Rotating Disk Electrode -a hydrodynamic method

Similar documents
Capítulo. Three Dimensions

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER

19 The Born-Oppenheimer Approximation

1. A body will remain in a state of rest, or of uniform motion in a straight line unless it

Rigid Bodies: Equivalent Systems of Forces

Integral Vector Operations and Related Theorems Applications in Mechanics and E&M

PHY126 Summer Session I, 2008

V. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. "Flux": = da i. "Force": = -Â g a ik k = X i. Â J i X i (7.

Review of Vector Algebra and Vector Calculus Operations

2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles

UNIT10 PLANE OF REGRESSION

PHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor

Chapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41.

Chapter 8. Linear Momentum, Impulse, and Collisions

COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS

Set of square-integrable function 2 L : function space F

Test 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o?

ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.

Exam 1. Sept. 22, 8:00-9:30 PM EE 129. Material: Chapters 1-8 Labs 1-3

Scalars and Vectors Scalar

1. Starting with the local version of the first law of thermodynamics q. derive the statement of the first law of thermodynamics for a control volume

UNIVERSITÀ DI PISA. Math thbackground

PHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite

Engineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems

Chapter 3 Vector Integral Calculus

Physics 1501 Lecture 19

Some Approximate Analytical Steady-State Solutions for Cylindrical Fin

PRINCIPLES OF MASS TRANSFER

PO with Modified Surface-normal Vectors for RCS calculation of Scatterers with Edges and Wedges

iclicker Quiz a) True b) False Theoretical physics: the eternal quest for a missing minus sign and/or a factor of two. Which will be an issue today?

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1

LASER ABLATION ICP-MS: DATA REDUCTION

Stellar Astrophysics. dt dr. GM r. The current model for treating convection in stellar interiors is called mixing length theory:

Description Linear Angular position x displacement x rate of change of position v x x v average rate of change of position

The Forming Theory and the NC Machining for The Rotary Burs with the Spectral Edge Distribution

CSU ATS601 Fall Other reading: Vallis 2.1, 2.2; Marshall and Plumb Ch. 6; Holton Ch. 2; Schubert Ch r or v i = v r + r (3.

EE 5337 Computational Electromagnetics (CEM)

A Brief Guide to Recognizing and Coping With Failures of the Classical Regression Assumptions

A Most Useful Device of Studying Electrode Processes: The Rotating Disk Electrode

CSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4

A. Thicknesses and Densities

Thermodynamics of solids 4. Statistical thermodynamics and the 3 rd law. Kwangheon Park Kyung Hee University Department of Nuclear Engineering

Part V: Velocity and Acceleration Analysis of Mechanisms

3. A Review of Some Existing AW (BT, CT) Algorithms

COLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER /2017

LINEAR MOMENTUM. product of the mass m and the velocity v r of an object r r

24-2: Electric Potential Energy. 24-1: What is physics

A Method of Reliability Target Setting for Electric Power Distribution Systems Using Data Envelopment Analysis

CBE Transport Phenomena I Final Exam. December 19, 2013

Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law

Rotating Variable-Thickness Inhomogeneous Cylinders: Part II Viscoelastic Solutions and Applications

MHD Oscillatory Flow in a Porous Plate

Rotary motion

Chapter 5 Circular Motion

Chapter 31 Faraday s Law

Physics 2A Chapter 11 - Universal Gravitation Fall 2017

Chapter 13 - Universal Gravitation

Correspondence Analysis & Related Methods

Math Section 4.2 Radians, Arc Length, and Area of a Sector

Physics Exam II Chapters 25-29

A Study about One-Dimensional Steady State. Heat Transfer in Cylindrical and. Spherical Coordinates

Physics 111 Lecture 11

Dynamics of Rigid Bodies

4.4 Continuum Thermomechanics

Event Shape Update. T. Doyle S. Hanlon I. Skillicorn. A. Everett A. Savin. Event Shapes, A. Everett, U. Wisconsin ZEUS Meeting, October 15,

Chapter IV Vector and Tensor Analysis IV.2 Vector and Tensor Analysis September 29,

Physics 201 Lecture 4

Applied Statistical Mechanics Lecture Note - 13 Molecular Dynamics Simulation

Density Functional Theory I

Physics 1: Mechanics

A new Approach for Solving Linear Ordinary Differential Equations

ANALYSIS OF AXIAL LOADED PILE IN MULTILAYERED SOIL USING NODAL EXACT FINITE ELEMENT MODEL

Amplifier Constant Gain and Noise

Physics 2020, Spring 2005 Lab 5 page 1 of 8. Lab 5. Magnetism

Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness

, the tangent line is an approximation of the curve (and easier to deal with than the curve).

