Download or read book Numerical Approximations of Population Balance Equations in Particulate Systems written by Jitendra Kumar and published by . This book was released on 2006 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Population Balances written by Doraiswami Ramkrishna and published by Elsevier. This book was released on 2000-08-08 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Numerical Solution of Multicomponent Population Balance Systems with Applications to Particulate Processes written by Darren Donald Obrigkeit and published by . This book was released on 2001 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) A survey of the representations used in numerical implementations is fol- lowed by an analysis of model complexity as new components are added. The numerical implementation of a split composition distribution method for multicomponent systems is presented, and the solution is verified against analytical results. Numerical stability requirements under varying growth rate laws are used to develop new scaling methods which enable the description of particles over many orders of magnitude in size. Numerous examples are presented to illustrate the utility of these methods and to familiarize the reader with the development and manipulations of the representations, governing equations, and numerical implementations of population balance systems.
Download or read book Numerical Simulation of Multiphase Reactors with Continuous Liquid Phase written by Chao Yang and published by Academic Press. This book was released on 2014-09-04 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of multiphase reactors with continuous liquid phase provides current research and findings in multiphase problems, which will assist researchers and engineers to advance this field. This is an ideal reference book for readers who are interested in design and scale-up of multiphase reactors and crystallizers, and using mathematical model and numerical simulation as tools. Yang and Mao’s book focuses on modeling and numerical applications directly in the chemical, petrochemical, and hydrometallurgical industries, rather than theories of multiphase flow. The content will help you to solve reacting flow problems and/or system design/optimization problems. The fundamentals and principles of flow and mass transfer in multiphase reactors with continuous liquid phase are covered, which will aid the reader’s understanding of multiphase reaction engineering. Provides practical applications for using multiphase stirred tanks, reactors, and microreactors, with detailed explanation of investigation methods Presents the most recent research efforts in this highly active field on multiphase reactors and crystallizers Covers mathematical models, numerical methods and experimental techniques for multiphase flow and mass transfer in reactors and crystallizers
Download or read book Chemical Engineering in the Pharmaceutical Industry written by Mary T. am Ende and published by John Wiley & Sons. This book was released on 2019-04-08 with total page 1435 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the important chemical engineering concepts for the development of new drugs, revised second edition The revised and updated second edition of Chemical Engineering in the Pharmaceutical Industry offers a guide to the experimental and computational methods related to drug product design and development. The second edition has been greatly expanded and covers a range of topics related to formulation design and process development of drug products. The authors review basic analytics for quantitation of drug product quality attributes, such as potency, purity, content uniformity, and dissolution, that are addressed with consideration of the applied statistics, process analytical technology, and process control. The 2nd Edition is divided into two separate books: 1) Active Pharmaceutical Ingredients (API’s) and 2) Drug Product Design, Development and Modeling. The contributors explore technology transfer and scale-up of batch processes that are exemplified experimentally and computationally. Written for engineers working in the field, the book examines in-silico process modeling tools that streamline experimental screening approaches. In addition, the authors discuss the emerging field of continuous drug product manufacturing. This revised second edition: Contains 21 new or revised chapters, including chapters on quality by design, computational approaches for drug product modeling, process design with PAT and process control, engineering challenges and solutions Covers chemistry and engineering activities related to dosage form design, and process development, and scale-up Offers analytical methods and applied statistics that highlight drug product quality attributes as design features Presents updated and new example calculations and associated solutions Includes contributions from leading experts in the field Written for pharmaceutical engineers, chemical engineers, undergraduate and graduation students, and professionals in the field of pharmaceutical sciences and manufacturing, Chemical Engineering in the Pharmaceutical Industry, Second Edition contains information designed to be of use from the engineer's perspective and spans information from solid to semi-solid to lyophilized drug products.
Download or read book Dynamic Flowsheet Simulation of Solids Processes written by Stefan Heinrich and published by Springer Nature. This book was released on 2020-06-20 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest advances in flowsheet simulation of solids processes, focusing on the dynamic behaviour of systems with interconnected solids processing units, but also covering stationary simulation. The book includes the modelling of solids processing units, for example for comminution, sifting and particle formulation and also for reaction systems. Furthermore, it examines new approaches for the description of solids and their property distributions and for the mathematical treatment of flowsheets with multivariate population balances.
