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Spectral analysis of hydrodynamic tracer dispersion with an electrochemical measurement technique

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We report tracer dispersion measurements in a capillary tube performed in the frequency domain using an electrochemical technique. Tracer Fe+++ ions are produced by oxidizing Fe++ ions at an emission anode; the inverse reaction allows to detect the tracer on a measurement electrode at the outlet of the sample. The amplitude and phase of the steady state signal detected at the outlet of the sample are measured as a function of the frequency of a sinusoidal concentration modulation induced at the inlet of the tube. Measurement results at two flow velocities are in agreement with predictions of the Taylor-Aris model.

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A(f) :

output signal modulation amplitude at a modulation frequency f

a :

capillary tube radius

C ox :

concentration of the solution ferricyanide ions

C red :

concentration of the solution ferrocyanide ions

D ox :

diffusion coefficient of tracer ions

D m :

molecular diffusion coefficient

D :

longitudinal dispersion coefficient

E e :

potential of emission electrode

E d :

potential of detection electrode

F :

Faraday constant

J m :

number of ions-g of tracer

I :

electrical current intensity on emitter electrode

I′ :

limiting current on detection electrode

k x , k y :

real and imaginary part of tracer concentration modulation wavevector

L :

total capillary tube length

Pe L :

(= UL/D m ) global Peclet number

S :

flow section

T f :

characteristic exchange time with low velocity regions and dead zones

T 0 :

mean transit time through the capillary

U :

mean fluid velocity

δ′ :

boundary layer thickness on detection electrode

ϕ :

phase shift between tracer concentration modulations at the inlet and the outlet of the sample

λ :

tracer concentration modulations spatial wavelength along the capillary tube

τ a :

(= a 2/D m ) characteristic diffusion time across the capillary section

ω :

tracer concentration modulation pulsation

ω c :

cut-off frequency for concentration modulations at the capillary outlet


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Baudet, C., Hulin, J.P. & Deslouis, C. Spectral analysis of hydrodynamic tracer dispersion with an electrochemical measurement technique. Experiments in Fluids 7, 329–334 (1989).

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  • Steady State
  • Flow Velocity
  • Frequency Domain
  • Spectral Analysis
  • Measurement Technique