Hydrodynamic Interactions Between Solid Particles at a Fluid–Gas Interface - Drops and Bubbles in Contact with Solid Surfaces - page 93

Hydrodynamic Interactions Between Solid Particles at a
Fluid-Gas Interface

B. Cichocki a , M. L. Ekiel-Jezewska b , G. Nägele c and E. Wajnryb b

a

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

b

Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21,
00-049 Warsaw, Poland

c

Institut für Festkörperforschung, Soft Matter Division, Forschungszentrum Jülich,
D-52425 Jülich, Germany

Abstract
We analyze the hydrodynamic interactions between spherical solid particles which are suspended in a qui-
escent fluid and in contact with a planar fluid-gas interface. Stick boundary conditions are assumed on the
sphere surfaces, and the free surface boundary conditions are accounted for by the method of images. The
one-sphere hydrodynamic resistance operator of such a quasi-two-dimensional system is calculated numer-
ically. Using a spherical multipole expansion with symmetry-adjusted basis functions, explicit results are
derived for the long-distance terms of the two-sphere mobility tensor up to cubic order in the inverse in-
terparticle distance. The point particle model is also constructed, taking into account the constraint forces
necessary to keep the point-particles at a fixed 'radius' a apart from the interface. The accuracy of both far
field approximations is discussed by comparing them with the precise many-sphere mobility, evaluated by
the multipole expansion.

Contents

A. Introduction ............................................... 94

B.TheoreticalMethod........................................... 96

C. Single-Sphere Mobilities ........................................ 99

D. Many-Sphere Mobility Tensor for Large Interparticle Distances . ................. 100

E. Point-Particle Mobility ......................................... 101

F.Discussion................................................ 102

1. Comparison with the Three-Dimensional Unbounded Fluid . ................. 102

2.Accuracyoffar-field]Far-FieldApproximations ........................ 102

G.Acknowledgements........................................... 103

H.References................................................ 103