Electrodiffusion Probes Research Articles

Theory for electrodiffusional wall shear stress measurement by directionally sensitive twin semicircular probe

This study investigates the theoretical aspects of mass transport at the surface of a twin semicircular electrodiffusion probe tailored to measure the magnitude and direction of near-wall fluid flows. A critical aspect of this research is the development of a theoretical framework that facilitates experimental measurements by analytically relating measured electric currents to the wall shear stress vector. Central to the study is the derivation of analytical expressions for the mass transfer coefficients of the front and rear segments of the probe, which are essential for quantifying near-wall hydrodynamics. Validation of these analytical relations is achieved through numerical solutions of the convection–diffusion equation, providing a robust confirmation of the underlying theory. A comprehensive procedure for experimental data processing is proposed, taking into account both frontal and reverse flow conditions across the probe. In addition, a sensitivity analysis of the twin semicircular probe is performed. This analysis focuses on the response of current ratios to changes in the flow direction, an aspect critical to understanding the operational performance of the probe. The results of this analysis are compared to the characteristics of two-segment strip probes, highlighting the distinct sensitivity nuances of the twin semicircular probe. Our findings provide insight into the optimal application of this probe in various fluid dynamics scenarios.

Near-wall flow response to large air bubbles rising in inclined water channels

The two-strip electrodiffusion probe is employed to investigate the wall shear rate induced by large air bubbles rising in stagnant or coflowing water within inclined rectangular channels. Synchronized video recordings of bubble movements captured by a high-speed camera provide additional information on the bubble shapes and terminal velocities. The measurements are carried-out in a channel with easily adaptable geometry (three heights and various widths) over a wide range of operation parameters (air volumes and liquid velocities) and inclination angles (from horizontal to vertical arrangement). The main objective of this experimental study is to elucidate the influence of individual operating parameters on the bubble-induced wall shear rate. The typical profile of wall shear rate measured at the center of a flat channel can be characterized by a positive peak at the bubble front location, a negative plateau corresponding to the reverse flow in a liquid film around the bubble, and highly fluctuating values in a wake behind the bubble. Just as the large bubbles in flat channels exhibit a close similarity in their frontal shapes, so do the wall shear rate profiles induced by differently sized bubbles. The magnitude and profile of measured wall shear rate is found to be controlled primarily by the distance between two opposite walls squeezing the rising bubble, thus in flat channels by the channel height. By contrast, widening the channel has no significant effect, even though it contributes to a significant increase in the bubble rise velocity. When the channel is tilted, the rising bubbles are pushed towards the roof wall and thus two distinct wall shear rate profiles are measured at the opposite walls of the channel. The liquid coflow then contributes positively not only to the bubble velocity but also to the magnitude of wall shear rate in the near-wall flow region.

Experimental investigation of Taylor-Couette-Poiseuille flow at low Taylor and Reynolds numbers.

Flow patterns of a Taylor-Couette-Poiseuille flow were studied at low axial Reynolds and rotational Taylor numbers (Re ≤ 10.5, Ta ≤ 319). The radius ratio of the inner and outer cylinders was 0.804 and the ratio of the length of the annulus to the gap width was 44.5. Complete map of the studied flow regimes was elaborated. The axial and azimuthal components of the wall shear rate γ were measured at the outer fixed cylinder using a three-segment electrodiffusion probe. The components of the wall shear rate of helices have never been measured in previous investigations. Spatio-temporal description of multiple flow patterns was obtained using flow visualizations and simultaneous measurements of wall shear rate components. The flow structures include Taylor vortices, helices winding in the same direction as the base flow or in the opposite direction, helices that were stagnant or moving in the axial direction, smooth or with superposed azimuthal waves, among others. The influence of different flow structures on the wall shear stress components is discussed with and without axial base flow. It was found that the wall shear stress is a function of Ta but no significant dependence on Re was observed for the studied flow regimes and that the mean wall shear stress increases with the number of azimuthal waves. It was also noted that the ED probes provide a more detailed information about flow patterns than torque measurements and visualizations described in the literature.

