Enhanced mass transport to a reticulated vitreous carbon rotating cylinder electrode using jet flow

The mass transport characteristics of a porous, rotating cylinder electrode (RCE, 1.0 cm diameter; 0.5, 0.9 or 1.2 cm long; 1.25, 2.25, 3.00 cm³ overall volume; 250-2000 rpm speed) fabricated from reticulated vitreous carbon (RVC, 60 ppi or 100 ppi) were investigated. The deposition of copper from an acid sulfate electrolyte (typically, deoxygenated 1 mM CuSO₄ in pH 2, 0.5 M Na₂SO₄ at 298 K) was used as a test reaction. The effect of a jet flow of electrolyte towards the electrode and the introduction of polypropylene baffles in the electrochemical cell were studied at controlled rotation rates of the RCE. The product of mass transport coefficient and volumetric electrode area (k_mA_e) is related to the rotation speed of the electrode. For the 60 ppi RVC RCE, the jet electrolyte flow (3.5 cm³ s⁻¹) enhanced the mass transport rates by a factor of 1.46 at low rotation speeds; this factor was reduced to 1.08 at high rotation speeds. For a 100 ppi electrode, the enhanced mass transport decreased from 1.26 to 1.03 at low and high rotation rates, respectively. Under the experimental conditions, baffles showed little effect on the mass transport rates to the RVC RCE. Mass transport to jet flow at an RVC RCE is compared to other RCEs using dimensionless group correlation.     

Overall mass transfer to the rotating inner electrode of a concentric cylindrical reactor with axial flow

Overall mass transfer coefficients between a liquid flowing axially in an annulus and the surface of the rotating inner cylinder have been determined electrochemically. The experiments concern mainly the laminar vortex regime and the results show the combined effect of rotation and axial flow. The value 300 of the axial Reynolds number separates two domains; for each domain the results are satisfactorily correlated using dimensionless numbers.     

Electrolytic mass transport at a rotating outer cylinder electrode with developing axial flow in the annulus

Mass transport in an experimental horizontal electrochemical reactor with a rotating outer cylinder and axial flow in the annulus has been investigated, and appropriate dimensionless relationships for the estimation of mass transport rates have been developed by employing statistical regression analysis of experimentally measured flow rates and current density.Nomenclature c _O active ion concentration in electrolyte bulk - c _a supporting electrolyte concentration in electrolyte bulk - D electrolyte diffusivity - d _e equivalent diameter - F Faraday's constant - I electric current - i _c cathodic current density - Nu Nusselt number - L electrode length - Pe Peclet number (Re ·Sc) - R ₁ inner cylinder radius (outer) - R ₂ outer cylinder radius (inner) - R ² square of the multiple correlation coefficient - Re Reynolds number (2(R ₂–R ₁)/v) - Sc Schmidt number (v/D) - Sh Sherwood number (2i _c(R ₂–R ₁)/zFDc _o) - Ta _m modified Taylor number (R ₂(R₂–R ₁ ^3/2/vR ₁ ^1/2 ) - axial electrolyte velocity - z valency (z=2 in the current case) - v electrolyte kinematic viscosity - rotation speed     

Enhanced mass transfer using roughened rotating cylinder electrodes in turbulent flow

Cylindrical electrodes have been roughened by machining groove patterns, pyramidal knurling, and superimposing wires and meshes for which the degree of roughness has been calculated. By rotating the electrodes in a turbulent regime, mass transfer for cathodic copper electrodeposition has been measured and the degree of consequent enhancement (relative to an equivalent smooth cylinder) calculated. Typically, the surface area has been increased by 10–40% and the mass transfer rate by 100–300% for turbulent flow defined by 7000<Re<80 000.Nomenclature A (A _R) area of cathodic (rough) cylinder (cm²) - C exponent - C _B metal ion concentration in bulk solution (mol cm^–3) - d _s (d _R) diameter of smooth (rough) cylinders (cm) - D diffusion coefficient of metal ion (cm²s^–1) - F Faraday's constant - I _L limiting current density (mA cm^–2) - j ₀ dimensionless mass transfer factor (=ShSc ^c) - k _L mass transfer coefficient (=I _L/zFC _B) - k _s,k _R k _L values for smooth and rough cylinders - m, n exponents - P pitch, or roughness element spacing (cm) - Re Reynolds number (=Ud/v) - Ré d _R U _R/v - Re _s dU _s/v - Sc Schmidt number (=v/D) - Sh Sherwood number (=k _L d/D) - St Stanton number (=k _L/U) - U _s (U _R) peripheral velocity at smooth (rough) cylinders (cm s^–1) - U ₀ friction velocity (cm s^–1) - w width of wire mesh opening (cm) - z valency change, number of electrons - groove depth (cm) - kinematic viscosity (cm² s^–1) - groove width     

