Mass-Transfer Measurements by the Limiting-Current Technique

Publisher Summary Limiting-current density refers to the maximum rate at 100% current efficiency, at which a particular electrode reaction can proceed in the steady state. This rate is determined by the composition and transport properties of the electrolytic solution and by the hydrodynamic condition at the electrode surface. It has been observed that in many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. Major conditions for valid measurement and interpretation of limiting currents include reaction characterized by slow surface kinetics, progress of the electrode position reaction, use of low concentrations of the reacting ionic species in free convection studies. This chapter outlines the underlying principles, discusses the conditions of validity, and highlights some selected applications and basic features of the limiting-current phenomenon. The chapter also illustrates a synopsis of electrochemical mass-transfer theory, to the extent required for analysis of limiting-current conditions. Various complicating factors—migration effects, the choice of appropriate diffusivity values, unsteady-state conditions, current distribution below and at the limiting current, and the effect of formation of rough metallic deposits—in the interpretation of limiting-current measurements are considered.

[1]  C. V. King,et al.  The Rate of Dissolution of Magnesium in Acids , 1937 .

[2]  N. Riley,et al.  Unsteady heat transfer for flow over a flat plate , 1963, Journal of Fluid Mechanics.

[3]  D. B. Spalding,et al.  Contribution to the theory of heat transfer across a turbulent boundary layer , 1964 .

[4]  T. J. Hanratty,et al.  Determination of the direction of surface velocity gradients in three-dimensional boundary layers , 1968, Journal of Fluid Mechanics.

[5]  Thomas J. Hanratty,et al.  Rates of turbulent transfer to a pipe wall in the mass transfer entry region , 1963 .

[6]  E. N. Lightfoot,et al.  Correlation of Heat and Mass Transfer Data for High Schmidt and Reynolds Numbers , 1966 .

[7]  A. Al-Taweel,et al.  Effect of vibration on the rate of mass transfer , 1974 .

[8]  T. J. Hanratty,et al.  Limiting Behavior of Transverse Turbulent Velocity Fluctuations Close to a Wall , 1969 .

[9]  S. Marchiano,et al.  Ionic mass transfer at rotating electrodes formed by solids of revolution. Rotating one-base spherical segment electrodes , 1972 .

[10]  R. Sioda Distribution of potential in a porous electrode under conditions of flow electrolysis , 1971 .

[11]  N. Ibl,et al.  Note on the electrodeposits obtained at the limiting current , 1972 .

[12]  D. Chin,et al.  Mass Transfer to a Continuous Moving Surface , 1977 .

[13]  A. Wragg,et al.  Mass transfer between a falling liquid film and a plane vertical surface , 1968 .

[14]  J. Newman ENGINEERING DESIGN OF ELECTROCHEMICAL SYSTEMS , 1968 .

[15]  A. A. Al Taweel,et al.  Comparative analysis of mass transfer at vibrating electrodes , 1976 .

[16]  D. A. Dawson,et al.  Mass transfer at rough surfaces , 1972 .

[17]  B. Mahato,et al.  Effect of surface roughness on mass transfer , 1968 .

[18]  N. Ibl,et al.  Surface Roughness Effects in the Electrodeposition of Copper in the Limiting Current Range , 1967 .

[19]  K. Tokuda,et al.  Theory of stationary current-voltage curves of redox-electrode reactions in hydrodynamic voltammetry: IX. Double electrodes in channel flow , 1974 .

[20]  J. Podestá,et al.  Ionic mass transfer at horizontals disc electrodes under longitudinal vibration , 1974 .

[21]  L. S. Cheema,et al.  Unsteady heat transfer in laminar boundary layer over a flat plate , 1968 .

[22]  L. M. Mukherjee,et al.  Correlation of Limiting Currents; Electrodeposition of Copper in Microelectrolytic Cells , 1964 .

[23]  T. J. Hanratty,et al.  Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360 , 1968, Journal of Fluid Mechanics.

[24]  R. D. Naybour,et al.  The Effect of Electrolyte Flow on the Morphology of Zinc Electrodeposited from Aqueous Alkaline Solution Containing Zincate Ions , 1969 .

[25]  A. A. Zatout,et al.  Mass-transfer rates at rough surfaces , 1969 .

[26]  P. Noordsij,et al.  Mass transfer coefficients to a rotating and to a vibrating sphere , 1967 .

[27]  B. Levich The theory of concentration polarisation , 1947 .