Chapter IV Vector and Tensor Analysis IV.2 Vector and Tensor Analysis September 23,

Detection and Estimation Theory

Molecular Dynamic Simulations of Nickel Nanowires at Various Temperatures

One-dimensional kinematics

Simulation of Surface Chemical Reactions in a Monolith Channel for Hydrogen Production

Classical Models of the Interface between an Electrode and an Electrolyte

(8) Gain Stage and Simple Output Stage

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer

APPLICATIONS OF SEMIGENERALIZED -CLOSED SETS

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law

Spiral Magnetic Gradient Motor Using Axial Magnets

Chapter Fifiteen. Surfaces Revisited

Lecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES

Energy in Closed Systems

P 365. r r r )...(1 365

Synopsis : 8. ELECTROMAGNETISM

Objectives. Chapter 6. Learning Outcome. Newton's Laws in Action. Reflection: Reflection: 6.2 Gravitational Field

1. Physics for Scientists and Engineers by Serway and Jewett. V.1, 9 th ed. Chapter 11.5, pp

8 Baire Category Theorem and Uniform Boundedness

Complex atoms and the Periodic System of the elements

Supporting Information

Tian Zheng Department of Statistics Columbia University

Supporting Information Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulator Bi 2 Se 3 Probed by Electron Beams

Transcription:

Rotatng Dsk Electode -a hdodnamc method Fe Lu Ma 3, 0 ente fo Electochemcal Engneeng Reseach Depatment of hemcal and Bomolecula Engneeng

Rotatng Dsk Electode A otatng dsk electode RDE s a hdodnamc wokng electode used n a thee electode sstem. The RDE s one of the few convectve electode sstems fo whch the hdodnamc equatons and the convectve-dffuson equaton have been solved goousl fo the stead state. ente fo Electochemcal Engneeng Reseach, ho Unvest

onstuct of RDE Shaft bass Insulato Teflon Bush contact Dsk RDE Rotatng Dsk Electode RDE s constucted fom a dsk of electode mateal mbedded n a od of nsulatng mateal. The electode s attached to a moto and otated at a cetan fequenc. Insulatng mateal : Teflon, epox esn o othe plastc []. Bottom Vew ente fo Electochemcal Engneeng Reseach, ho Unvest 3

Veloct Pofle At Dsk Suface, 0, v 0, 0 and v. The soluton s dagged along at the suface of the dsk at the angula veloct ω. In the bulk soluton, v 0, v 0 and v U 0. Fo electochemcal studes, the mpotant veloct s v and v, Nea the suface of the otatng dsk 0, these veloctes ae gven b: 3/ / v 0.5 3/ / v 0.5 Fo, the lmt veloct n decton, / U 0 s: U lm v 0.88447 Hdodnamc bounda lae thckness / 3.6, v 0.8U 0, h 3.6 / ente fo Electochemcal Engneeng Reseach, ho Unvest v 0 h / 4 At

ente fo Electochemcal Engneeng Reseach, ho Unvest onvectve-dffuson Equaton 5 Stead-state convectve-dffuson equaton n tems of clndcal coodnates: Lmt cuent condton: Substtuton of the value of : D v v v dffuson convecton D v v / 3/.5 0 v

Soluton of onvectve-dffuson Equaton 0.5 Bounda condton: uent s the flux at the electode suface, that s: Unde lmt condtons: 3/ / Soluton of convectve-dffuson equaton: 0 0 nfad l, c l, c 6 D 0 /3 / /6 0. nfad ente fo Electochemcal Engneeng Reseach, ho Unvest 6

