Three-segment electrodiffusion probes for measuring velocity fields close to a wall

Three-segment electrodiffusion probes embedded in a wall allow to determine simultaneously the three kinematic parameters of flow close to the probe surface: the flow direction, the wall shear rateq, and the normal velocity coefficientA,v _z = –A z ². A well-controlled three-dimensional flow, generated by a rotating disk, was used to demonstrate the capabilities of this new kind of electrodiffusion probes by comparing experimental results with the prediction based on the well-known hydrodynamical theory.List of symbols A normal flow coefficient, Eq. (1) - A axis of the adjustment rod, Fig. 2 - c ₀ concentration of depolarizer (mol/m³) - D diffusivity of depolarizer (m²/s) - E correction of total current on normal flow effect - e _x reference direction of the probe, Figs. 1 and 3 - F Faraday constant (F = 96,464 C/mol) - F _s normalized directional characteristic fors-th segment - f _sm ,g _sm Fourier coefficients of directional characteristics, Eq. (4) and Table 3 - h _m corrections of Fourier coefficients on normal flow effect, Eqs. (4) and (7) - i _s limiting diffusion current throughs-th segment (A) - i _tot (r) total current through the probe in dependence on its eccentricity (A) - K transport coefficient, Eqs. (3) and (5) - n number of electrons involved in redox reaction - O axis of the rotating disk, Fig. 2 - P centre of the probe, Fig. 2 - q magnitude of vectorial wall shear rate (s^-1) - q _x ,q _y components of vectorial wall shear rate - Q ratio of the currents in an eccentric and the central position of the probe, Eq. (15) - r radial coordinate, eccentricity of the probe - r _A eccentricity of the adjustment rod (r _A = , Fig. 2) - r, , z polar coordinates on the rotating disk - R effective radius of the probe (R = 0.337 mm) - S macroscopic area of the probe (S = 0.357 mm²) - x, y, z Cartesian coordinates moving with the probe - adjustment angle, Figs. 2 and 3 - angle included between local radius-vector ¯P of the probe and local direction of flow, Fig. 3 - angle included between reference directione _x of the probe and local direction of flow, Fig. 3 - ₀ theoretical prediction of, Eq. (11) - x ₀ theoretical prediction ofx, Eq. (14) - x _exp x calculated from experimental data using Eq. (4) - v kinematic viscosity (m²/s) - angle implied between gradient ofq and direction of flow, Eq. (8) - angular speed of the rotating disk (rad/s)