On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability

© 2014 Cambridge University Press. This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of ∼ 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of ∼ 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R=585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R=565 to 590 and to a fully turbulent boundary layer above 650.

The turbulent rotating-disk boundary layer

© 2014 Elsevier Masson SAS. All rights reserved. The turbulent boundary layer on a rotating disk is studied with the aim of giving a statistical description of the azimuthal velocity field and to compare it with the streamwise velocity of a turbulent two-dimensional flat-plate boundary layer. Determining the friction velocity accurately is particularly challenging and here this is done through direct measurement of the velocity distribution close to the rotating disk in the very thin viscous sublayer using hot-wire anemometry. Compared with other flow cases, the rotating-disk flow has the advantage that the highest relative velocity with respect to a stationary hot wire is at the wall itself, thereby limiting the effect of heat conduction to the wall from the hot-wire probe. Experimental results of mean, rms, skewness and flatness as well as spectral information are provided. Comparison with the two-dimensional boundary layer shows that turbulence statistics are similar in the inner region, although the rms-level is lower and the maximum spectral content is found at smaller wavelengths for the rotating case. These features both indicate that the outer flow structures are less influential in the inner region for the rotating case.

Electrochemical characterisation and anodic stripping voltammetry at mesoporous platinum rotating disc electrodes

Using the technique of liquid crystal templating a rotating disc electrode (RDE) was modified with a high surface area mesoporous platinum film. The surface area of the electrode was characterised by acid voltammetry, and found to be very high (ca. 86 cm(2)). Acid characterisation of the electrode produced distorted voltammograms was interpreted as being due to the extremely large surface area which produced a combination of effects such as localised pH change within the pore environment and also ohmic drop effects. Acid voltammetry in the presence of two different types of surfactant, namely Tween 20 and Triton X-100, suggested antifouling properties associated with the mesoporous deposit. Further analysis of the modified electrode using a redox couple in solution showed typical RDE behaviour although extra capacitive currents were observed due to the large surface area of the electrode. The phenomenon of underpotential deposition was exploited for the purpose of anodic stripping voltammetry and results were compared with data collected for microelectrodes. Underpotential deposition of metal ions at the mesoporous RDE was found to be similar to that at conventional platinum electrodes and mesoporous microelectrodes although the rate of surface coverage was found to be slower at a mesoporous RDE. It was found that a mesoporous RDE forms a suitable system for quantification of silver ions in solution.

Scanned stripping chronopotentiometry at bismuth film rotating disc electrodes: a method for quantitative dynamic metal speciation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the steady-state assumption and its application to the rotating disk voltammetry of adsorbed enzymes

Rotating disk voltammetry is routinely used to study electrochemically driven enzyme catalysis because of the assumption that the method produces a steady-state system. This assumption is based on the sigmoidal shape of the voltammograms. We have introduced an electrochemical adaptation of the King-Altman method to simulate voltammograms in which the enzyme catalysis, within an immobilized enzyme layer, is steadystate. This method is readily adaptable to any mechanism and provides a readily programmable means of obtaining closed form analytical equations for a steady-state system. The steady-state simulations are compared to fully implicit finite difference (FIFD) simulations carried out without any steady-state assumptions. On the basis of our simulations, we conclude that, under typical experimental conditions, steady-state enzyme catalysis is unlikely to occur within electrode-immobilized enzyme layers and that typically sigmoidal rotating disk voltammograms merely reflect a mass transfer steady state as opposed to a true steady state of enzyme intermediates at each potential.

Wireless Rotating Disk Electrode (wRDE) for assessing Heterogeneous Water Oxidation Catalysts (WOCs)

A novel method for assessing the activity of a powdered water oxidation catalyst (WOC) is described, utilising an easily-prepared wireless rotating disc electrode of the WOC, thereby allowing its activity to be probed, via the observed kinetics of water oxidation by Ce(IV) ions, and so provide invaluable electrochemical information.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

ELECTROCHEMICAL CATALYSIS AT AN ULTRAMICROELECTRODE MODIFIED WITH REDOX SPECIES

General equations of the electrocatalytic reaction at an ultramicroelectrode modified with redox species have been described according to the Andrieux Saveant model. The electrocatalytic kinetic process has been discussed for the whole set of cases, ie (R), (R + S), (SR) (SR + E), (E), (R + E), (ER), (S), (ER + S) and (S + E) limiting situations. The effect of gamma on the catalytic steady state current shows that the higher the value of gamma, the lower the catalytic current. The kinetic process shifts rapidly from R to E with increasing values of gamma. It is favorable for catalysis only when gamma is very low. Therefore, the redox species modified ultramicroelectrode with thin film is utilized for electrocatalysis, and the larger the radius of ultramicroelectrode, the higher the catalytic efficiency.