[28]  D. J. Pickett,et al.  The influence of hydrodynamic and mass transfer entrance effects on the operation of a parallel plate electrolytic cell , 1974 .

[29]  Thomas J. Hanratty,et al.  Turbulent mass transfer rates to a wall for large Schmidt numbers , 1977 .

[30]  A. Wragg,et al.  An electrochemical study of mass transfer in free convection at vertical arrays of horizontal cylinders , 1974 .

[31]  A. Wragg Free convection mass transfer at horizontal electrodes , 1968 .

[32]  J. Newman,et al.  Simultaneous Reactions on a Rotating-Disk Electrode , 1977 .

[33]  B. Howland,et al.  Use of electrochemiluminescence in visualizing separated flows , 1966, Journal of Fluid Mechanics.

[34]  J. Newman Simultaneous Reactions at Disk and Porous Electrodes , 1977 .

[35]  R. Greif,et al.  Mass Transfer to a Rough Rotating Cylinder , 1971 .

[36]  R. Greif,et al.  EXPERIMENTAL AND THEORETICAL RESULTS FOR MASS TRANSFER TO A ROTATING CONE IN A NON-NEWTONIAN SALINE SOLUTION , 1973 .

[37]  E. Gileadi,et al.  The Rotating Cone Electrode , 1976 .

[38]  J. N. Agar,et al.  Diffusion and convection at electrodes , 1947 .

[39]  R. Jansson,et al.  Mass transfer and pressure distributions in electrochemical pump cells , 1977 .

[40]  J. Yamada,et al.  Limiting diffusion currents in hydrodynamic voltammetry: I. Fixed disk and ring electrodes in laminar uniform flow , 1971 .

[41]  F. Coeuret,et al.  APPLICATIONS OF FLUIDIZED BEDS IN ELECTROCHEMISTRY , 1969 .

[42]  T. Fahidy The chemical engineering approach to some electrochemical processes , 1973 .

[43]  A. Wragg,et al.  Free convection flow patterns at horizontal surfaces with ionic mass transfer , 1970 .

[44]  Der-Tau Chin,et al.  Mass Transfer to a Continuous Moving Sheet Electrode , 1975 .

[45]  S. Müller,et al.  Zur Rührabhängigkeit des Grenzstromes an teilweise bedeckten rotierenden Scheibenelektroden bei relativ grossen Umdrehungszahlen , 1969 .

[46]  R. O'brien,et al.  AN INTERFEROMETRIC DETERMINATION OF DIFFUSION CONSTANTS OF COPPER(II) ION IN COPPER(II) SULFATE SOLUTIONS , 1963 .

[47]  C. Tobias,et al.  Selected Physical Properties of Ternary Electrolytes Employed in Ionic Mass Transfer Studies , 1956 .

[48]  T. K. Ross,et al.  Superposed free and forced convective mass transfer in an electrochemical flow system , 1967 .

[49]  H. Angelino,et al.  Transferts de matiere a la paroi d'une cuve mecaniquement agitee , 1974 .

[50]  A. Ahmed,et al.  Mass transfer by free convection at inclined electrodes , 1969 .

[51]  A. Wragg A note on electrochemical mass transfer from flowing solutions to cylindrical electrodes , 1975 .

[52]  R. Mani,et al.  Mass transfer through horizontal liquid films in wavy motion , 1968 .

[53]  A. Arvia,et al.  Diffusional flow under non-isothermal laminar free convection—II. Experimental approach , 1969 .

[54]  N. Tanaka,et al.  Kinetic parameters of electrode reactions , 1964 .

[55]  A. Riddiford,et al.  Limiting Currents for the Reduction of the Tri‐iodide Ion at a Rotating Platinum Disk Cathode , 1961 .

[56]  Eugene J. Fenech,et al.  Mass transfer by free convection at horizontal electrodes , 1960 .

[57]  T. R. Galloway,et al.  Inquiries into turbulence enhanced local mass transfer and skin friction from a sphere using electrochemical probes , 1975 .

[58]  C. Deslouis,et al.  Impédance électromécanique obtenue au courant limite de diffusion à partir d'une modulation sinusoidale de la vitesse de rotation d'une électrode à disque , 1977 .

[59]  J. Yamada,et al.  Limiting diffusion currents in hydrodynamic voltammetry: II. Wedge electrodes in laminar uniform flow , 1971 .

