## Description

Natural phenomena consist of simultaneously occurring transport processes and chemical reactions. These processes may interact with each other and lead to instabilities, fluctuations, and evolutionary systems. This book explores the unifying role of thermodynamics in natural phenomena. *Nonequilibrium Thermodynamics, Second Edition * analyzes the transport processes of energy, mass, and momentum transfer processes, as well as chemical reactions. It considers various processes occurring simultaneously, and provides students with more realistic analysis and modeling by accounting possible interactions between them.
This second edition updates and expands on the first edition by focusing on the balance equations of mass, momentum, energy, and entropy together with the Gibbs equation for coupled processes of physical, chemical, and biological systems. Every chapter contains examples and practical problems to be solved.
This book will be effective in senior and graduate education in chemical, mechanical, systems, biomedical, tissue, biological, and biological systems engineering, as well as physical, biophysical, biological, chemical, and biochemical sciences.

## Key Features

- Will help readers in understanding and modelling some of the coupled and complex systems, such as coupled transport and chemical reaction cycles in biological systems
- Presents a unified approach for interacting processes - combines analysis of transport and rate processes
- Introduces the theory of nonequilibrium thermodynamics and its use in simultaneously occurring transport processes and chemical reactions of physical, chemical, and biological systems
- A useful text for students taking advanced thermodynamics courses

## Readership

For graduate students in chemical, biological, mechanical, biomedical, environmental, and systems engineering programs, as well as for graduate students in biophysical and biochemical science programs. Some parts may also be beneficial for advanced students in diverse engineering programs.

## Table of Contents

Chapter 1

Fundamentals of equilibrium thermodynamics 1

1.1 Introduction 1

1.2 Basic definitions 1

1.3 Reversible and irreversible processes 6

1.4 Equilibrium 8

Example 1.1 Equilibrium in subsystems 9

1.5 The fundamental equations 10

1.6 The thermodynamic laws 11

Example 1.2 Relationships between the molar heat capacities Cp and Cv 12

Example 1.3 Entropy and distribution of probability 14

1.7 Balance equations 14

1.8 Entropy and entropy production 16

Example 1.4 Entropy production and subsystems 17

Example 1.5 Entropy production in a chemical reaction in a closed system 17

Example 1.6 Entropy production in mixing 18

1.9 The Gibbs equation 20

1.10 Equations of state 22

Example 1.7 Heat capacities for real gases 22

Example 1.8 van der Waals isotherms 23

Example 1.9 Estimation of molar volume of a gas at high pressure 24

Example 1.10 Estimation of volume of a gas at high pressure using generic cubic equation of state 25

Example 1.11 Entropy of a real gas 26

Example 1.12 Chemical potential of a real gas 27

Example 1.13 Henry’s law constant 35

Example 1.14 Estimation of partial excess properties 37

Example 1.15 Binary liquid mixture phase diagrams 39

Example 1.16 Estimation of fugacity coefficients from virial equation 40

Example 1.17 Heterogeneous azeotrope 43

1.11 Thermodynamic potentials 46

1.12 Cross relations 47

1.13 Extremum principles 48

Problems 49

References 52

References for further reading 52

Chapter 2

Transport and rate processes 53

2.1 Introduction 53

2.2 Nonequilibrium systems 53

2.3 Kinetic approach 55

2.4 Transport phenomena 56

Example 2.1 Estimation of momentum flow 59

Example 2.2 Estimation of viscosity at specified temperature and pressure 62

Example 2.3 Estimation of viscosity of gas mixtures at low density 62

Example 2.4 Estimation of heat flow through a composite wall with constant thermal conductivities 64

Example 2.5 Estimation of heat flow with temperature-dependent thermal conductivity 66

Example 2.6 Estimation of thermal conductivity at specified temperature and pressure 68

