Simultaneous Mass Transfer and Chemical Reactions in Engineering Science

Cover
Half Title
Simultaneous Mass Transfer and Chemical Reactions in Engineering Science
Copyright
Dedication
Contents
Preface
Author Biography
1. Introduction to Simultaneous Mass Transfer and Chemical Reactions in Engineering Science
	1.1 Gas–Liquid Reactions
		1.1.1 Simultaneous Biomolecular Reactions and Mass Transfer
			1.1.1.1 The Biomedical Environment
			1.1.1.2 The Industrial Chemistry and Chemical Engineering Environment
		1.1.2 Conclusions
		1.1.3 Summary
	1.2 The Modeling of Gas–Liquid Reactions
		1.2.1 Film Theory of Mass Transfer
		1.2.2 Surface Renewal Theory of Mass Transfer
		1.2.3 Absorption into a Quiescent Liquid
			1.2.3.1 Absorption Accompanied by Chemical Reactions
			1.2.3.2 Irreversible Reactions
		1.2.4 Absorption into Agitated Liquids
			1.2.4.1 An Example of a First‐Order Reaction
			1.2.4.2 The Film Model
	1.3 The Mathematical Theory of Simultaneous Mass Transfer and Chemical Reactions
		1.3.1 Physical Absorption
		1.3.2 Chemical Absorption
			1.3.2.1 Preliminary Remarks on Simultaneous Mass Transfer (Absorption) with Chemical Reactions
			1.3.2.2 Some Solutions to the Mathematical Models of the Theory of Simultaneous Mass Transfer and Chemical Reactions
			1.3.2.3 Approximate Closed Form Solutions
		1.3.3 Numerical Solutions
	1.4 Diffusive Models of Environmental Transport
	Further Reading
2. Data Analysis Using R Programming
	2.1 Data and Data Processing
		2.1.1 Introduction
		2.1.2 Data Coding
			2.1.2.1 Automated Coding Systems
		2.1.3 Data Capture
		2.1.4 Data Editing
		2.1.5 Imputations
		2.1.6 Data Quality
		2.1.7 Quality Assurance
		2.1.8 Quality Control
		2.1.9 Quality Management in Statistical Agencies
		2.1.10 Producing Results
	2.2 Beginning R
		2.2.1 R and Statistics
		2.2.2 A First Session Using R
		2.2.3 The R Environment (This is Important!)
	2.3 R as a Calculator
		2.3.1 Mathematical Operations Using R
		2.3.2 Assignment of Values in R, and Computations Using Vectors and Matrices
		2.3.3 Computations in Vectors and Simple Graphics
		2.3.4 Use of Factors in R Programming
			2.3.4.1 Body Mass Index
		2.3.5 Simple Graphics
		2.3.6 x as Vectors and Matrices in Statistics
		2.3.7 Some Special Functions that Create Vectors
		2.3.8 Arrays and Matrices
		2.3.9 Use of the Dimension Function dim() in R
		2.3.10 Use of the Matrix Function matrix() in R
		2.3.11 Some Useful Functions Operating on Matrices in R: colnames, rownames, and t (for transpose)
		2.3.12 NA “Not Available” for Missing Values in Datasets
		2.3.13 Special Functions that Create Vectors
	2.4 Using R in Data Analysis in Human Genetic Epidemiology
		2.4.1 Entering Data at the R Command Prompt
			2.4.1.1 Creating a Data‐Frame for R Computation Using the EXCEL Spreadsheet (on a Windows Platform)
			2.4.1.2 Obtaining a Data Frame from a Text File
			2.4.1.3 Data Entry and Analysis Using the Function data.entry()
			2.4.1.4 Data Entry Using Several Available R Functions
			2.4.1.5 Data Entry and Analysis Using the Function scan()
			2.4.1.6 Data Entry and Analysis Using the Function Source()
			2.4.1.7 Data Entry and Analysis Using the Spreadsheet Interface in R
			2.4.1.8 Human Genetic Epidemiology Using R: The CRAN Package Genetics