Dffuson Lae Thckness Levch equaton: Fo smple stead-state dffuson lae model: Fo RDE: l, c 6 /3 / /6 0. nfad D l, c nfam nfa m D 0.6D /3 / / 6 /3 / /6.6D ente fo Electochemcal Engneeng Reseach, ho Unvest 7

ente fo Electochemcal Engneeng Reseach, ho Unvest Geneal uent-potental uves at RDE 8 Bounda condton: uent s the flux at the electode suface, that s: Soluton of convectve-dffuson equaton: ombne wth Levch equaton: 3 0.50 D 0 0 0 nfad 0] [ 0.6 /6 / /3 nfad 0, c l

Kouteck-Levch Equaton Fo Levch equaton, s popotonal to / l c. A devaton of a / plot of vs. fom a staght lne ntesectng the ognal suggest a knetc lmtaton s nvolved n the electon-tansfe eacton. Fo totall vesble one-step one-electon eacton, the dsk cuent s : E 0 Whee : E s fowad eacton ate at E. k f, FAk FAk f f E l, c Wth eaangement and defnng: K FAk Kouteck-Levch equaton: K l, c K 0. 6nFAD f E /3 ente fo Electochemcal Engneeng Reseach, ho Unvest / / 6 9

Kouteck-Levch Equaton K l, c K 0. 6nFAD /3 / / 6 Vaaton of і wth ω / at an RDE fo an electode eacton wth slow knetcs ente fo Electochemcal Engneeng Reseach, ho Unvest 0

Advantages of RDE A stead state s attaned athe quckl and measuements can be made wth hgh pecson at RDE []. RDE gves good epoducblt and stable polazaton cuve. In stagnant soluton, dffuson lae thckness s the same as bounda lae thckness, t s eas to be dstub b extenal dstubance. But fo RDE: h.6 3.6 D / The dffuson lae thckness s fa less than bounda lae thckness, the dffuson lae s potect b bounda lae whch makes the polazaton cuve stable and has good epoducblt. [] L.H. Mendoza-Huza,.H. Ros Rees, M. Rvea and.a. Galán-Vdal, A Voltammetc Stud f The Undepotental Deposton f obalt nto A Glass abon Electode, AZojomo ISSN 833-X Volume 3 Janua 007 ente fo Electochemcal Engneeng Reseach, ho Unvest

Applcatons of RDE I. Measue Fe + /Fe 3+ oncentatons Fom the Levch equaton, Levch cuent the concentaton: l, c onsde a eacton:, 0.6nFAD a 0.6nFAD Fe 3 /3 /3 / /, s dectl popotonal to f the l c s known, the concentaton of Fe + /Fe 3+ can be calculated b lnea egesson usng the followng model [3] : / 6 / 6 e Fe /3 / l, c 0. 6nFAD l, c a a /6 b [3] Xn Jn, Geadne G. Botte, Electochemcal technque to measue FeII and FeIII concentatons smultaneousl, J Appl Electochem 009 39:709 77 ente fo Electochemcal Engneeng Reseach, ho Unvest

Applcatons of RDE II. Detemne Dffuson oeffcent Levch equaton: l, c 6 /3 / /6 0. nfad Plottng і l,s vs. ω / elds staght lne wth slope: slope /3 /6 0.6nFAD Dffuson coeffcent can be calculated b: Plots of і l,s vs ω /. Wokng soluton: K 3 FeN 6 0 mm + K 4 FeN 6 0 mm n Na S40. M at a vteous cabon RDE. D Slope / 6 0.60 nfa 3 ente fo Electochemcal Engneeng Reseach, ho Unvest 3

/ Applcaton fo cuent eseach III. Detemne knetc paametes 0. 0. 0.08 =.07x + 0.048 Kouteck-Levch equaton: 0.06 0.04 0.0 / K K 0.6nFAD /3 / / 6 0 0 0.0 0.04 0.06 0.08 / K s the ntecept at axs. ω -/ Plots of і - vs ω /. Wokng soluton: 0.33 M Uea and 5 M KH wth N base RDE at 0.5V. ente fo Electochemcal Engneeng Reseach, ho Unvest 4

Thank You! ente fo Electochemcal Engneeng Reseach, ho Unvest 5