Example 2.7 Estimation of thermal conductivity of monatomic gases 70

Example 2.8 Estimation of thermal conductivity of polyatomic gases 71

Example 2.9 Estimation of thermal conductivity of gas mixtures at low density 71

Example 2.10 Estimation of thermal conductivity of pure liquids 72

Example 2.11 Mass flow across a stagnant film 74

Example 2.12 Estimation of diffusivity in a gas mixture at low density 77

Example 2.13 Estimation of diffusivity in a gas mixture at low pressure 79

Example 2.14 Estimation of diffusivity in a gas mixture of isotopes 79

Example 2.15 Estimation of diffusivity in a gas mixture 80

Example 2.16 Estimation of diffusivity of a component through a gas mixture 81

Example 2.17 Estimation of diffusivity in a dilute liquid mixture 83

2.5 The Maxwell–Stefan equations 86

2.6 Transport coefficients 87

2.7 Electric charge flow 87

2.8 The relaxation theory 89

2.9 Chemical reactions 89

2.10 Coupled processes 90

Problems 92

References 96

References for further reading 96

Chapter 3

Fundamentals of nonequilibrium thermodynamics 97

3.1 Introduction 97

3.2 Local thermodynamic equilibrium 97

3.3 The second law of thermodynamics 98

Example 3.1 Total entropy change of an air flow in a nozzle 102

Example 3.2 Total entropy change in a polytropic compressing of methane 103

Example 3.3 Energy dissipation in a nozzle 106

Example 3.4 Energy dissipation in a compressor 107

Example 3.5 Energy dissipation in an adiabatic mixer 108

Example 3.6 Energy dissipation in a mixer 109

Example 3.7 Energy dissipation in a turbine 110

Example 3.8 Entropy production in a composite system 112

3.4 Balance equations and entropy production 112

Example 3.9 Conservation of energy 120

3.5 Entropy production equation 121

3.6 Phenomenological equations 127

3.7 Onsager’s relations 132

3.8 Transformation of forces and flows 133

Example 3.10 Relationships between the conductance and resistance phenomenological coefficients 135

Example 3.11 Transformation of phenomenological equations: dependent flows 135

Example 3.12 Transformation of phenomenological equations: dependent forces 137

Example 3.13 Transformation of phenomenological equations: dependent flows and forces 138

3.9 Chemical reactions 139

3.10 Heat conduction 139

Example 3.14 Entropy production and dissipation function in heat conduction 140

3.11 Diffusion 141

3.12 Validity of linear phenomenological equations 142

Example 3.15 Gibbs energy and distance from global equilibrium 143

3.13 Curie–Prigogine principle 143

3.14 Time variation of entropy production 144

Example 3.16 Entropy production and the change of the rate of entropy production with

time in heat conduction 145

3.15 Minimum entropy production 146

Example 3.17 Minimum entropy production in a two-flow system 147

Example 3.18 Minimum entropy production in an elementary chemical reaction system 148

Example 3.19 Minimum energy dissipation in heat conduction 149

Example 3.20 Minimum entropy production in electrical circuits 151

Problems 152

References 154

References for further reading 154

Chapter 4

Using the second law: Thermodynamic analysis 155

4.1 Introduction 155

4.2 Second-law analysis 155

Example 4.1 Lost work in throttling processes 158

Example 4.2 Dissipated energy in an adiabatic compression 159

Example 4.3 Thermomechanical coupling in a Couette flow between parallel plates 161

Example 4.4 Thermomechanical coupling in a circular Couette flow 164

Example 4.5 Entropy production in a flow through an annular packed bed 166

Example 4.6 Entropy production in a packed duct flow 168

Example 4.7 Heat and mass transfer 172

Example 4.8 Chemical reactions and reacting flows 174

4.3 Equipartition principle 176

Example 4.9 Entropy production in separation process: distillation 178

4.4. Exergy analysis 184

Example 4.10 Thermodynamic efficiency in a power plant 191

4.5 Applications of exergy analysis 192

Example 4.11 Energy dissipation in countercurrent and cocurrent heat exchangers 192

Example 4.12 Exergy analysis of a power plant 194

Example 4.13 Simple reheat Rankine cycle in a steam power plant 196

Example 4.14 Actual reheat Rankine cycle in steam power generation 198

Example 4.15 Ideal regenerative Rankine cycle 201

Example 4.16 Actual regenerative Rankine cycle 204

Example 4.17 Ideal reheat regenerative cycle 208

Example 4.18 Actual reheat regenerative Rankine cycle 211

Example 4.19 Energy dissipation in a cogeneration plant 215

Example 4.20 Energy dissipation in an actual cogeneration plant 218

Example 4.21 A steam power plant using a geothermal energy source 222

Example 4.22 Exergy analysis of a refrigeration cycle 225

Example 4.23 Analysis of the Claude process in liquefying natural gas 227

Example 4.24 Power plant analysis 229

Example 4.25 Column exergy efficiency 236

Example 4.26 Assessment of separation section of a methanol plant 237

Example 4.27 Assessment of separation of a 15-component mixture in two columns 239

