterogeneous chemical reactions, LBM for 3D Chemical Reactors, LBM Simulations of PEM fuel cells, LBM for separation processes, LBM for two-phase flow (bio)reactors, and more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Advances in Chemical Engineering series - Includes the latest information on Lattice Boltzmann Modeling for Chemical Engineering
This book includes the seven papers that contributed to the Special Issue of Mathematics entitled “Mathematical Methods in Applied Sciences”. The papers are authored by eminent specialists and aim at presenting to a broad audience some mathematical models which appear in different aspects of modern life. New results in Computational Mathematics are given as well. Emphasis is on Medicine and Public Health, in relation also with Social Sciences. The models in this collection apply in particular to the study of brain cells during a stroke, training management efficiency for elite athletes, and optimal surgical operation scheduling. Other models concern Industry and Economy, as well as Biology and Chemistry. Numerical Methods are represented in particular by scattered data interpolation, spectral collocation, and the use of eigenvalues and eigenvectors of the Laplacian matrix. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Numerical Analysis, and will be of interest for scholars in Applied Sciences, particularly in Medicine and Public Health.
Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB® scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away.
Theoretical discussions covering granulation and engineering perspectives. Covers new advances in expert systems, process modelling and bioavailability Chapters on emerging technologies in particle engineering Updated Current research and developments in granulation technologies
Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization, Second Edition covers the numerous population balance-based particulate studies. This edition emerged from the notes for an industrial short course on crystallization. This book is divided into 10 chapters and begins with an outline of the methods for representation of particle distributions and a systematic approach to the predictive modeling of processes where there is a need to characterize distributions in time and space and by some identifying property. The succeeding chapters provide a specific and more elementary approach to modeling crystal size distributions, as well as the modeling the kinetics of crystal nucleation and growth rates. Other chapters discuss a wide range of system analysis and design considerations specific to crystallization for both the steady state and unsteady state. The final chapters illustrate the use of a population balance analysis to interpret data from both laboratory and process equipment. These chapters also explore a wide variety of particulate processes and systems for which the population balance analysis is useful. This book is of great value to graduate students with particulate systems course.