[60]  F. Berger,et al.  MASS TRANSFER IN TURBULENT PIPE FLOW MEASURED BY THE ELECTROCHEMICAL METHOD , 1977 .

[61]  R. Whitehead,et al.  A mass-transfer study of two-phase flow in an electrochemical reactor , 1975 .

[62]  L. Müller,et al.  Der einfluss des leitsalzes auf die geschwindigkeit des elektronenaustausches im redoxsystem [Fe(CN)6]3−/[Fe(CN)6]4− , 1975 .

[63]  A. Arvia,et al.  Electrochemical study of the diffusion of cupric ion in aqueous and aqueous-glycerol solutions containing sulphuric acid , 1966 .

[64]  N. Ibl Probleme des Stofftransportes in der angewandten Elektrochemie , 1963 .

[65]  Erich Brunner,et al.  Reaktionsgeschwindigkeit in heterogenen Systemen , 1904 .

[66]  W.G.B. Mandersloot,et al.  The effect of viscous forces on heat and mass transfer in systems with turbulence promoters and in packed beds , 1968 .

[67]  D. Gabe,et al.  Electrodeposition from a fluidised bed electrolyte—I The mass transport correlation , 1974 .

[68]  T. K. Ross,et al.  The effect of surface roughness upon electrochemical processes , 1965 .

[69]  U. Böhm,et al.  Mass transfer in packed beds of screens , 1977 .

[70]  A. Arvia,et al.  Ionic mass transfer in channel electrodes under laminar flow , 1970 .

[71]  Moustafa Soliman,et al.  Transient heat transfer for forced convection flow over a flat plate of appreciable thermal capacity and containing an exponential time-dependent heat source , 1968 .

[72]  R. Sioda Limiting current on porous graphite electrodes under flow conditions , 1975 .

[73]  T. Fahidy,et al.  Mass transfer in cylindrical magnetoelectrolytic cells , 1976 .

[74]  R. Sioda Electrolysis with flowing solution , 1968 .

[75]  J. Dekker,et al.  Mass transfer to a moving continuous cylinder , 1969 .

[76]  A. Arvia,et al.  Mass transfer in the electrolysis of CuSo4− H2SO4 in aqueous solutions under limiting current and forced convection employing a cylindrical cell with rotating electrodes , 1962 .

[77]  R. Sioda Flow-through electrodes composed of parallel screens , 1977 .

[78]  H. Matsuda Zur theorie der stationären strom-spannungs-kurven von redox-elektrodenreaktionen in hydrodynamischer voltammetrie III. Laminare keilströmungen , 1969 .

[79]  S. Bruckenstein,et al.  The Frequency Response of Limiting Currents to Sinusoidal Speed Modulation at a Rotating Disk Electrode , 1975 .

[80]  T. J. Hanratty,et al.  Fluctuations in the local rate of turbulent mass transfer to a pipe wall , 1964 .

[81]  F. Ogino,et al.  Turbulent heat and mass transfer between wall and fluid streams of large Prandtl and Schmidt numbers , 1971 .

[82]  H. Ueda,et al.  TURBULENT MASS TRANSFER IN THE ENTRANCE REGION OF A CIRCULAR TUBE , 1971 .

[83]  G. Sedahmed,et al.  Mass transfer at gas evolving screen electrodes , 1975 .

[84]  T. J. Hanratty,et al.  Limiting relation for the eddy diffusivity close to a wall , 1967 .

[85]  B. Stanmore,et al.  Ionic mass transfer in parallel plate electrochemical cells , 1972 .

[86]  M. Eisenberg,et al.  Ionic Mass Transfer and Concentration Polarization at Rotating Electrodes , 1953 .

[87]  J. Newman The effect of migration in laminar diffusion layers , 1967 .

[88]  D. Gabe,et al.  Mass transfer in a rotating cylinder cell—I. Laminar flow , 1972 .

[89]  J. Newman,et al.  THE EFFECT OF VARIABLE TRANSPORT PROPERTIES ON MASS TRANSFER TO A ROTATING DISK , 1967 .

[90]  H. El-Abd,et al.  The combined effect of gas evolution and surface roughness on the rate of mass transfer , 1973 .

[91]  L. Doraiswamy,et al.  A model for solid—gas reactions , 1971 .

[92]  F. P. Bowden,et al.  The kinetics of electrode reactions. I and II , 1938 .

[93]  Thomas J. Hanratty,et al.  An experimental study of the unsteady nature of the viscous sublayer , 1963 .