Example 4.28 Assessment of separation section of vinyl chloride monomer (VCM) plant 241

4.6 Chemical exergy 243

4.7 Depletion number 244

4.8 Optimization problem 245

4.9 Information capacity and exergy 245

4.10 Pinch analysis 246

Example 4.29 Minimum utilities by composite curve method 250

Example 4.30 Pinch analysis by temperature interval method and grand composite curve 257

Example 4.31 Column grand composite curves in a distillation column with a five-component mixture 261

Example 4.32 Column grand composite curves in methanol plant 263

Problems 264

References 273

References for further reading 274

Chapter 5

Thermoeconomics 275

5.1 Introduction 275

5.2 Thermodynamic cost 275

Example 5.1 Cost of power generation 278

Example 5.2 Cost of power and process steam generation 278

Example 5.3 Thermoeconomic consideration of a refrigeration system 279

5.3 Ecological cost 285

5.4 Availability 286

5.5 Thermodynamic optimum 287

Example 5.4 Minimization of entropy production 287

5.6 Equipartition and optimization in separation systems 289

Example 5.5 Equipartition principle in separation processes: extraction 289

Example 5.6 Thermoeconomics of extraction 291

Example 5.7 Equipartition principle: heat exchanger 292

Example 5.8 Characterization of the deviation from equipartition 294

Example 5.9 Distribution of driving forces 295

Example 5.10 Variance and heat exchangers 295

Example 5.11 Hot fluid flow rate effect 296

Example 5.12 Equipartition principle in an electrochemical cell with a specified duty 297

Example 5.13 Optimal distillation column: diabatic configuration 298

Example 5.14 Optimal feed state for a binary distillation 299

Example 5.15 Retrofits of distillation columns by thermodynamic analysis 300

5.7 Thermoeconomics of latent heat storage 307

Example 5.16 Cash flow diagram for seasonal latent heat storage 312

Problems 315

References 318

References for further reading 318

Chapter 6

Diffusion 319

6.1 Introduction 319

6.2 Maxwell–Stefan equation 319

Example 6.1 Maxwell-Stefan equation for binary mixtures 322

Example 6.2 Diffusion in a ternary ideal gas mixture 330

Example 6.3 Diffusion of species from a gas mixture to a falling liquid film 332

Example 6.4 Wetted wall column with a ternary liquid mixture 333

6.3 Diffusion in nonelectrolyte systems 335

6.4 Diffusion in electrolyte systems 336

Example 6.5 Diffusion in aqueous solutions 338

Example 6.6 Diffusion across a membrane 339

6.5 Diffusion without shear forces 344

Example 6.7 Binary and ternary isothermal gas mixtures 346

Example 6.8 Diffusion in a dilute isothermal gas mixture 347

6.6 Statistical rate theory 351

Example 6.9 Transport in biological cells: osmotic and pressure driven mass transport

across a biological cell membrane 351

Example 6.10 Prediction of diffusion coefficients of macromolecules 359

Example 6.11 Diffusion of solutes in biological cells 359

Problems 360

References 362

References for further reading 362

Chapter 7

Heat and mass transfer 363

7.1 Introduction 363

7.2 Coupled heat and mass transfer 363

7.3 Heat of transport 369

7.4 Degree of coupling 371

7.5 Coupling in liquid mixtures 372

Example 7.1 Mass diffusion flow in term of mole fractions 372

7.6 Coupled mass and energy balances 384

7.7 Separation by thermal diffusion 387

Example 7.2 Separation by thermal diffusion 388

Example 7.3 Total energy flow and phenomenological equations 389

Example 7.4 Modified Graetz problem with coupled heat and mass flows 390

Example 7.5 Cooling nuclear pellets 391

7.8 Nonlinear approach 394

Example 7.6 Fokker-Planck equation for Brownian motion in a temperature gradient:

