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

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Abstract

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 directionθ, 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.

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Abbreviations

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 =Ō Ā, Fig. 2)

r, Φ, 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

α :

adjustment angle, Figs. 2 and 3

β :

angle included between local radius-vectorō ¯P of the probe and local direction of flow, Fig. 3

θ :

angle included between reference directione x of the probe and local direction of flow, Fig. 3

θ 0 :

theoretical prediction ofθ, Eq. (11)

x 0 :

theoretical prediction ofx, Eq. (14)

x exp x :

calculated from experimental data using Eq. (4)

v :

kinematic viscosity (m2/s)

σ :

angle implied between gradient ofq and direction of flow, Eq. (8)

Ω :

angular speed of the rotating disk (rad/s)

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Authors and Affiliations

  1. Institute of Chemical Process Fundamentals, Czechoslovak Academy of Sciences, 165 02 Praha, 6 Suchdol, Czechoslovakia

    V. Sobolík & O. Wein

  2. LP 14 of C.N.R.S., University of P. and M. Curie, Tour 22, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    O. Gil & B. Tribollet

Authors
  1. V. Sobolík
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  2. O. Wein
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  3. O. Gil
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  4. B. Tribollet
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Sobolík, V., Wein, O., Gil, O. et al. Three-segment electrodiffusion probes for measuring velocity fields close to a wall. Experiments in Fluids 9, 43–48 (1990). https://doi.org/10.1007/BF00575334

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  • DOI: https://doi.org/10.1007/BF00575334

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