Abstract:
The rheology of a two-dimensional dry foam is probed with quasi-static bubblescale
simulations of the sedimentation of circular discs and elliptical objects. The sedimenting
objects move in response to a combination of their weight and the forces
exerted on them by the network of soap films and the pressures in the bubbles.
Viewed macroscopically, the plasticity and elasticity of the foam combine to determine
the rate of descent of a circular disc. A critical disc weight is found that determines
whether the disc is supported by the foam or not. This critical weight increases linearly
with disc diameter and decreases with the liquid fraction of the foam with a power-law
relation. Similarly, the drag force exerted on a disc increases linearly with its diameter
and decreases with the liquid fraction of the foam with a power-law relation. An attractive
force between a disc and a nearby wall is seen when the disc is further than two
bubble diameters from the wall. Such wall effects are minimal when the disc sediments
from a central position in a channel of sufficient width.
The interaction between two sedimenting discs is quantified by placing them in one
of two configurations: one in which the discs are placed side by side and the other
in which the discs are initially one above the other. The discs descend through the
foam and move towards a stable orientation in which they are positioned directly above
one another with a constant separation of one or two bubbles. Above a critical initial
separation of the order of 5 bubble diameters, the discs do not interact. The existence
of the critical separation is shown to be a result of the discrete nature of a dry foam.
The descent and rotational motion of an ellipse of similar size and weight to one
of the circular discs is then considered. An ellipse rotates towards a stable orientation
in which its major axis becomes parallel to gravity, driven by the local structure of the
foam. This rotational motion is much slower than the downward motion.