Oxygen reduction on PtFe/C electrocatalysts prepared in microemulsions

PtFe/C nanocatalysts of different compositions and nearly constant particle size were prepared by a microemulsion method. Crystallite sizes and degree of alloying were determined by X-ray diffraction. Particle size and distribution were characterized by transmission electron microscopy and average composition was determined by energy dispersive X-ray analysis. Measurements of electrocatalytic activity for oxygen reduction were done using the rotating disk electrode technique in O2 saturated 0.5 mol L-1 sulfuric acid solutions, at room temperature. For all catalysts oxygen reduction begins at ̃ 0.90V. Tafel plots show slopes of c.a. 60 and 120 mV dec in the regions of low and high overpotentials, respectively. The best results for the ORR were obtained for the PtFe/C catalyst of composition Pt:Fe 70:30. This catalyst was also found to exhibit the largest methanol tolerance. © The Electrochemical Society.

Altering the adsorptive and electronic properties of Pt through poly(vinyl alcohol) adsorption

In the present paper we investigated the effect of adsorbed PVA on Pt electrodes on classic electrochemical processes such as hydrogen UPD, oxygen reduction and CO electro-oxidation. Upon adsorption PVA blocks roughly 50% of the hydrogen sites and can not be removed from the Pt surface through cycling in the potential range of 0.05-1.0 V vs. RHE. Potentiodynamic experiments under controlled hydrodynamic conditions provided by rotating disk electrode experiments showed a negative impact of the adsorbed PVA on the oxygen reduction reaction (ORR). Cyclic-voltammetry results revealed that not even CO was able to remove PVA from the Pt surface. Regarding the oxidation of CO, the adsorbed polymer positively shifted the CO oxidation peak potential, therefore higher potentials are required to free the Pt surface from CO poisoning. In situ Fourier transform infrared spectroscopy evidenced that the presence of PVA shifted the linearly bound CO frequency toward higher wavenumbers, a process found to be independent of the Pt surface orientation. In situ electrochemical X-ray absorption spectroscopy results showed that PVA also impacted the electronic properties of platinum by decreasing the occupancy of the Pt conducting 5d band. Our findings clearly support the efforts toward understanding the nature of the interaction between polymers and metallic surfaces as well as the impact on technological applications (e.g. in PEMFCs). © 2013 Elsevier Ltd. All rights reserved.

Electrochemical reduction of oxygen on gold and boron-doped diamond electrodes in ambient temperature, molten acetamide-urea-ammonium nitrate eutectic melt

The electrochemical reduction of oxygen has been studied on gold, boron-doped diamond (BDD) and glassy carbon (GC) electrodes in a ternary eutectic mixture of acetamide (CH3CONH2), urea (NH2CONH2) and ammonium nitrate (NH4NO3). Cyclic voltammetry (CV), differential pulse voltammetry (DPV), chronoamperometry and rotating disk electrode (RDE) voltammetry techniques have been employed to follow oxygen reduction reaction (ORR). The mechanism for the electrochemical reduction of oxygen on polycrystalline gold involves 2-step. 2-electron pathways of O-2 to H2O2 and further reduction of H2O2 to H2O. The first 2-electron reduction of O-2 to H2O2 passes through superoxide intermediate by 1-electron reduction of oxygen. Kinetic results suggest that the initial 1-electron reduction of oxygen to HO2 is the rate-determining step of ORR on gold surfaces. The chronoamperometric and ROE studies show a potential dependent change in the number of electrons on gold electrode. The oxygen reduction reaction on boron-doped diamond (BOO) seems to proceed via a direct 4-electron process. The reduction of oxygen on the glassy carbon (GC) electrode is a single step, irreversible, diffusion limited 2-electron reduction process to peroxide. (C) 2010 Elsevier Ltd. All rights reserved.

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.

Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.

A comparison of electrocatalytic ability of various mediators adsorbed onto paraffin impregnated graphite electrodes for oxidation of reduced nicotinamide coenzymes

Twelve mediators have been modified by adsorption onto the paraffin impregnated graphite electrodes (IGE). The resulting electrodes exhibit electrocatalytic activity of different degrees towards oxidation of 1,4-dihydronicotinamide adenine dinucleotide (NADH). The electrocatalytic ability of the chemically modified electrode (CME) depends mainly on the formal potential and molecular structure of mediator. The formation of the charge transfer complex between NADH and adsorbed mediator has been demonstrated by the experiments using a rotating disk electrode. An electrocatalytic scheme obeying Michaelis-Menten kinetics has been confirmed, and some kinetic parameters were estimated. The solution pH influences markedly the electrocatalytic activity of the modified electrode. Various possible reasons are discussed.