Abstract
In Ch. III of the “Second Report on Viscosity and Plasticity” a few remarks have been made concerning the problem of the mutual influence of the particles of a suspension upon their velocity of sedimentation, and von Smoluchowskl’s work on this problem has been mentioned1). A formula giving the magnitude of the effect to be expected was not developed. In the following lines it will be attempted to supplement this point, at least for particles of spherical form.
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References
J. M. Burgers, Ch. III of the “Second Report on Viscosity and Plasticity”, Verhand. Kon. Nederl. Akad. v. Wetenschappen (le sectie) Vol. 16, No. 4 (Amsterdam 1938), pp. 178/179.
Compare e.g.: Th. Svedberg and K. O. Pedersen, The Ultracentrifuge (Oxford 1940), pp. 5, 47, where it is stated that — in the notation used by the authors of that work — “ϱ is the density of the solution”; and p. 59, where the specific volume V == 1/ϱ of the solution is defined.
This remark has been inserted November 8, 1941.
As the liquid is assumed to be incompressible, we have: D 1 + D 2 + D 3 = 0, and consequently also: M 1 + M 2 + M 3 = 0. The magnitude of the components of the rotational velocity taken up by the particle can be obtained from the equations which express that the system of doublets shall have no resulting moment about the centre of the particle. The coefficient k introduced in the text corresponds to the quantity Λ II/s in the notation of the “Second Report”, s again denoting the volume of a particle. For a spherical particle, where the question of the orientation does not present itself, Λ II = 5/2 (“Second Report”, p. 132); for elongated particles (cylindrical particles and rotational ellipsoids) values are given in the “Second Report” at p. 148 and pp. 151—153. Values for oblate rotational ellipsoids have been given in a paper in these Proceedings 43, p. 314, 1940; values for some model systems consisting of a few rigidly connected spheres of equal radius ibidem pp. 425, 645.
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Burgers, J.M. (1995). Hydrodynamics. — On the influence of the concentration of a suspension upon the sedimentation velocity (in particular for a suspension of spherical particles). 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_16
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