An inverse problem to assess the two-component unsteady wall shear rate

The instantaneous two-dimensional wall shear rate is assessed through an inverse problem using mass transfer data from a three-segment electrodiffusion probe. The method is validated numerically in complex flow conditions involving (i) high amplitude periodic fluctuations on both wall shear rate magnitude and direction and (ii) direct numerical simulation (DNS) data from a turbulent three-dimensional channel flow. The approach is shown to outperform every other post-treatments available for mass transfer sensors, especially regarding its versatility and application range. The impact of the three-segment probe gap size is also examined numerically.

Wall shear stress induced by a large bubble rising in an inclined rectangular channel

The rise of single air bubbles in inclined rectangular channels was experimentally investigated. Two-segment electrodiffusion probes were used to measure wall shear rate profiles along the passing bubbles. They provided information on reverse flow in a liquid film separating the bubble from the wall, capillary waves appearing at the bubble tail, and near-wall flow fluctuations in the bubble wake. The corresponding bubble shapes and rise velocities were obtained from simultaneous visual observations done by a high-speed camera. The experiments were carried out for three channel depths (1.5, 4, and 8mm), various channel inclinations (from 5° to 90°), bubble volumes (from 1 to 80ml), and liquid up-flow velocities (from 0 to 0.2m/s). In vertical channels, the wall shear rate trace of a bubble rise is primarily influenced by the channel depth. As the frontal shape of large bubbles does not change with the bubble size, also the wall shear rate measured under these bubbles evolves in the same manner. In inclined channels, the liquid film is unequally distributed above and under the bubble with the maximum reverse flow observed under the bubble at middle inclinations. Laminar liquid co-flow makes the liquid film around the bubble thicker and in inclined channels slightly pushes the bubble toward the center-line position. The bubble velocity scaling based on the channel perimeter is confirmed to be suitable for vertical channels with stagnant liquid. The linear relationship between the bubble rise and liquid mean velocity is identified under co-flowing conditions at all channel inclinations.

Calibration of electrodiffusion probes for turbulent flow measurements

Calibration of electrodiffusion (ED) probes with respect to the wall velocity gradient measurements has been experimentally studied in a fully developed turbulent channel flow over the Reynolds number range 14000–23000. In steady state conditions, direct calibration concerning the mean wall velocity gradient can be provided using simultaneous transient and steady state diffusion limiting current measurements. Indirect calibration of the ED probes regarding the turbulent fluctuation has been undertaken using a spectral analysis performed with probes of different size and geometry. This indirect calibration method has been supported using the measurements of thermo-dependence of molecular diffusivity. In this case, only one ED probe can be used for calibration. Dynamic calibration provides necessary information about critical longitudinal dimension of ED probes. When the longitudinal dimension of the probes exceeds the critical length, the probes becomes sensitive to the normal fluctuation as well. This fact has been confirmed using different orientation of the rectangular ED probe with respect to the flow direction.

Wall Shear Stress Induced by Taylor Bubbles in Inclined Flow Channels

The motion of single air bubbles in flat channels is experimentally investigated. The electrodiffusion technique of near-wall flow diagnostics is applied to measure the wall shear stress distribution under large rising bubbles. The measurements are synchronized with the visual observation of bubble movement by a high-speed camera. The analysis of video records provides information on the bubble shape and terminal velocity. The experiments are carried out for three different channel configuration (with heights of 1.5, 4, and 8 mm), cover a wide range of channel inclination angles (from horizontal to vertical position), and dealing with both the bubbles in stagnant and in co-flowing water. The directionally sensitive, two-strip electrodiffusion probe is proved to be an effective tool to investigate the near-wall flow response to translating bubbles. It provides information not only on the wall shear rate distribution, but also detects the location of near-wall flow reversal, gives an estimate of the thickness of liquid film separating the large bubble from the wall, and provides also the characteristics of capillary waves appearing in the bubble tail region. The effect of channel inclination angle on the modification of wall shear stress distribution along the upper and bottom wall is also discussed.

Components of wall shear rate in wavy Taylor–Couette flow

The time-resolved axial and azimuthal components of the wall shear rate were measured as function of Reynolds number by a three-segment electrodiffusion probe flush mounted in the inner wall of the outer fixed cylinder. The geometry was characterized by a radius ratio of 0.8 and an aspect ratio of 44. The axial distribution of the wall shear rate components was obtained by sweeping the vortices along the probe using a slow axial flow. The wavelength and phase celerity of azimuthal waves, axial wavelength of vortices and their drifting velocity were calculated from the limiting diffusion currents measured by three simple electrodiffusion probes.