[94]  A. Arvia,et al.  Ionic mass transfer in the electrolysis of flowing solutions. The electrodeposition of copper under mass-transfer control on tubular electrodes. , 1964 .

[95]  I. Cornet,et al.  Mass Transfer to a Rotating Disk , 1971 .

[96]  T. K. Ross,et al.  Diffusivity and ionic mass transfer in the cupric sulphate system , 1968 .

[97]  Thomas J. Hanratty,et al.  Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5 × 103 to 105 , 1969, Journal of Fluid Mechanics.

[98]  P. Javet,et al.  Étude de la cinétique de consommation d'un additif nivelant, la thiourée, durant le dépôt électrolytique , 1967 .

[99]  H. Gibert,et al.  Transferts de matiere entre une sphere soumise a des vibrations et un liquide en mouvement , 1974 .

[100]  W. Nernst,et al.  Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen , 1904 .

[101]  J. Bazán,et al.  Ionic mass transfer in flowing solutions. Electrochemical reactions under ionic mass-transfer rate control on cylindrical electrodes☆ , 1964 .

[102]  P. Nadebaum,et al.  The rate of mass transfer at a rotating cylindrical electrode with wiper blades , 1975 .

[103]  J. Couderc,et al.  Etude des transferts de matière entre une sphère et un liquide en convection forcée , 1972 .

[104]  A. Tvarusko Dimensionless Correlation of Mass Transfer in Wire Electroplating Cells of Various Designs , 1973 .

[105]  M. Keddam,et al.  Emploi d'electrodes a anneau tournant a l'etude du transport de matiere dans un fluide en regime hydrodynamique laminaire ou turbulent , 1973 .

[106]  D. Gabe,et al.  Electrodeposition from a fluidized bed electrolyte. II. Effects of bed porosity and particle size , 1975 .

[107]  D. Chin Turbulent flow and mass transfer on a rotating hemispherical electrode , 1974 .

[108]  J. Newman,et al.  CURRENTS LIMITED BY GAS SOLUBILITY , 1970 .

[109]  G. Schütz Natural convection mass-transfer measurements on spheres and horizontal cylinders by an electrochemical method , 1963 .

[110]  J. Selman,et al.  UNSTEADY-STATE EFFECTS IN LIMITING CURRENT MEASUREMENTS , 1975 .

[111]  S. Müller,et al.  Gesetzmässigkeit für den Diffusionsgrenzstrom an teilweise blockierten Modellelektroden , 1968 .

[112]  W. Blaedel,et al.  A hydrodynamic voltammetric study of the ferricyanide/ferrocyanide system with convective electrodes of platinum, gold, glassy carbon, carbon film, and boron carbide , 1977 .

[113]  N. Hackerman,et al.  Dissolution of Metals in Aqueous Acid Solutions II . Depolarized Dissolution of Mild Steel , 1955 .

[114]  M. Daguenet Etude du transport de matiere en solution, a l'aide des electrodes a disque et a anneau tournants , 1968 .

[115]  D. Gabe,et al.  Mass transfer in a rotating cylinder cell—II. turbulent flow , 1972 .

[116]  T. Fahidy,et al.  The effect of anodic bubble formation on cathodic mass transfer under natural convection conditions , 1977 .

[117]  R. Müller,et al.  Studies of Natural Convection at Vertical Electrodes , 1958 .

[118]  R. Homsy Mass transfer to a plane below a rotating disk , 1973 .

[119]  N. Ibl,et al.  Natural convection mass transfer at vertical electrodes under turbulent flow conditions , 1960 .

[120]  D. Gabe,et al.  High Speed Electrodeposition of Copper from Conventional Sulphate Electrolytes , 1970 .

[121]  H. Matsuda Theory of stationary current-voltage curves of redox-electrode reactions in hydrodynamic voltammetryVI. Ring electrodes , 1972 .

[122]  J. Bockris,et al.  Galvanostatic studies of the kinetics of deposition and dissolution in the copper + copper sulphate system , 1959 .

[123]  G. Schütz Untersuchung des Stoffaustausch-Anlaufgebietes in einem Rohr bei vollausgebildeter hydrodynamischer strömung mit einer elektrochemischen Methode , 1964 .

[124]  N. Ibl,et al.  Zur kenntnis der natürlichen konvektion bei der elektrolyse in engen räumen , 1966 .

[125]  R. Smith,et al.  Laminar convection to rotating cones and disks in non-newtonian power-law fluids , 1975 .

