Basic Equations Of The Mass Transport Through A Membrane Layer

Basic Equations of Mass Transport Through a Membrane Layer, Second Edition, has been fully updated to deliver the latest research in the field. This volume covers the essentials of compound separation, product removal, concentration, and production in the chemical, biochemical, pharmaceutical, and food industries. It outlines the various membrane processes and their applications, offering a detailed mathematical description of mass transport and defining basic mass transport and concentration distribution expressions. Additionally, this book discusses the process parameters and application of the expressions developed for a variety of industrial applications. Comprehensive explanations of convective/diffusive mass transport are provided, both with and without polarization layers, that help predict and process performance and facilitate improvements to operation conditions and efficiency. Basic Equations of Mass Transport Through a Membrane Layer is an ideal resource for engineers and technologists in the chemical, biochemical, and pharmaceutical industries, as well as researchers, professors, and students in these areas at both an undergraduate and graduate level. Cites and analyzes mass transport equations developed for different membrane processes. Examines the effect of biochemical/chemical reactions in the presence of convective and diffusive flows in plane and cylindrical spaces. Defines the mass transfer rate for first- and zero-order reactions and analytical approaches are given for other-order reactions in closed mathematical forms. Analyzes the simultaneous convective and diffusive transports with same or different directions.

With a detailed analysis of the mass transport through membrane layers and its effect on different separation processes, this book provides a comprehensive look at the theoretical and practical aspects of membrane transport properties and functions. Basic equations for every membrane are provided to predict the mass transfer rate, the concentration distribution, the convective velocity, the separation efficiency, and the effect of chemical or biochemical reaction taking into account the heterogeneity of the membrane layer to help better understand the mechanisms of the separation processes. The reader will be able to describe membrane separation processes and the membrane reactors as well as choose the most suitable membrane structure for separation and for membrane reactor. Containing detailed discussion of the latest results in transport processes and separation processes, this book is essential for chemistry students and practitioners of chemical engineering and process engineering. Detailed survey of the theoretical and practical aspects of every membrane process with specific equations Practical examples discussed in detail with clear steps Will assist in planning and preparation of more efficient membrane structure separation

Molecular mass transport phenomena in fluids -- Transport phenomena and the basic equations of change -- Molecular mass transport phenomena in liquids -- Mass transport phenomena in solids -- Unsteady-state diffusion -- Mass transfer coefficients in laminar and turbulent flow -- Interphase mass transport -- Continuous two-phase mass transport processes -- Mass transport in state processes -- Analog computer methods.

This book is unique as the first effort to expound on the subject of systematic scaling analysis. Not written for a specific discipline, the book targets any reader interested in transport phenomena and reaction processes. The book is logically divided into chapters on the use of systematic scaling analysis in fluid dynamics, heat transfer, mass transfer, and reaction processes. An integrating chapter is included that considers more complex problems involving combined transport phenomena. Each chapter includes several problems that are explained in considerable detail. These are followed by several worked examples for which the general outline for the scaling is given. Each chapter also includes many practice problems. This book is based on recognizing the value of systematic scaling analysis as a pedagogical method for teaching transport and reaction processes and as a research tool for developing and solving models and in designing experiments. Thus, the book can serve as both a textbook and a reference book.

Teaches the fundamentals of mass transport with a unique approach emphasizing engineering principles in a biomedical environment Includes a basic review of physiology, chemical thermodynamics, chemical kinetics, mass transport, fluid mechanics and relevant mathematical methods Teaches engineering principles and mathematical modelling useful in the broad range of problems that students will encounter in their academic programs as well as later on in their careers Illustrates principles with examples taken from physiology and medicine or with design problems involving biomedical devices Stresses the simplification of problem formulations based on key geometric and functional features that permit practical analyses of biomedical applications Offers a web site of homework problems associated with each chapter and solutions available to instructors Homework problems related to each chapter are available from a supplementary website (

The field of matter transport is central to understanding the processing of materials and their subsequent mechanical properties. While thermodynamics determines the final state of a material system, it is the kinetics of mass transport that governs how it gets there. This book, first published in 2000, gives a solid grounding in the principles of matter transport and their application to a range of engineering problems. The author develops a unified treatment of mass transport applicable to both solids and liquids. Traditionally matter transport in fluids is considered as an extension of heat transfer and can appear to have little relationship to diffusion in solids. This unified approach clearly makes the connection between these important fields. This book is aimed at advanced undergraduate and beginning graduate students of materials science and engineering and related disciplines. It contains numerous worked examples and unsolved problems. The material can be covered in a one semester course.

This short primer provides a concise and tutorial-style introduction to transport phenomena in Newtonian fluids , in particular the transport of mass, energy and momentum. The reader will find detailed derivations of the transport equations for these phenomena, as well as selected analytical solutions to the transport equations in some simple geometries. After a brief introduction to the basic mathematics used in the text, Chapter 2, which deals with momentum transport, presents a derivation of the Navier-Stokes-Duhem equation describing the basic flow in a Newtonian fluid. Also provided at this stage are the derivations of the Bernoulli equation, the pressure equation and the wave equation for sound waves. The boundary layer, turbulent flow and flow separation are briefly reviewed. Chapter 3, which addresses energy transport caused by thermal conduction and convection, examines a derivation of the heat transport equation. Finally, Chapter 4, which focuses on mass transport caused by diffusion and convection, discusses a derivation of the mass transport equation.

Membrane science and technology is an expanding field and has become a prominent part of many activities within the process industries. It is relatively easy to identify the success stories of membranes such as desali nation and microfiltration and to refer to others as developing areas. This, however, does not do justice to the wide field of separations in which membranes are used. No other 'single' process offers the same potential and versatility as that of membranes. The word separation classically conjures up a model of removing one component or species from a second component, for example a mass transfer process such as distillation. In the field of synthetic membranes, the terminology 'separation' is used in a wider context. A range of separations of the chemical/mass transfer type have developed around the use of membranes including distillation, extraction, absorption, adsorption and stripping, as well as separations of the physical type such as filtration. Synthetic membranes are an integral part of devices for analysis, energy generation and reactors (cells) in the electrochemical industry.