		2.4.2 The Function list() and the Construction of data.frame() in R
		2.4.3 Stock Market Risk Analysis
			2.4.3.1 Univariate, Bivariate, and Multivariate Data Analysis
	2.A Appendix. Documentation for the Plot Function
		2.A.1 Description
		2.A.2 Usage
		2.A.3 Arguments
		2.A.4 Details
		2.A.5 See Also
	Further Reading
3. A Theory of Simultaneous Mass Transfer and Chemical Reactions with Numerical Solutions
	3.1 Introduction
		3.1.1 A Classical Experimental Study of Simultaneous Absorption of Carbon Dioxide and Ammonia in Water
		3.1.2 Physical Absorption
			3.1.2.1 Results
	3.2 Biomolecular Reactions
		3.2.1 Occurrences of Simultaneous Biomolecular Reactions and Mass Transfer Are Common in Many Biomedical Environments
	3.3 Some Examples in Chemical Engineering Sciences
		3.3.1 Simultaneous Chemical Reactions and Mass Transfer
	3.4 Some Models in the Diffusional Operations of Environmental Transport Unaccompanied by Chemical Reactions
		3.4.1 Diffusion Models of Environmental Transport
		3.4.2 Advection–Diffusion Models of Environmental Transport
	3.5 The Concept of Diffusion
		3.5.1 Publishers' Remarks
		3.5.2 Fick's Laws of Diffusion
			3.5.2.1 Fick's First Law of Diffusion (Steady‐State Law)
			3.5.2.2 Fick's Second Law of Diffusion
		3.5.3 Derivation of Fick's Laws of Diffusion
			3.5.3.1 Remarks: Additional Remarks on Fick's Laws of Diffusion
			3.5.3.2 Example Solution in One Dimension: Diffusion Length
	3.6 The Concept of the Mass Transfer Coefficient
	3.7 Theoretical Models of Mass Transfer
		3.7.1 Nernst One‐Film Theory Model and the Lewis–Whitman Two‐Film Model
			3.7.1.1 Gas Transfer Rates
			3.7.1.2 The Nernst One‐Film Model
			3.7.1.3 Mass Transfer Coefficients
			3.7.1.4 The Lewis–Whitman Two‐Film Model
			3.7.1.5 The Two‐Film Model
			3.7.1.6 Single‐Film Control
			3.7.1.7 Applications
		3.7.2 Higbie's Penetration Theory Model
		3.7.3 Danckwerts' Surface Renewal Theory Model
		3.7.4 Boundary Layer Theory Model
			3.7.4.1 Fluid–Fluid Interfaces
			3.7.4.2 Fluid–Solid Interfaces
			3.7.4.3 Example: Prandtl's Experimental Mass Transfer from a Flat Plate
		3.7.5 Mass Transfer Under Laminar Flow Conditions
		3.7.6 Mass Transfer Past Solids Under Turbulent Flow
		3.7.7 Some Interesting Special Conditions of Mass Transfer
			3.7.7.1 Equimolar Counter‐Diffusion of A and B (NA = − NB)
			3.7.7.2 For Liquid‐Phase Diffusion
			3.7.7.3 Conversions Formulas for Mass Transfer Coefficients in Different Forms
		3.7.8 Applications to Chemical Engineering Design
			3.7.8.1 Designing a Packed Column for the Absorption of Gaseous CO2 by a Liquid Solution of NaOH, Using the Mathematical Model of Simultaneous Gas Absorption with Chemical Reactions
			3.7.8.2 Calculation of Packed Height Requirement for Reducing the Chlorine Concentration in a Chlorine–Air Mixture
	3.8 Theory of Simultaneous Bimolecular Reactions and Mass Transfer in Two Dimensions
		3.8.1 Numerical Solutions of a Model in Terms of Simultaneous Semi‐linear Parabolic Differential Equations
			3.8.1.1 Theory of Simultaneous Bimolecular Reactions and Mass Transfer in Two Dimensions
		3.8.2 Existence and Uniqueness Theorems of First‐Order Linear Ordinary Differential Equations
			3.8.2.1 Differential Equations
