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Spectral analysis of hydrodynamic tracer dispersion with an electrochemical measurement technique

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Abstract

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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Abbreviations

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

References

  1. Ambari, A.; Deslouis, C; Tribollet, B. 1984: Coil stretch transition in laminar flow around a small cylinder. Chem. Eng. Comm. 29, 63–78

  2. Aris, R. 1956: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. London Ser. A 235, 67

  3. Baker, L. E. 1975: Effects of dispersion and dead end pore volume in miscible flooding. Soc. Pet. Eng. J. 263, 219–227

  4. Baudet, C. 1987: Dispersion en milieux poreux: effects hydrodynamiques locaux. Thèse de Doctorat de l'Université Paris XI (Orsay)

  5. Baudet, C.; Deslouis, C.; Hulin, J. P.; Guyon, E. 1987: Une méthode électrochimique d'analyse de la dispersion en milieu poreux. C.R.Acad. Sci. Paris 305, 429–432

  6. Bear, J. 1972: Dynamics of fluids in porous media, Chapt. 10. New York: Elsevier

  7. Coats, K. H.; Smith B. D. 1964: Dead end pore volume and dispersion in porous media. Soc. Pet. Eng. J. 231, 73–84

  8. Deslouis, C.; Tribollet, B.; Viet, L. 1980: Local and overall mass transfert rates to a rotating disk in turbulent and transition flows. Electrochim. Acta 25, 1027

  9. Fleischmann, M.; Janson, R. E. W. 1979: Dispersion in electrochemical cells with radial flow between parallel electrodes. 1. A dispersive plug flow mathematical model. J. Appl. Electrochem. 9, 427–435

  10. Fleischmann, M.; Ghoroghchian, L.; Janson, R. E. W. 1979: Dispersion in electrochemical cells with radial flow between parallel electrodes. 2. Experimental results for capillary gap cell and pump cell configurations. J. Appl. Electrochem. 9, 437–444

  11. Gennes, P. G. de 1983: Hydrodynamic dispersion in unsaturated porous media. J. Fluid. Mech. 136, 189–200

  12. Guyon, E.; Pomeau, Y.; Hulin, J. P.; Baudet, C. 1987: Dispersion in the presence of recirculation zones. Nucl. Phys. B (Proc. Suppl.) 2, 271–280

  13. Hulin, J. P.; Salin, D. 1989: Experimental study of tracer dispersion in model and natural porous media. In: Disorder and mixing (eds. Guyon, E.; Nadal, J. P.; Pomeau, Y.). Proc. 1987 NATO Conf. Disorder and Mixing, June 14–27, 1987, Cargese/Corsica, France. Dordrecht: Nijhoff

  14. Koch, D. L.; Brady, J. F. 1985: Dispersion in fixed beds. J. Fluid Mech. 154, 399–427

  15. Robertson, S.; Tribollet, B.; Deslouis, C. 1988: Measurement of diffusion coefficients by DC and EHD electrochemical methods. J. Electrochem. Soc. (in press)

  16. Taylor, G. I. 1953: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. London Ser. A 219, 186–203

  17. Vetter, K. J. 1967: Electrochemical kinetics. New York: Academic Press

  18. Wesfreid, J. E.; Croquette, V. 1980: Forced phase diffusion in Rayleigh-Bénard convection. Phys. Rev. Lett. 45, 634–637

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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). https://doi.org/10.1007/BF00198451

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Keywords

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