Abstract
In Ch. III of the “Second Report on Viscosity and Plasticity” formulae have been given for the resistance of small particles of elongated form, and for their influence upon the effective viscosity of the liquid in which they are suspended; and the application has been discussed of these formulae to the results obtained with suspensions of polystyrenes by Staudinger and Signer 1). A discussion of their application to suspensions of methyl cellulose has been given by Signer and V. Tavel 2). Polson has applied the formula for the influence of such particles upon the effective viscosity to the analysis of data obtained with suspensions of proteins 3), and a report of this work recently has been given by Pedersen in Part I, Ch. B, of Svedberg and Pedersen’s new book “The Ultra-centrifuge” 4).
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Referrences
J. M. Burgers, Ch. III of the “Second Report on Viscosity and Plasticity”, Verhand. Kon. Nederl. Akad. v. Wetenschappen (1e sectie) Vol. 16, No. 4 (Amsterdam 1938), pp. 122–126 (resistance formulae), 145–153 (influence upon the effective viscosity), 168–181 (application to polystyrenes).
R. Signer und P. V. Tavel, Die Form und Grösse von Methylcellulose-Molekeln in Lösung, Helv. Chim. Acta 21, 535 (1938). R. Signer und P. V. Tavel, The subject also has been treated in the chapter contributed by R. Signer to Th. Svedberg and Kai O. Pedersen’s book “The Ultracentrifuge” (Oxford 1940), pp. 431–442, whereas cellulose acetates and some other linear high polymers are considered by E. O. Kraemer and J. B. Nichols, “The Ultracentrifuge” (Oxford 1940), pp. 416–431. — See also footnote 20) below.
A. Polson, Ueber die Berechnung der Gestalt von Proteinmolekülen, Kolloid-Zeitschr. 88, 51 (1939).
A. Polson, Ueber die Berechnung der Gestalt von Proteinmolekülen, Nature 137, 740 (1936).
Th. Svedberg and Kai O. Pedersen, The Ultracentrifuge (Oxford 1940), pp. 38–44.
Th. Svedberg and Kai O. Pedersen, The results of the calculations also have been given by Th. Svedberg in the “Opening Address to a discussion on the protein molecule”, Proc. Roy. Soc. (London) B 127, 9–10 (1939).
Th. Svedberg and Kai O. Pedersen, It may be mentioned that the problem of the determination of the shape of tobacco mosaic virus particles in solution has been discussed by J. R. Robinson, Nature 143, 923 (1939).
See A. Polson, Nature 137, 740 (1936),
where it is stated that the diffusion constants were measured by the refractometric method of O. Lamm, Zeitschr. f. physik. Chem. A 138, 313 (1928)
where it is stated that the diffusion constants were measured by the refractometric method of O. Lamm, Zeitschr. f. physik. Chem. B 143, 177 (1929).
“The Ultracentrifuge”, Table 5, p. 44.
The same table occurs in Th. Svedberg, Proc. Roy. Soc. (London) B 127, 10 (1939)
A. Polson, Kolloid-Zeitschr. 88, 59 (1939).
W. Kuhn, Zeitschr. f. physik. Chemie A 161, 24 (1932).
Second Report, pp. 152–153.
This formula can be written in our notation as follows: \( {{{{\eta_{{sp}}}}} \left/ {{c = V[4,0 + 0,098({{L} \left/ {{d{)^2}}} \right.}}} \right.}] \) as the quantity G used by Polson is equal to cV. See A. Polson, Kolloid-Zeitschr. 88, 56 (1939);
K. O. Pedersen, The Ultracentrifuge, p. 43.
Second Report, p. 184.
Th. Svedberg, The Ultracentrifuge, p. 9. — The fact that the two methods, in those cases where both can be applied, practically lead to the same values for the molecular weight, proves that diffusion and sedimentation velocity are both governed by the same mean frictional coefficient.
A. Polson, Kolloid-Zeitschr. 88, 58, Tab. VI (1939).
Second Report, p. 153.
The formulae for the resistance of an ellipsoid have been derived by Oberbeck, and are given e.g. in C. W. Oseen, Hydrodynamik (Leipzig 1927), pp. 186–189.
See also: J. Perrin, Journ. de Physique et le Radium (VII) 5, 409 (1934)
J. Perrin, Journ. de Physique et le Radium (VII) 7, 10–11 (1936).
See “The Ultracentrifuge”, p. 5.
The data used in the calculations mostly have been taken from table 48, p. 406, of “The Ultracentrifuge”. For the molecular weight the value of M e has been taken, with the exception of that of Octopus haemocyanin, where M s is used. The values of ŋ sp /cVhave been derived from Polson’s data, Kolloid-Zeitschr. 88, 58, Tab. VI (1939); in the cases of serum globulin and Helix pomatia haemocyanin, however, the values of ŋ sp /c V have been derived from Polson’s Tab. III, l.c. p. 56, as it was not evident how the most suitable mean value should be obtained from the numbers given in Tab. VI.
See A. Polson, Kolloid-Zeitschr. 88, 56 (1939);
K. O. Pedersen, The Ultra-centrifuge, p. 43.
According to Polson the so-called electroviscous effect can be neglected under suitably chosen conditions (see also Pedersen, The Ultracentrifuge, p. 26).
E. O. Kraemer, The Ultracentrifuge, p. 63.
A. Polson, Kolloid-Zeitschr. 88, 56, Tab. III (1939).
A. Polson, Kolloid-Zeitschr. 57, (1939).
G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. Roy. Soc. (London) A 102, 174–175 (1922–1923).The expressions for C l, C 2, C 3 can be derived from eq. (61), p. 174, in which the values given at p. 175, eqs. (68), have to be substituted for \( {a'_0}, {\beta '_0}, \beta '' \) \( {a''_0} = {b^2}{a'_0} - {{{{{\beta ''}_0}}} \left/ {2} \right.} \) according to p. 173).
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Burgers, J.M. (1995). Hydrodynamics. — On the application of viscosity data to the determination of the shape of protein molecules in solution . In: Nieuwstadt, F.T.M., Steketee, J.A. (eds) Selected Papers of J. M. Burgers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0195-0_13
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