Skip to main content
SpringerLink
Log in

The diffusion analogy for solvent flow in paper

  • Originalarbeiten
  • Published:
Kolloid-Zeitschrift Aims and scope Submit manuscript

Abstract

The mathematics of diffusion have been found valid in the description of the flow of liquids in paper. Cases of linear and radial flow have been observed experimentally for several solvent-paper systems. The dependence of the diffusion coefficient on concentration for various systems has been determined and these relations have been used in the numerical calculation of the flow rate and concentration profiles. The agreement of theory and experiment is, in all cases, satisfactory, indicating the validity of the diffusion analogy.

Zusammenfassung

Es ließ sich zeigen, daß zur Beschreibung des Steigens von Flüssigkeiten in Papier der mathematische Formalismus der Diffusion gültig ist. Es wurden Fälle von linearem und radialem Fluß für mehrere Lösungsmittel-Papier-Kombinationen experimentell durchgemessen. Die Abhängigkeit des „Diffusionskoeffizienten“ von der Konzentration wurde bestimmt und in numerischen Rechnungen Fließgeschwindigkeiten und Konzentrationsprofile ermittelt. Die Übereinstimmung von Theorie und Experiment erwies sich in allen Fällen als befriedigend und zeigt damit, daß die Diffusionsanalogie sinnvoll ist.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

D :

diffusion coefficient

g :

reduced radial distance

g :

r/r 0

h :

mesh unit for numerical calculation

k :

time unit for numerical calculation

x :

the flow rate coefficient for parabolic flow

x r :

flow rate coefficient for radial flow

λ :

theBoltzmann transform variable

L :

length of a wick

q :

flux, weight of solvent through a unit crosssectional area per unit time

r :

radial distance from center

r 0 :

radial distance of origin from the center

t :

time

T :

reduced time for radial flow

T :

t/r 0 2

w :

concentration, grams of solvent per gram of pretreated paper

W :

width of wick

z :

linear distance

z f :

distance to the front from the origin

Bibliography

  1. Ackerman, B. J. andH. G. Cassidy, Anal. Chem.26, 1874 (1954).

    Article  CAS  Google Scholar 

  2. Block, R. J., E. L. Durrum andG. Zweig, A Manual of Paper Chromatography and Paper Electrophoresis, Second Edition (New York 1958).

  3. Boltzmann, L., Ann. Phys. (Leipzig)53, 959 (1894).

    Google Scholar 

  4. Cassidy, H. G., Anal. Chem.24, 1415 (1952).

    Article  CAS  Google Scholar 

  5. Cassidy, H. G., Techniques of Organic Chemistry, Vol. X, Fundamentals of Chromatography, ed.A. Weissberger (New York 1957).

  6. Crank, J., The Mathematics of Diffusion (London 1956).

  7. Fugita, H., J. Chem. Phys.56, 625 (1952).

    Article  Google Scholar 

  8. Kress, O. andH. Bialkousky, Paper Trade J.93, 35 (1931).

    CAS  Google Scholar 

  9. Muller, R. H. andD. L. Clegg, Anal. Chem.23, 396 (1951).

    Article  CAS  Google Scholar 

  10. Peak, R. L., Jr. andD. A. McLean, Ind. Eng. Chem., Anal. Ed.6, 85 (1934).

    Article  Google Scholar 

  11. Rutter, L., Analyst75, 37 (1950).

    Article  CAS  Google Scholar 

  12. Wood, S. E. andH. E. Strain, Anal. Chem.26, 260, (1954).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Utah, USA

    Arthur L. Ruoff, Denver L. Prince, J. Calvin Giddings & George H. Stewart

  2. Dept. of Mechanics and Materials, Cornell University, Ithaca, N. Y.

    Arthur L. Ruoff

Authors
  1. Arthur L. Ruoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Denver L. Prince
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Calvin Giddings
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. George H. Stewart
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruoff, A.L., Prince, D.L., Giddings, J.C. et al. The diffusion analogy for solvent flow in paper. Kolloid-Zeitschrift 166, 144–151 (1959). https://doi.org/10.1007/BF01681187

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01681187

Keywords

Search

Navigation