short-term behavior of the Brownian particles 395

Example 7.7 Absorption of ammonia vapor by lithium nitrate-ammonia solution 399

7.9 Heat and mass transfer in discontinuous system 401

7.10 Thermoelectric effects 406

Problems 410

References 413

References for further reading 413

Chapter 8

Chemical reactions 415

8.1 Introduction 415

8.2 Chemical reaction equilibrium constant 415

Example 8.1 Equilibrium constant of a reaction 416

Example 8.2 Equilibrium compositions 416

Example 8.3 Temperature effect on equilibrium conversion 418

8.3 The principle of detailed balance 419

8.4 Dissipation for chemical reactions 423

8.5 Reaction velocity (flow) 425

Example 8.4 Affinity and heat of reaction 426

8.6 Multiple chemical reactions 426

Example 8.5 Conservation of mass in chemical reactions 428

Example 8.6 Calculation of entropy production for a reversible reaction 429

8.7 Stationary states 430

Example 8.7 Entropy production for series of reactions at stationary state 433

Example 8.8 Entropy production in a homogeneous chemical system 435

Example 8.9 Chemical reactions far from global equilibrium 437

Example 8.10 Time variation of affinity 440

Example 8.11 Time variation of entropy production in simultaneous chemical reactions 441

Example 8.12 Minimum entropy production 442

8.8 Michaelis–Menten kinetics 443

Example 8.13 Growth of a pathogenic bacterium Brucella abortus 445

8.9 Coupled chemical reactions 447

Problems 449

References 451

Chapter 9

Coupled systems of chemical reactions and transport processes 453

9.1 Introduction 453

9.2 Nonisothermal reaction–diffusion systems 453

Example 9.1 Effective diffusivity 455

Example 9.2 Maximum temperature difference in the hydrogenation of benzene 459

Example 9.3 Effectiveness factor for first-order irreversible reaction-diffusion system 459

Example 9.4 Effectiveness for a first-order reversible reaction 462

Example 9.5 Maximum overall temperature difference in the hydrogenation of benzene 464

9.3 Chemical reaction with coupled heat and mass flows 465

Example 9.6 Coupled heat and mass flows in oxidation of CH3OH to CH2O 467

9.4 Coupled system of chemical reaction and transport processes 470

Example 9.7 Diffusion in a liquid film with a reversible homogeneous reaction 473

Example 9.8 Stationary coupling of chemical reactions with heat and mass flows 481

Example 9.9 Chemical reaction velocity coupled to mass flow 482

Example 9.10 Chemical reaction velocity coupled to heat flow 482

Example 9.11 Modeling of a nonisothermal plug flow reactor 483

9.5 Evolution of coupled systems 484

9.6 Facilitated transport 485

Example 9.12 Steady-state substrate flow in a facilitated transport 487

Example 9.13 Effect of temperature on myoglobin-facilitated transport 489

Example 9.14 Nonisothermal facilitated transport 492

9.7 Active transport 495

Example 9.15 Long-term asymptotic solution of reversible reaction diffusion system 496

Example 9.16 Nonisothermal heterogeneous autocatalytic reactions-diffusion system 499

9.8 Nonlinear macrokinetics in a reaction–diffusion system 500

Problems 501

References 503

References for further reading 504

Chapter 10

Membrane transport 505

10.1 Introduction 505

10.2 Membrane equilibrium 505

Example 10.1 Membrane equilibrium 507

10.3 Passive transport 508

Example 10.2 Gas permeation in a binary gas mixture 509

Example 10.3 Time necessary to reach equilibrium in a membrane transport 514

Example 10.4 Diffusion cell with electrolytes 518

Example 10.5 Diffusion cell and transference numbers 519

Example 10.6 Estimation of flow in a diffusion cell 520

Example 10.7 Energy conversion in the electrokinetic effect 524

10.4 Facilitated and active transports in membranes 525

10.5 Biomembranes 526

Example 10.8 Coupled system of flows and a chemical reaction 534

Example 10.9 A representative active transport and energy conversions 537

Problems 538

References 539

References for further reading 540

Chapter 11

Thermodynamics and biological systems 541

11.1 Introduction 541

11.2 Simplified analysis in living systems 541

Example 11.1 Cell electric potentials 542

Example 11.2 Excess pressure in the lungs 542

Example 11.3 Enthalpy and work changes of blood due to the pumping work of the heart 543