Download or read book Approximation of Population Processes written by Thomas G. Kurtz and published by SIAM. This book was released on 1981-01-01 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population processes are stochastic models for systems involving a number of similar particles. Examples include models for chemical reactions and for epidemics. The model may involve a finite number of attributes, or even a continuum. This monograph considers approximations that are possible when the number of particles is large. The models considered will involve a finite number of different types of particles.
Download or read book Design and Processing of Particulate Products written by Jim Litster and published by Cambridge University Press. This book was released on 2016-10-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique text providing comprehensive coverage of fundamental particle science, processing and technology. Including quantitative tools, real-world case studies and end-of-chapter problems, it is ideal for students in engineering and applied sciences, as well as for practitioners in a range of industries manufacturing particulate products.
Download or read book Micro Macro Interactions written by Albrecht Bertram and published by Springer Science & Business Media. This book was released on 2008-10-23 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.
Download or read book Mathematical Methods in Applied Sciences written by Luigi Rodino and published by MDPI. This book was released on 2020-03-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Simulations for Modelling of Population Balance Equations of Particulate Processes Using the Discrete Particle Model DPM written by Narni Nageswara Rao and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiphase Particulate Systems in Turbulent Flows written by Wioletta Podgórska and published by CRC Press. This book was released on 2019-09-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase Particulate Systems in Turbulent Flows: Fluid-Liquid and Solid-Liquid Dispersions provides methods necessary to analyze complex particulate systems and related phenomena including physical, chemical and mathematical description of fundamental processes influencing crystal size and shape, suspension rheology, interfacial area of drops and bubbles in extractors and bubble columns. Examples of mathematical model formulation for different processes taking place in such systems is shown. Discussing connections between turbulent mixing mechanisms and precipitation, it discusses influence of fine-scale structure of turbulence, including its intermittent character, on breakage of drops, bubbles, cells, plant cell aggregates. An important aspect of the mathematical modeling presented in the book is multi-fractal, taking into account the influence of internal intermittency on different phenomena. Key Features Provides detailed descriptions of dispersion processes in turbulent flow, interactions between dispersed entities, and continuous phase in a single volume Includes simulation models and validation experiments for liquid-liquid, gas-liquid, and solid-liquid dispersions in turbulent flows Helps reader learn formulation of mathematical models of breakage or aggregation processes using multifractal theory Explains how to solve different forms of population balance equations Presents a combination of theoretical and engineering approaches to particulate systems along with discussion of related diversity, with exercises and case studies
Download or read book Combinatorial Scientific Computing written by Uwe Naumann and published by CRC Press. This book was released on 2012-01-25 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Scientific Computing explores the latest research on creating algorithms and software tools to solve key combinatorial problems on large-scale high-performance computing architectures. It includes contributions from international researchers who are pioneers in designing software and applications for high-performance computing systems. The book offers a state-of-the-art overview of the latest research, tool development, and applications. It focuses on load balancing and parallelization on high-performance computers, large-scale optimization, algorithmic differentiation of numerical simulation code, sparse matrix software tools, and combinatorial challenges and applications in large-scale social networks. The authors unify these seemingly disparate areas through a common set of abstractions and algorithms based on combinatorics, graphs, and hypergraphs. Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations and their importance continues to grow with the demands of new applications and advanced architectures. By addressing current challenges in the field, this volume sets the stage for the accelerated development and deployment of fundamental enabling technologies in high-performance scientific computing.
Download or read book Handbook of Industrial Crystallization written by Allan Myerson and published by Butterworth-Heinemann. This book was released on 2002-01-08 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Optimization of Pharmaceutical Processes written by Antonios Fytopoulos and published by Springer Nature. This book was released on 2022-04-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative. The volume, which includes new methods as well as review contributions will benefit a wide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.
Download or read book Computational Models for Polydisperse Particulate and Multiphase Systems written by Daniele L. Marchisio and published by Cambridge University Press. This book was released on 2013-03-28 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Orthogonal Polynomials written by Walter Gautschi and published by OUP Oxford. This book was released on 2004-04-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.