Unsteady mass transfer in turbulent flow close to a rotating cylinder

Electrodiffusional methods of studying unsteady turbulent mass transfer involved measurement of a transient current characteristicI() after step polarization of a rotating annular cylindrical 46 mm dia electrode at a fixed rotational velocity atRe=(2–9)×10⁴ andSc=2.4×10³. The potassium ferri-ferrocyanide system with NaOH background electrolyte was used. An initial asymptote at 0 served as a test. The similarity of the normalized transfer coefficientK ₊=/u _* with respect to the Reynolds number demonstrated turbulent flow development. Tests were aimed at determining the powern in the approximate law of attenuation of turbulent diffusionD _t in they-direction normal to the wallD _t/v=by ₊ ⁿ .A numerical solution of the unsteady turbulent diffusion equation obtained as a set of lg ()=f() curves for 3n4 with an interval 0.2, where ()=I/I()_#x2212;1 has been achieved.Notation I diffusion current - C C ₀ andC _p concentration, concentration in the bulk liquid and polymer concentration, respectively - C _f drag of a Newtonian fluid - time - U linear velocity - v kinematic viscosity - angular velocity - j flow - y ₊ yu _*/v, ₊ = u _* ² and =(1-C/C ₀), dimensionless quantities This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

Enhanced mass transfer at the rotating cylinder electrode: III. Pilot and production plant experience

Enhanced mass transfer at a rotating cylinder electrode, due to the development of surface roughness of a metal deposit, has been studied in a range of commercial and pilot scale reactors known as ECO-CELLS. The data obtained for relatively restricted ranges of process parameters show reasonable agreement with the more definitive data obtained under laboratory conditions. With scale-up factors of approximately six times in terms of the rotating cylinder diameter, enhanced mass transfer factors of up to 30 times are reported (in comparison with hydrodynamically smooth electrodes) due to the development of roughened deposits during the process of metal extraction from aqueous solution.Nomenclature a, b, c constants in Equation 15 - A active area of rotating cylinder (cm²) - C (bulk) concentration of metal (mol cm^–3 or mg dm–3) - c concentration change over reactor (mol cm^–3 or mg dm^–3) - C _IN,C _OUT,C _CELL inlet, outlet and reactor concentrations of metal (mol cm^–3 or mgdm^–3) - d diameter of rotating cylinder (cm) - D diffusion coefficient (cm₂ s_–1) - f _R fractional conversion - F Faraday constant=96 500 A s (mo1^–1) - I current (A) - I _L limiting current (A) - I _o useful current (A) - j _D ^' mass transport factor (=St Sc ^c) - K constant in Equation 27 - K _L mass transport coefficient (cm s^–1) - m slope of Fig. 8 (s^–1) - M molar mass of copper = 63.54 g mol^–1 - n number of elements in the cascade - N volumetric flow rate (cm^{3 –1}) - P Reynolds number exponent for powder formation (Equation 28) - R total cell resistance (Q) - t time (s) - U peripheral velocity of cylinder (cm s^–1) - V _cell cell voltage (V) - V _R,V _T effective cell, reservoir volume (cm³) - W electrolytic power consumption (W) - x velocity index in Equation 27 - z number of electrons - Re Reynolds number=Ud/v - Sc Schmidt number=v/D - St Stanton number=K _L/U - gu kinematic viscosity (cm² s^–1) - cathode current efficiency - rotational speed (revolutions min^–1) - peak to valley roughness (cm)     

Enhanced mass transfer at the rotating cylinder electrode. I. Characterization of a smooth cylinder and roughness development in solutions of constant concentration

A versatile rotating cylinder electrode (RCE) assembly has been constructed in order to study the development of surface roughness during the prolonged cathodic deposition of metal at high overpotential. The initial smooth cylindrical surface and its behaviour have been characterized and the onset of rough deposits is described by an empirical power law (based on the mass transfer correlation)I _L= (constant)U ^x where x～-0.74 for a smooth surface and x～-0.90 for a roughened surface. The uses and limitations of this power law are discussed.     

Enhanced mass transfer at the rotating cylinder electrode. II. Development of roughness for solutions of decreasing concentration

The development of roughness at a rotating cylinder electrode has been investigated in the context of a metal recovery system — the ECO-CELL — where the solution concentration necessarily falls with time under batch processing. Roughness has been quantified using knurled cylinders and the use of thiourea as an additive has been considered. The development of a rough surface allows a reactor to recover metal at enhanced rates and the exploitation of this feature is discussed.     

