Volume 67, Number 3, August 2004
|Page(s)||383 - 389|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 July 2004|
Hydrodynamic interactions between widely separated particles at a free surface
Institute of Theoretical Physics, Warsaw University Hoża 69, 00-618 Warsaw, Poland
2 Institute of Fundamental Technological Research, Polish Academy of Sciences Świętokrzyska 21, 00-049 Warsaw, Poland
3 Institut für Festkörperforschung, Soft Matter Division, Forschungszentrum Jülich D-52425 Jülich, Germany
Corresponding author: email@example.com
Accepted: 24 May 2004
In this letter, we consider a quasi–two-dimensional (Q2D) system of widely separated spheres suspended in a quiescent fluid and in contact with a planar fluid-gas interface. We construct and estimate the accuracy of two generic approximations to the translational-translational mobility, needed, e.g., in Brownian simulations. Both simplifications for Q2D systems are shown to be essentially different than their three-dimensional well-known analogs. First, we discuss the asymptotic form of the Q2D two-sphere mobility up to cubic order in the inverse inter-particle distance and compare it with the corresponding three-dimensional Rotne-Prager expression. We also explain how to avoid divergences due to lubrication forces at the contact. Next, we construct the Q2D mobility of point-particles, which —unlike in 3D— is not pairwise additive. Finally, we determine the range of validity of both long-distance approximations by computing numerically exact results.
PACS: 47.15.Gf – Low-Reynolds-number (creeping) flows / 82.70.-y – Disperse systems; complex fluids
© EDP Sciences, 2004
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