Wall Shear Rates in Taylor Vortex Flow

Wall shear rate and its axial and azimuthal components were evaluated in stable Taylor vortices. The measurements were carried out in a broad interval of Taylor numbers (52-725) and several gap width (R1/R2 = 0.5 – 0.8) by two three-segment electrodiffusion probes and three single probes flush mounted in the wall of the outer fixed cylinder. The axial distribution of wall shear rate components was obtained by sweeping the vortices along the probes using a slow axial flow. The experimental results were verified by CFD simulations. The knowledge of local wall shear rates and its fluctuations is of primordial interest for industrial applications like tangential filtration, membrane reactors and bioreactors containing shear sensitive cells.

Calibration of a segmented friction probe flush mounted in a sphere

A calibration theory for segmented probes flush mounted in a sphere exposed to uniform fluid flow was developed. The theory was checked experimentally by towing the sphere of diameter 2R = 22.2 mm with a three-segment circular electrodiffusion probe of diameter 2RE = 0.526 mm through a pool of aqueous solution of potassium ferro/ferricyanide. Oriented wall shear rates were detected and analysed at Reynolds number 660. Hydrodynamic models of the wall shear rate distribution along the sphere surface in a uniform stream are reviewed. The principles of the direction specific flow measurements using three-segment electrodiffusion friction probes are explained.

On the electrochemical flow measurements using carbon-based screen-printed electrodiffusion probes

In this article, we have studied the possibility of using carbon-based screen-printed probes for electrochemical flow and mass flux measurements. Such probes have, up to now, been mainly used as biosensors to study in vivo reactions. Our study shows that screen-printed sensors allow the measurement of mass flux and mean wallp shear stress with good accuracy and high reproducibility. The existence of a micro-porous layer covering the surface of screen-printed electrodes has been revealed by means of the impedance measurements and has been confirmed by Scanning Electron Microscopy. This layer influences the statistical characteristics of the turbulent limiting diffusion current and should be taken into account as an additional transfer function between the current and the velocity fluctuations. The use of screen-printed sensors opens new possibilities in the field of electrochemical flow diagnostics. The advantage of this new manufacturing technology lies in the possibility of serial mass production at very competitive prices (disposable sensors) combined with the possibility of the manufacture of segmented electrodes or matrix of electrodes. These new possibilities can be used for various industrial applications as well as for scientific studies on near-wall turbulent mass transfer. Furthermore, it is possible to envisage the development of a hybrid sensor (electrodiffusional/biochemical) allowing the study of in situ biochemical reactions in a flow.

Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer

Two non-intrusive techniques, namely laser Doppler anemometry (LDA) and the electrochemical method, have been used for simultaneous measurements of the instantaneous streamwise velocity (U) and longitudinal wall shear stress (S), evaluated in a zero pressure gradient turbulent boundary layer. The space–time correlation between the fluctuating velocity and shear stress suggests that the coherent flow structures are propagated (i) under a slight angle of 5° in the near-wall region and (ii) at an average angle of 15.5° for y+>30. It is shown that the time shift obtained from the correlation between the LDA and the electrochemical signals is due to the dynamic behaviour of the electrodiffusion probe, but also to the leaning character of the coherent structures.

Near-wall investigation of backward-facing step flows

The electrodiffusion technique has been used to investigate reattaching and recirculating flows behind a backward-facing step. The instantaneous wall shear rate vectors were determined using the current signals provided by a three-segment electrodiffusion probe. The near-wall extents of two counter-rotating recirculation zones located behind the step were determined under turbulent flow conditions in a water channel. The near-wall flow inside these recirculation zones was found to be very unsteady, with strong low-frequency fluctuations. The streamwise profiles of the wall shear stress were measured at several values of the Reynolds number and a high level of skin friction was obtained in the reverse-flow region. The strong dependence of the peak value of skin friction on the Reynolds number confirms the viscous-dominated character of the reverse flow appearing inside the recirculation zone.

