Hydrodynamic interactions between widely separated particles at a free surface
Abstract
In this letter, we consider a quasi twodimensional (Q2D) system of widely separated spheres suspended in a quiescent fluid and in contact with a planar fluidgas interface. We construct and estimate the accuracy of two generic approximations to the translationaltranslational mobility, needed, e.g., in Brownian simulations. Both simplifications for Q2D systems are shown to be essentially different than their threedimensional wellknown analogs. First, we discuss the asymptotic form of the Q2D twosphere mobility up to cubic order in the inverse interparticle distance and compare it with the corresponding threedimensional RotnePrager expression. We also explain how to avoid divergences due to lubrication forces at the contact. Next, we construct the Q2D mobility of pointparticles, which—unlike in 3D—is not pairwise additive. Finally, we determine the range of validity of both longdistance approximations by computing numerically exact results.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 August 2004
 DOI:
 10.1209/epl/i2004100779
 Bibcode:
 2004EL.....67..383C