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Fluid displacement in capillaries

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Summary

The displacement of a liquid or gas in a capillary by another fluid of equal density and viscosity depends upon the hydrodynamic behaviour in the tube as well as on the molecular diffusivity. The case of Poiseuille flow is discussed in the light of the theories of Taylor, Bos worth and of an approach by the authors. The theoretical curves are compared with experimental results.

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Abbreviations

a :

tube radius

c :

concentration

c 0 :

initial concentration

D :

molecular diffusion coefficient

E T :

Taylor diffusivity

H :

holdback

L :

tube length

r :

radial distance

Re=2au/v :

Reynolds group

Sc=v/D :

Schmidt group

t=L/u :

mean residence time

u :

mean fluid velocity

X :

axial distance

α=Dt/a 2 :

radial diffusion group

v :

kinematic viscosity

τ:

dimensionless residence time

ϕ:

\(\int\limits_0^\infty {cdx} \),

ω n :

zero of J1(ω)

J0, J1 :

Bessel functions

I0, I1 :

modified Bessel functions

Erf:

error function

In erfc:

repeated integrals of the complementary error function

References

  1. 1)

    Bosworth, R. C. L., Phil. Mag.39 (1948) 847.

  2. 2)

    Taylor, Sir Geoffry, Proc. Roy. Soc. (London)A 219 (1953) 186.

  3. 3)

    Taylor, Sir Geoffry, Proc. Roy. Soc. (London)A 225 (1954) 473.

  4. 4)

    Danckwerts, P. V., Chem. Engng. Sci.2 (1953) 1.

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Author information

Correspondence to J. J. Van Deemter.

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Van Deemter, J.J., Broeder, J.J. & Lauwerier, H.A. Fluid displacement in capillaries. Appl. sci. Res. 5, 374–388 (1955). https://doi.org/10.1007/BF03184600

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Keywords

  • Molecular Diffusion
  • Sodium Chloride Solution
  • Radial Diffusion
  • Poiseuille Flow
  • Equal Density