Europhys. Lett.
Volume 72, Number 6, December 2005
Page(s) 936 - 942
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 23 November 2005
Europhys. Lett., 72 (6), pp. 936-942 (2005)
DOI: 10.1209/epl/i2005-10341-6

Steady-state particle distribution of a dilute sedimenting suspension

B. Cichocki and K. Sadlej

Warsaw University, Institute of Theoretical Physics - Hoza 69, 00-681 Warsaw, Poland

received 23 August 2005; accepted in final form 22 October 2005
published online 23 November 2005

The stationary state of a non-Brownian dilute sedimenting suspension of hard particles is studied. The configurational distribution of these particles is the main subject of interest. A hierarchy of equations for the correlation functions, analogous to the BBGKY hierarchy known from kinetic theory, is derived. Next, assuming integrability of the correlations, it is shown that in the low-concentration limit the hierarchy can be truncated leading to an effective equation for the two-particle correlation function. This function has been explicitly calculated, and used to compute the sedimentation coefficient $\lambda$. The obtained result is $\lambda=-3.87$ which agrees perfectly with the experiment.

47.15.Gf - Low-Reynolds-number (creeping) flows.
82.70.Kj - Emulsions and suspensions.

© EDP Sciences 2005