Hydrodynamic Interactions Between Solid Particles at a Fluid–Gas Interface - Drops and Bubbles in Contact with Solid Surfaces - page 94

A. Introduction
In the past, a substantial amount of research in the soft condensed matter field has
been done on the dynamics of model suspensions of spherical colloidal particles.
The dynamics of colloidal particles is strongly influenced, in addition to direct in-
terparticle and Brownian forces, by complicated hydrodynamics interactions (HI)
mediated by the embedding solvent [1]. While research was mainly focused on
the dynamics of three-dimensional bulk dispersions, the center of intense interest
has shifted meanwhile to static and dynamic properties of colloids near boundaries
like a single hard wall [2-5]. Of considerable interest are, in particular, so-called
quasi-two-dimensional (Q2D) dispersions, where the particles are spatially con-
fined to form a planar or curved monolayer. In such systems the particle dynamics
is more complicated as in unbounded bulk dispersions, since additional fluid bound-
ary conditions need to be satisfied, and the particle interactions are usually strongly
different from the bulk ones. A prominent example of such a Q2D system are
macroscopically extended monolayers of colloidal spheres confined between two
narrow parallel plates. For this system, diffusion properties like lateral particle
mean-squared displacements [6, 7], relative pair mobilities [8-11], and real-space
van Hove and wave-number dependent hydrodynamic functions [7, 10] have been
studied in great detail both in experiment, theory and simulation. Another class of
Q2D systems relevant to emulsion technology, food science and biomedicine are
particles trapped at liquid-liquid interfaces such as in water and oil mixtures [12-
16], and in liquid-gas interfaces [12, 14] such as in foams [17]. In many of these
systems, the colloidal particles or proteins in the case of biological systems [12],
become trapped at the interface by the effects of surface tension or image charges.
The presence of particles in the interface of water-in-oil emulsions can stabilize
the droplets against coalescence even in the absence of emulsifiers, giving rise to
so-called Pickering emulsions [18]. The work on particles at liquid interfaces noted
above deals in particular with interfacial rheological features and the formation of
aggregated structures. Hydrodynamic interactions between colloidal particles close
to a clean or surfactant-covered planar fluid-fluid interface have been discussed in
[19, 20] and [21], respectively.
A particularly clean-cut and well-studied Q2D model system of particles con-
fined to a fluid-gas interface is given by micron-sized super-paramagnetic colloidal
spheres suspended in water next to a planar water-air interface [22-27]. By means
of an experimental hanging-drop geometry, the spheres are gravitationally confined
to lateral motion along the interface without capillary forces, since the they are
completely wetted by the water. The spheres repel each other through long-range
dipolar magnetic forces induced by an external magnet field pointing perpendicular
to the interface. This model system is of particular interest both from the theoret-
ical and experimental point of view since the direct magnetic interaction are very
well characterized. The strength of the dipolar interactions can be precisely tuned
by the magnetic field strength, and the two-dimensional particle trajectories can be
monitored over an extended range of time using video imaging. This method has