			3.8.2.2 Contraction Mappings on a Banach Space
			3.8.2.3 Application to Differential Equations
		3.8.3 An Existence Theorem of the Governing Simultaneous Semi‐linear Parabolic Partial Differential Equations
		3.8.4 A Uniqueness Theorem of the Governing Simultaneous Semi‐linear Parabolic Partial Differential Equations
	3.9 Theory of Simultaneous Bimolecular Reactions and Mass Transfer in Two Dimensions: Further Cases of Practical Interests
		3.9.1 Case of Stagnant Film of Finite Thickness – Second‐Order Irreversible Reactions
		3.9.2 Case of Unsteady‐State Absorption in the Stagnant Liquid – Slow First‐Order Reaction (S&P 325, 328)
		3.9.3 Simultaneous Absorption of Two Gases in a Liquid in Which Each Then Reacts With a Third Component in the Liquid
			3.9.3.1 Mathematical Modeling
			3.9.3.2 Analysis of the Model: A + B →
			3.9.3.3 Discussions
			3.9.3.4 Further Theoretical Analysis
		3.9.4 Simultaneous Absorption of Two Gases in a Liquid in Which Each Then Reacts with a Third Component in the Liquid
			3.9.4.1 The Mathematical Model
			3.9.4.2 Analysis of the Model
			3.9.4.3 Boundary Conditions
			3.9.4.4 Mass Transfer Coefficients
		3.9.5 Cases of Slow First‐Order Reactions
			3.9.5.1 Case of Unsteady‐State Absorption in the Stagnant Liquid
			3.9.5.2 Case of Unsteady‐State Absorption in the Stagnant Liquid – Slow First‐Order Reactions
	3.10 Further Theoretical Analysis
	Further Reading
4. Numerical Worked Examples Using R for Simultaneous Mass Transfer and Chemical Reactions
	4.1 Advection and Convection
		4.1.1 Advection
		4.1.2 Advection vs. Convection
			4.1.2.1 Meteorology
			4.1.2.2 The Mathematics of Advection
			4.1.2.3 The Advection Equation
			4.1.2.4 The Advection Operator in the Incompressible Navier–Stokes Equations
	4.2 Worked Examples
	4.3 Partial Differential Equations
	4.4 A Parabolic PDE
		4.4.1 Steady‐State Solution
		4.4.2 The Method of Lines
	Further Reading
5. More Numerical Worked Examples Using R for Simultaneous Mass Transfer and Chemical Reaction
	5.1 Introduction
	5.2 Advection
		5.2.1 Advection vs. Convection
			5.2.1.1 Meteorology
			5.2.1.2 The Mathematics of Advection
			5.2.1.3 The Advection Equation
			5.2.1.4 Solving the Advection Equation
			5.2.1.5 The Advection Operator in the Incompressible Navier–Stokes Equations
	5.3 Solving Partial Differential Equations Using the R Package ReacTran
		5.3.1 Worked Examples
	5.4 Some Final Remarks on Solving Partial Differential Equations Using the R Package ReacTran
		5.4.1 Partial Differential Equations
		5.4.2 A Parabolic PDE
			5.4.2.1 Steady‐State Solution
			5.4.2.2 The Method of Lines
	Further Reading
6. Solving Partial Differential Equations, Generally Applicable to Modeling Simultaneous Mass Transfer and Chemical Reactions, Using the R Package ReacTran
	6.1 Partial Differential Equations (PDE)
	6.2 A Parabolic PDE
	6.3 Steady‐State Solution
		6.3.1 The Method of Lines
		6.3.2 A Hyperbolic PDE
	6.4 The General 3D Advective–Diffusive Transport PDE
	6.5 The General 3D Advective–Diffusive Transport PDE
		6.5.1 The Advection Equation
		6.5.2 Solving the Advection Equation
		6.5.3 The Advection Operator in the Incompressible Navier–Stokes Equations
	See Also
	Further Reading
References
Further Reading
Index