自由摆动方柱强化微流体通道内传热传质

提出了一种基于自由摆动方柱提高微流体通道内传热传质效率的新方法。基于有限体积法并结合动网格技术,对微通道内液体流经自由摆动方柱（有旋转自由度、无平移自由度）时产生的扰流及强化传热传质现象进行了数值研究。研究显示,在低雷诺数（Re=10）下,自由摆动方柱几乎无运动,其对流动和传热传质的影响同固定方柱类似;随着雷诺数的增加,自由摆动方柱在流场作用下会自发产生周期性摆动,并在较低雷诺数（Re=50）下提前促使其后方产生交替性的涡脱落现象;随着雷诺数进一步增加（Re=100）,方柱的自由摆动及其后方的涡街结构均显著增强。与同Re数下的固定方柱相比,自由摆动方柱能够更显著地扰动微通道内原有的泊肃叶流场,破坏通道内壁面处热边界层,提高其传热效率;同时通道内液体的横向流动可有效促进溶质混合,强化传质进程。当Re=100时,自由摆动方柱微通道内的平均换热努塞尔数Nu较固定方柱和无方柱时分别提高了17.5%和29.6%;同时,出口截面混合效率可较固定方柱和无方柱时分别提高了70.5%和65500%。     

An experimental study of mass transfer in rotating couette flow with low axial reynolds number

An experimental investigation has been undertaken to determine the oxygen transfer rate of a rotating Couette flow oxygenator for low axial annular flow rates. The purpose of this study was to determine if such a device might provide a rational basis for the subsequent design of a blood oxygenator for respiratory support in clinical situations. Using oxygen and degassed water as an analog to oxygen and blood the Sherwood number was determined as a function of the axial Reynolds number and the Taylor number. Results show that oxygen transfer rates can be enhanced by at least ten times over that of the non-rotating situation, the flow being laminar with vortex flow superposed. The present results were correlated as Sh vs. Ta/Ta_c over the range of parameters studied.     

The rotating cylinder electrode

The transfer of mass onto a rotating cylindrical nickel electrode was investigated at relatively low rates. The simple electrochemical reaction of ferricyanide ion in an alkali medium was applied for this purpose. In the investigations particular attention was paid to the phenomenon of the penetration of eddies into the laminar sublayer. A modification and broadening of the basic Taylor expression, namely Taylor's linear theory, was proposed for the systems with a greater interelectrode distance. The experimental results can be better interpreted with a thus modified expression.Symbols A surface area - b constant - c _b,c _s bulk and surface concentrations - d _c diameter of rotating inner cylinder - D diffusion coefficient - zF Faradaic equivalence - h height - k _f friction factor - i ₁ limiting current density - I ₁ limiting current - dimensionless number - k _L mass transfer coefficient - N rotation per minute - r _i,r _o radii of inner and outer cylinders - = r _i peripheral velocity - x distance along the electrode - y distance normal to the electrode - _N, _Pr thickness of Nernst diffusion and Prandtl hydrodynamic boundary layers - _o thickness of laminar or viscous sublayer - coefficient of viscosity - density - kinematic viscosity - angular velocity - (Re) Reynolds number,d _c/ - (Sc) Schmidt number,/D - (Sh) Sherwood number,k _L d _c/D - (St) Stanton number,k _L/     

The rate of mass transfer at a rotating cylindrical electrode with wiper blades

A theoretical analysis of mass transfer at a rotating cylindrical electrode with wiper blades yields the dimensionless equation where w is the number of the symmetrically located wiper blades, d is the wiper blade thickness and R₁ is the radius of the wiped electrode. Nu_R, Re_R and Sc are defined in terms of the cell and electrolyte parameters. Experimental evidence via the reduction of oxygen and ferrocyanide ions indicates that mass transfer rates can thus be predicted at no more than ±5% inaccuracy for Sc>200. The two-wiper blade system is shown to effect an increase in mass transfer rates by a factor of 7-8 with respect to a rotating cylindrical electrode without wiper blades.     

The rate of mass transfer at a rotating cylindrical electrode with wiper blades

A theoretical analysis of mass transfer at a rotating cylindrical electrode with wiper blades yields the dimensionless equation where w is the number of the symmetrically located wiper blades, d is the wiper blade thickness and R₁ is the radius of the wiped electrode. Nu_R, Re_R and Sc are defined in terms of the cell and electrolyte parameters. Experimental evidence via the reduction of oxygen and ferrocyanide ions indicates that mass transfer rates can thus be predicted at no more than ±5% inaccuracy for Sc > 200. The two-wiper blade system is shown to effect an increase in mass transfer rates by a factor of 7–8 with respect to a rotating cylindrical electrode without wiper blades.     

Mass transfer in a rotating cylinder cell—I. Laminar flow

The relationship between mass transfer and rotation rate for a concentric cylinder cell, in which the inner cylinder rotates and the outer cylinder remains stationary, has been derived for a simple model assuming linear velocity gradients near the rotating cylinder surface. A previous treatment by Kimla and > Stráfelda has been shown to be in error, but when corrected it takes essentially the same form as that derived in this paper.