[126]  P. M. Heertjes,et al.  Simultaneous heat and mass transfer in laminar free convection from a vertical plate , 1968 .

[127]  H. Thirsk,et al.  The rate-determining step in the electro-deposition of copper on copper from aqueous cupric sulphate solutions , 1965 .

[128]  A. Wragg Combined free and forced convective ionic mass transfer in the case of opposed flow , 1971 .

[129]  A. Arvia,et al.  The diffusion of ferrocyanide and ferricyanide ions in aqueous solutions of potassium hydroxide , 1967 .

[130]  H. Gaskill,et al.  Diffusion-Controlled Electrode Reactions , 1951 .

[131]  A. Kuhn,et al.  Combined effects in mass transfer to a planar electrode , 1977 .

[132]  G. Sedahmed,et al.  Natural convection mass transfer at horizontal screens , 1976 .

[133]  J. Newman,et al.  The Role of Bisulfate Ions in Ionic Migration Effects , 1971 .

[134]  F. Coeuret,et al.  Experimental study of copper deposition in a fluidized bed electrode , 1977 .

[135]  A. Wragg Free convection mass transfer at mesh electrodes , 1968 .

[136]  M. Eisenberg,et al.  Fiftieth Anniversary: Diffusion and Convection in Electrolysis—A Theoretical Review , 1952 .

[137]  D. Gabe The rotating cylinder electrode , 1974 .

[138]  A. Storck,et al.  Mass and momentum transfer at a wall in the presence of turbulence promoters , 1977 .

[139]  E. Ravoo,et al.  Theoretical and electrochemical investigation of free convection mass transfer at vertical cylinders , 1970 .

[140]  J. Newman,et al.  Ring‐Disk and Sectioned Disk Electrodes , 1972 .

[141]  D. J. Robinson Mass transfer in the presence of opposing flows , 1972 .

[142]  John Newman,et al.  Application of the limiting current method to mass transfer in packed beds at very low reynolds numbers , 1976 .

[143]  D. Spalding,et al.  A theoretical and experimental investigation of diffusion-controlled electrolytic mass transfer between a falling liquid film and a wall , 1967 .

[144]  T. Mizushina,et al.  The Electrochemical Method in Transport Phenomena , 1971 .

[145]  D. Chin,et al.  An electrochemical study of flow instability on a rotating disk , 1972, Journal of Fluid Mechanics.

[146]  A. Gordon,et al.  The Diffusion of Copper Sulfate in Aqueous Solutions of Sulfuric Acid , 1935 .

[147]  J. Newman,et al.  Current Distributions on Plane, Parallel Electrodes in Channel Flow , 1970 .

[148]  M. Fouad,et al.  Natural convection mass transfer at vertical electrodes , 1964 .

[149]  J. Newman,et al.  Mass Transfer to a Rotating Disk in Transition Flow , 1976 .

[150]  G. Pini,et al.  Influence of suspended particles on mass transfer under turbulent conditions at a rotated disk electrode , 1977 .

[151]  J. Newman Effect of Ionic Migration on Limiting Currents , 1966 .

[152]  C. Tobias,et al.  Correlation of Limiting Currents under Free Convection Conditions , 1953 .

[153]  M. Spiro Standard exchange current densities of redox systems at platinum electrodes , 1964 .

[154]  J. Hostomský,et al.  Limiting Local Current Densities for Electrodes Located on the Walls of a Rectangular Channel with Laminar Flow; Asymptotic Solution and Experimental Verification , 1971 .

[155]  J. Mandelbaum,et al.  Mass transfer in packed beds at low Reynolds numbers , 1973 .

[156]  T. Fahidy,et al.  Ionic mass transfer in open channel flow , 1976 .

[157]  D. Gabe,et al.  Electrodeposition from a fluidized bed electrolyte. III. Electrodeposit structure , 1975 .

[158]  F. B. Leitz,et al.  Enhanced mass transfer in electrochemical cells using turbulence promoters , 1977 .

[159]  T. Dickinson,et al.  The kinetics of the ferrous/ferric and ferro/ferricyanide reactions at platinum and gold electrodes , 1972 .

[160]  A. B. Metzner,et al.  Turbulent heat transfer inside tubes and the analogy among heat, mass, and momentum transfer , 1958 .

[161]  B. Py Étude tridimensionnelle de la sous-couche visqueuse dans une veine rectangulaire par des mesures de transfert de matière en paroi , 1973 .

