B. Cichocki et al 2004 Europhys. Lett. 67 383 doi:10.1209/epl/i2004-10077-9
Hydrodynamic interactions between widely separated particles at a free surface
B. Cichocki1, M. L. Ekiel-Jeżewska2, G. Nägele3 and E. Wajnryb2
Show affiliationsIn 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.
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Issue 3 (August 2004)
Received 13 April 2004, accepted for publication 24 May 2004, in final form 24 May 2004
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Hydrodynamic interactions between widely separated particles at a free surface
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