Example 11.4 Energy expenditure in small organisms 544

Example 11.5 Energy expenditure in an adult organism 545

Example 11.6 Oxidation of glucose 546

Example 11.7 Unimolecular isomerization reaction 547

11.3 Bioenergetics 548

Example 11.8 Efficiency of energy conversion of photosynthesis 556

11.4 Proper pathways 557

Example 11.9 A linear pathway 562

Example 11.10 Sensitivity of the rate of the enzymatic reaction to substrate concentration 563

11.5 Coupling in mitochondria 567

11.6 Regulation in bioenergetics 574

Example 11.11 Approximate analysis of transport processes in a biological cell 579

11.7 Exergy use in bioenergetics 581

Example 11.12 Exergy efficiency 590

Example 11.13 Approximate exergy balances in a representative active transport 592

11.8 Molecular evolution 593

11.9 Molecular machines 593

11.10 Evolutionary criterion 595

Problems 596

References 597

References for further reading 598

Chapter 12

Stability analysis 599

12.1 Introduction 599

12.2 The Gibbs stability theory 599

12.3 Stability and entropy production 604

Example 12.1 Distance of a chemical reaction from equilibrium 606

Example 12.2 Stability of chemical systems 607

12.4 Thermodynamic fluctuations 607

Example 12.3 Stability under both dissipative and convective effects 608

12.5 Stability in nonequilibrium systems 608

Example 12.4 Stability of an autocatalytic reaction 610

Example 12.5 Macroscopic behavior in systems far from equilibrium 613

12.6 Linear stability analysis 614

Example 12.6 Evolution in chemical systems 615

12.7 Oscillating systems 616

Example 12.7 Linear stability analysis: Brusselator scheme 617

Example 12.8 Linear stability analysis with two variables 618

Example 12.9 Chemical instability 623

Example 12.10 Multiple steady states 624

Example 12.11 Reaction–diffusion model 626

Example 12.12 Adiabatic stirred flow reactor 627

Problems 628

References 629

References for further reading 629

Chapter 13

Organized structures 631

13.1 Introduction 631

13.2 Equilibrium and nonequilibrium structures 631

13.3 Bifurcation 632

13.4 Limit cycle 633

13.5 Order in physical structures 634

Example 13.1 Lorenz equations: The strange attractor 635

Example 13.2 Van der Pol’s equations 637

13.6 Order in chemical systems 638

Example 13.3 The Brusselator system and oscillations 638

Example 13.4 Order in time and space with the Brusselator system 640

Example 13.5 The Belousov–Zhabotinsky reaction scheme 643

Example 13.6 Order in time: Thermodynamic conditions for chemical oscillations 644

13.7 Biological structures 650

Example 13.7 Chiral symmetry breaking 652

Example 13.8 Prey–predator system: Lotka–Volterra model 654

Example 13.9 Sustained oscillations of the Lotka–Volterra type 656

Example 13.10 Lotka–Volterra model 657

Example 13.11 Enzymatic reactions: Oscillations in the glycolytic cycle 657

Example 13.12 Long-wavelength instability in bacterial growth 660

Example 13.13 Instability in a simple metabolic pathway 661

Example 13.14 A model for an enzyme reaction inhibited by the substrate and product 662

Problems 663

References 668

References for further reading 669

Chapter 14

Nonequilibrium thermodynamics approaches 671

14.1 Introduction 671

14.2 Network thermodynamics with bond graph methodology 671

14.3 Mosaic nonequilibrium thermodynamics 678

14.4 Rational thermodynamics 679

14.5 Extended nonequilibrium thermodynamics 680

14.6 Generic formulations 683

14.7 Matrix model 684

14.8 Internal variables 685

References 686

References for further reading 686

Appendix 687

Appendix A 687

Tensors 687

Appendix B 688

Table B1 Lennard-Jones (6-12) potential parameters and critical properties 688

Table B2 Collision integrals for predicting transport properties of gases at low densities 688

Table B3 Heat capacities of gases in the ideal-gas state 689

Table B4 Heat capacities of solids 690

Table B5 Heat capacities of liquids 691

Table B6 Properties of some common liquids 691

Table B7 Standard enthalpies and Gibbs energies of formation at 298.15K 692

Table B8 Selected state properties 694

Table B9 Approximate standard reaction enthalpy and standard reaction Gibbs energy

for some selected reactions at standard state T5258C, P51atm 694

Appendix C 695

Table C1 Parameters for the thermal conductivity of alkanes in chloroform 695

Table C2 Parameters for the mutual diffusion coefficients of alkanes in chloroform 695