[162]  M. A. Patrick,et al.  Optical and electrochemical studies of transient free convection mass transfer at horizontal surfaces , 1975 .

[163]  P. Daum,et al.  Electrochemical kinetics of the ferri-ferrocyanide couple on platinum , 1969 .

[165]  C. Bakker,et al.  An experimental study of mass transfer from a liquid flow to wires and gauzes , 1963 .

[166]  A. Al-Taweel,et al.  Effect of longitudinal vibrations on the mass-transfer at vibrating electrodes† , 1974 .

[167]  F. Aimeur,et al.  Theorie et applications des microelectrodes , 1973 .

[168]  Charles W. Tobias,et al.  The solubility and diffusion coefficient of oxygen in potassium hydroxide solutions , 1967 .

[169]  R. Bucur,et al.  Stationary disk electrode in a uniformly rotating fluid , 1977 .

[170]  Thomas J. Hanratty,et al.  A study of turbulence at a wall using an electrochemical wall shear-stress meter , 1966, Journal of Fluid Mechanics.

[171]  R. W. Moulton,et al.  Mass Transfer between Solid Wall and Fluid Streams. Mechanism and Eddy Distribution Relationships in Turbulent Flow. , 1953 .

[172]  G. Wranglén,et al.  Mass transfer under forced laminar and turbulent convection at horizontal plane plate electrodes , 1962 .

[173]  K. Gubbins,et al.  The Solubility and Diffusivity of Oxygen in Electrolytic Solutions , 1965 .

[174]  D. Gabe,et al.  Electrochemical mass transfer in an annulus , 1974 .

[175]  R. K. Finn,et al.  Mass Transfer to a Cylinder at Low Reynolds Numbers , 1956 .

[176]  L. Müller,et al.  Elektrochemische Untersuchungen am Redoxsystem Hexacyanoferrat(II)/Hexacyanoferrat(III)an Graphitelektroden , 1974 .

[177]  T. K. Ross,et al.  Electrochemical mass transfer studies in annuli , 1965 .

[178]  J. Lloyd,et al.  Natural Convection Adjacent to Horizontal Surface of Various Planforms , 1974 .

[179]  S. Barnartt Primary Current Distribution Around Capillary Tips Used in the Measurement of Electrolytic Polarization , 1952 .

[180]  M. Daguenet,et al.  Calcul du flux limite de diffusion sur une microelectrode de section circulaire—equivalence avec une electrode de section rectangulaire. Verification experimentale dans le cas du disque tournant en regime laminaire , 1974 .

[181]  B. C. Sakiadis Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[182]  T. J. Hanratty,et al.  Measurement of instantaneous rates of mass transfer to a small sink on a wall , 1962 .

[183]  J. Newman,et al.  MASS TRANSFER AND POLARIZATION AT A ROTATING DISK ELECTRODE , 1967 .

[184]  A. Wragg,et al.  Ionic mass transfer by free convection with simultaneous heat transfer , 1973 .

[185]  J. Selman,et al.  Free‐Convection Mass Transfer with a Supporting Electrolyte , 1971 .

[186]  E. Weder Messung des gleichzeitigen Wärme- und Stoffübergangs am horizontalen Zylinder bei freier Konvektion , 1968 .

[187]  H. Matsuda Zur Theorie der Stationären Strom-spannungskurven von Redox-Elektrodenreaktionen in hydrodynamischer Voltammetrie: V. Schleichende Kugelströmungen , 1970 .

[188]  E. Weder Elektrochemische Untersuchung des Stoff?bergangs von einer Fl?ssigkeit an eine gasende D?se , 1967 .

[189]  B. C. Sakiadis Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[190]  P. Grassmann,et al.  Elektrochemische Messung von Stoffübergangszahlen , 1961 .

[191]  J. Venczel,et al.  Stofftransport bei der Elektrolyse mit Gasrührung , 1971 .

[192]  A. Colburn,et al.  Mass Transfer (Absorption) Coefficients Prediction from Data on Heat Transfer and Fluid Friction , 1934 .

[193]  C. Tobias,et al.  Application of Backside Luggin Capillaries in the Measurement of Nonuniform Polarization , 1955 .

[194]  K. R. Jolls,et al.  Use of electrochemical techniques to study mass transfer rates and local skin friction to a sphere in a dumped bed , 1969 .

[195]  L. Janssen,et al.  The effect of electrolytically evolved gas bubbles on the thickness of the diffusion layer , 1970 .