Experiments in Fluids

, Volume 9, Issue 1–2, pp 43–48 | Cite as

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

  • V. Sobolík
  • O. Wein
  • O. Gil
  • B. Tribollet
Originals

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 z2. 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.

Keywords

Velocity Field Probe Surface Normal Velocity Kinematic Parameter Hydrodynamical Theory 

List of symbols

A

normal flow coefficient, Eq. (1)

A

axis of the adjustment rod, Fig. 2

c0

concentration of depolarizer (mol/m3)

D

diffusivity of depolarizer (m2/s)

E

correction of total current on normal flow effect

ex

reference direction of the probe, Figs. 1 and 3

F

Faraday constant (F = 96,464 C/mol)

Fs

normalized directional characteristic fors-th segment

fsm,gsm

Fourier coefficients of directional characteristics, Eq. (4) and Table 3

hm

corrections of Fourier coefficients on normal flow effect, Eqs. (4) and (7)

is

limiting diffusion current throughs-th segment (A)

itot(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)

qx,qy

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

rA

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

θ0

theoretical prediction ofθ, Eq. (11)

x0

theoretical prediction ofx, Eq. (14)

xexpx

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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References

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • V. Sobolík
    • 1
  • O. Wein
    • 1
  • O. Gil
    • 2
  • B. Tribollet
    • 2
  1. 1.Institute of Chemical Process FundamentalsCzechoslovak Academy of Sciences6 SuchdolCzechoslovakia
  2. 2.LP 14 of C.N.R.S.University of P. and M. CurieParis Cedex 05France

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