Table C3 Parameters for the heats of transport of alkanes in chloroform 695

Table C4 Parameters for the thermal conductivity of alkanes in carbon tetrachloride 696

Table C5 Parameters for the mutual diffusion coefficients of alkanes in carbon tetrachloride 696

Table C6 Parameters for the heats of transport of alkanes in carbon tetrachloride 696

Appendix D 696

Table D1 Saturated water-temperature table 696

Table D2 Superheated steam 698

Appendix E 704

Table E1 Saturated refrigerant-134a properties-Temperature 704

Table E2 Saturated refrigerant-134a properties-Pressure 705

Table E3 Superheated refrigerant-134a 706

Table E4 Ideal-gas properties of air 709

Table E5 Ideal-gas properties of carbon dioxide, CO2 711

Appendix F 713

Table F1 Values of Z0 713

Table F2 Values of Z1 714

Table F3 Values of Z0 714

Table F4 Values of Z1 715

Table F5 Values of (HR)0/RTc 716

Table F6 Values of (HR)1/RTc 717

Table F7 Values of (HR)0/RTc 718

Table F8 Values of (HR)1/RTc 719

Table F9 Values of (SR)0/R 719

Table F10 Values of (SR)1/R 720

Table F11 Values of (SR)0/R 721

Table F12 Values of (SR)1/R 722

Table F13 Values of f0 723

Table F14 Values of f1 724

Table F15 Values of f0 724

Table F16 Values of f1 725

## Details

- No. of pages:
- 754

- Language:
- English

- Copyright:
- © Elsevier Science 2007

- Published:
- 31st August 2007

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080551364

- Hardcover ISBN:
- 9780444530790

## About the Author

### Yasar Demirel

Dr. Yasar Demirel earned his PhD degree in Chemical Engineering from the University of Birmingham, UK in 1981. He joined the faculty of Çukurova University in Adana, Turkey, and promoted to associate professorship in 1986. In 1993, he joined the faculty of King Fahd University of Petroleum and Minerals in Dhahran Saudi Arabia where he was promoted to full professorship in 2000. He carried out research and scholarly work at the University of Delaware between 1999 and 2001. He worked at Virginia Tech in Blacksburg as a visiting professor between 2002 and 2006. Currently, he is on the faculty of University of Nebraska, Lincoln. He has accumulated broad teaching and research experience over the years in diverse fields of engineering. He is the editor-in-chief of the International Journal of Thermodynamics. Dr. Demirel authored and co-authored three books, four book chapters, and 160 research papers. The first edition of Nonequilibrium Thermodynamics was published in 2002. After it was expanded to a graduate textbook, the third edition was published in 2014. The second edition new book titled “Energy: Production, Conversion, Storage, Conservation, and Coupling” is published in 2016. He has obtained several awards and scholarships, and presented invited seminars.

### Affiliations and Expertise

Department of Chemical and Biomolecular Engineering, University of Nebraska, Lincoln, USA

### Yasar Demirel

Dr. Yasar Demirel earned his PhD degree in Chemical Engineering from the University of Birmingham, UK in 1981. He joined the faculty of Çukurova University in Adana, Turkey, and promoted to associate professorship in 1986. In 1993, he joined the faculty of King Fahd University of Petroleum and Minerals in Dhahran Saudi Arabia where he was promoted to full professorship in 2000. He carried out research and scholarly work at the University of Delaware between 1999 and 2001. He worked at Virginia Tech in Blacksburg as a visiting professor between 2002 and 2006. Currently, he is on the faculty of University of Nebraska, Lincoln. He has accumulated broad teaching and research experience over the years in diverse fields of engineering. He is the editor-in-chief of the International Journal of Thermodynamics. Dr. Demirel authored and co-authored three books, four book chapters, and 160 research papers. The first edition of Nonequilibrium Thermodynamics was published in 2002. After it was expanded to a graduate textbook, the third edition was published in 2014. The second edition new book titled “Energy: Production, Conversion, Storage, Conservation, and Coupling” is published in 2016. He has obtained several awards and scholarships, and presented invited seminars.

### Affiliations and Expertise

Department of Chemical and Biomolecular Engineering, University of Nebraska, Lincoln, USA