Interaction between the Ekman layer and the Couette–Taylor instability

The finite aspect ratio effect on Couette–Taylor flow was studied by means of three-segment electrodiffusion probes. The geometry of the Couette apparatus was characterized by the cylinders radii R 1=100 mm and R 2=110 mm and by the aspect ratio Γ=L/ R 2−R 1 =9.85 . The velocity gradient components were measured by electrodiffusion probes placed at the steady outer wall and at a confining ring between cylinders. The distributions of the azimuthal and axial components of velocity gradient at the outer wall indicated the existence of Ekman vortices at rotation rates smaller than the critical rate of onset of Taylor vortices in an infinitely long gap. The amplitude of the azimuthal component of velocity gradient of Ekman vortex grows linearly with Taylor number. The results of measurements are in good agreement with numerical simulations made by a finite element method which in turn gives a complete description of the flow.

Electrochemical Study of Taylor-Couette Flow by Limiting Diffusion Current Method

Steady Taylor vortices were studied by electrodiffusion probes in the gap between coaxial cylinders. The inner cylinder was driven by a stepping motor and the outer cylinder was fixed. The viscosity of standard potassium hexacyanoferrates (III) and (IV) aqueous solution was increased to 2.52 mPa s by addition of poly(alkylene glycol) Emkarox 45. The velocity gradient components were measured by two three-segment probes at the wall of the outer cylinder for four radius ratios, R1/R2 = 0.8, 0.75, 0.65 and 0.6. The axial distribution of the azimuthal and axial components of velocity gradient was mapped while Taylor vortices were swept along the probes by a slow axial flow. The components of velocity gradient were described by fourth-order Fourier series. Generalized dependencies were found of the Fourier coefficients on Taylor number. A vertical shift of the probes made it possible to calculate the wavelength and the drifting velocity of Taylor vortices. Critical Taylor numbers were estimated from the axial component of velocity gradient and by the flow visualization using a rheoscopic liquid. The torque was calculated from the azimuthal component of velocity gradient.

Simultaneous wall shear rate measurements by a three segmented electrodiffusion probe and laser-Doppler-anemometry

In a fully developed turbulent channel flow, the instantaneous wall shear gradient was measured simultaneously by an electrodiffusion (ED) probe and by laser-Doppler anemometry (LDA). The LDA measurements were done in the viscous sublayer and the linear velocity profile was used to calculate the instantaneous shear gradient at the wall. The electrodiffusion probe requires presence of a suitable electrolyte (e.g. an iodine and potassium-iodine aqueous solution) for reduction of the species on the working electrode (cathode). This results in a concentration gradient of the ions due to the convective diffusion of the [I3]- to the cathode.

Dynamics of Electrodiffusion Friction Probes. II. Shape-Dependent Impedance

The existing linear (impedance) theory of frequency response is corrected and generalized for electrodiffusion friction probes of any shape. Special attention is paid to the dynamic calibration of real electrodiffusion probes with uncertain geometry by the potentiostatic (voltage-step) transient method.

Dynamics of Electrodiffusion Friction Probes. I. Shape-Dependent Potentiostatic Transient

An exact theory is given of the voltage-step transient under limiting diffusion conditions for an electrodiffusion friction probe of arbitrary convex shape. The actual transient courses are given for the strip, circular, elliptic, triangular, and rectangular probes of any orientation with respect to the flow direction. A simple formula for any probe with a single working electrode of convex shape is suggested to facilitate the calibration of electrodiffusion probes based on the voltage-step transient.

Flow measurement in an impinging jet cell with three-segment microelectrocles

Three-dimensional flow close to the stagnation point of an impinging jet cell was studied by means of three-segment electrodiffusion probes. The total current and the directional characteristics providing the wall velocity gradient and the flow direction respectively were measured at different distances from the stagnation point. The linear dependence of the wall velocity gradient on this distance was confirmed in the stagnation zone. The normal velocity component was evaluated from the flatness of the directional characteristics. The values of the normal velocity component were rather higher than those corresponding to the linear change of the velocity gradient and the dimensionless ratio of the probe radius to distance. The deviation appearing on the normal velocity component was explained by geometrical imperfections of the probes due to the technology of fabrication.

Dynamics of electrodiffusion probes in developing annular flows

Dynamics of electrodiffusion probes in developing annular flows