Fick’s Diffusion Experiments Revisited —Part I
Author(s)
Tad W. Patzek
Affiliation(s)
Department of Petroleum and Geosystems Engineering, The University of Texas, Austin, TX, USA.
Department of Petroleum and Geosystems Engineering, The University of Texas, Austin, TX, USA.
ABSTRACT
In this paper, we revisit Fick’s original diffusion experiments and reconstruct the geometry of his inverted funnel. Part I demonstrates that Fick’s experimental approach was sound and measurements were accurate despite his own claims to the contrary. Using the standard modern approach, we predict Fick’s cylindrical tube measurements with a high degree of accuracy. We calculate that the salt reservoir at the bottom of the inverted funnel must have been about 5 cm in height and the unreported depth of the deepest salt concentration measurement by Fick was yet another 3 cm above the reservoir top. We verify the latter calculation by using Fick’s own calculated concentration profiles and show that the modern diffusion theory predicts the inverted funnel measurements almost as well as those in the cylindrical tube. Part II is a translation of Fick’s discussion of diffusion in liquids in the first edition of his three-volume monograph on Medical Physics published in 1856, one year after his seminal Pogendorff Annalen paper On Diffusion.
In this paper, we revisit Fick’s original diffusion experiments and reconstruct the geometry of his inverted funnel. Part I demonstrates that Fick’s experimental approach was sound and measurements were accurate despite his own claims to the contrary. Using the standard modern approach, we predict Fick’s cylindrical tube measurements with a high degree of accuracy. We calculate that the salt reservoir at the bottom of the inverted funnel must have been about 5 cm in height and the unreported depth of the deepest salt concentration measurement by Fick was yet another 3 cm above the reservoir top. We verify the latter calculation by using Fick’s own calculated concentration profiles and show that the modern diffusion theory predicts the inverted funnel measurements almost as well as those in the cylindrical tube. Part II is a translation of Fick’s discussion of diffusion in liquids in the first edition of his three-volume monograph on Medical Physics published in 1856, one year after his seminal Pogendorff Annalen paper On Diffusion.
Cite this paper
Patzek, T. (2014) Fick’s Diffusion Experiments Revisited —Part I. Advances in Historical Studies, 3, 194-206. doi: 10.4236/ahs.2014.34017.
Patzek, T. (2014) Fick’s Diffusion Experiments Revisited —Part I. Advances in Historical Studies, 3, 194-206. doi: 10.4236/ahs.2014.34017.
References
[1] Achmatowicz, O. et al. (Ed.) (1954a). Chemical Calendar. Vol. I. Warsaw: PWN. (in Polish) [2] Achmatowicz, O. et al. (Ed.) (1954b). Chemical Calendar. Vol. 2, Part II. Warsaw: PWN. (in Polish) [3] Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (1960). Transport Phenomena. New York: John Wiley & Sons, Inc. [4] Fick, A. (1855a). On Liquid Diffusion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10, 30-39. [5] Fick, A. (1855b). Ueber Diffusion (On Diffusion). Annalen der Physik und Chemie von J. C. Pogendorff, 94, 59-86. [6] Fourier, J. B. J. (1807). Théorie des mouvements de la chaleur dans le corps solides. French Academy. [7] Fourier, J. B. J. (1822). Theory of Heat (Théorie Analytique del la Chaleur). Paris: F. Didot. [8] Garber, E., Brush, S. G., & Everitt, C. W. F. (Eds.) (1986). Maxwell on Molecules and Gases. Cambridge, Massachusetts: MIT Press. [9] Hirschfelder, J. O., Curtiss, C. F., & Bird, R. B. (1954). Molecular Theory of Gases and Liquids. New York: John Wiley & Sons, Inc. [10] Stefan, J. (1871). über das Gleichgewicht und die Bewegung, insbesondere die Diffusion von Gasmengen. Wiener Sitzungs- berichte, 63, 63-124. [11] Truesdell, C. (1962). Mechanical Basis of Diffusion. The Journal of Chemical Physics, 37. [12] Truesdell, C. (1966). The Elements of Continuum Mechanics. New York: Springer-Verlag.
[1] Achmatowicz, O. et al. (Ed.) (1954a). Chemical Calendar. Vol. I. Warsaw: PWN. (in Polish) [2] Achmatowicz, O. et al. (Ed.) (1954b). Chemical Calendar. Vol. 2, Part II. Warsaw: PWN. (in Polish) [3] Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (1960). Transport Phenomena. New York: John Wiley & Sons, Inc. [4] Fick, A. (1855a). On Liquid Diffusion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10, 30-39. [5] Fick, A. (1855b). Ueber Diffusion (On Diffusion). Annalen der Physik und Chemie von J. C. Pogendorff, 94, 59-86. [6] Fourier, J. B. J. (1807). Théorie des mouvements de la chaleur dans le corps solides. French Academy. [7] Fourier, J. B. J. (1822). Theory of Heat (Théorie Analytique del la Chaleur). Paris: F. Didot. [8] Garber, E., Brush, S. G., & Everitt, C. W. F. (Eds.) (1986). Maxwell on Molecules and Gases. Cambridge, Massachusetts: MIT Press. [9] Hirschfelder, J. O., Curtiss, C. F., & Bird, R. B. (1954). Molecular Theory of Gases and Liquids. New York: John Wiley & Sons, Inc. [10] Stefan, J. (1871). über das Gleichgewicht und die Bewegung, insbesondere die Diffusion von Gasmengen. Wiener Sitzungs- berichte, 63, 63-124. [11] Truesdell, C. (1962). Mechanical Basis of Diffusion. The Journal of Chemical Physics, 37. [12] Truesdell, C. (1966). The Elements of Continuum Mechanics. New York: Springer-Verlag.