5 research outputs found
Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams
The shear flow of two dimensional foams is probed as a function of shear rate
and disorder. Disordered foams exhibit strongly rate dependent velocity
profiles, whereas ordered foams show rate independence. Both behaviors are
captured quantitatively in a simple model based on the balance of the
time-averaged drag forces in the foam, which are found to exhibit power-law
scaling with the foam velocity and strain rate. Disorder modifies the scaling
of the averaged inter-bubble drag forces, which in turn causes the observed
rate dependence in disordered foams.Comment: 4 Figures, 4 page
The Jamming Perspective on Wet Foams
Amorphous materials as diverse as foams, emulsions, colloidal suspensions and
granular media can {\em jam} into a rigid, disordered state where they
withstand finite shear stresses before yielding. The jamming transition has
been studied extensively, in particular in computer simulations of
frictionless, soft, purely repulsive spheres. Foams and emulsions are the
closest realizations of this model, and in foams, the (un)jamming point
corresponds to the wet limit, where the bubbles become spherical and just form
contacts. Here we sketch the relevance of the jamming perspective for the
geometry and flow of foams --- and also discuss the impact that foams studies
may have on theoretical studies on jamming.
We first briefly review insights into the crucial role of disorder in these
systems, culminating in the breakdown of the affine assumption that underlies
the rich mechanics near jamming. Second, we discuss how crucial theoretical
predictions, such as the square root scaling of contact number with packing
fraction, and the nontrivial role of disorder and fluctuations for flow have
been observed in experiments on 2D foams. Third, we discuss a scaling model for
the rheology of disordered media that appears to capture the key features of
the flow of foams, emulsions and soft colloidal suspensions. Finally, we
discuss how best to confront predictions of this model with experimental data.Comment: 7 Figs., 21 pages, Review articl
Flow in linearly sheared two dimensional foams: from bubble to bulk scale
We probe the flow of two dimensional foams, consisting of a monolayer of
bubbles sandwiched between a liquid bath and glass plate, as a function of
driving rate, packing fraction and degree of disorder. First, we find that
bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous
(shear banded) velocity profiles, while monodisperse, ordered foams are also
shear banded, but essentially rate independent. Second, we introduce a simple
model based on balancing the averaged drag forces between the bubbles and the
top plate and the averaged bubble-bubble drag forces. This model captures the
observed rate dependent flows, and the rate independent flows. Third, we
perform independent rheological measurements, both for ordered and disordered
systems, and find these to be fully consistent with the scaling forms of the
drag forces assumed in the simple model, and we see that disorder modifies the
scaling. Fourth, we vary the packing fraction of the foam over a
substantial range, and find that the flow profiles become increasingly shear
banded when the foam is made wetter. Surprisingly, our model describes flow
profiles and rate dependence over the whole range of packing fractions with the
same power law exponents -- only a dimensionless number which measures the
ratio of the pre-factors of the viscous drag laws is seen to vary with packing
fraction. We find that , where , corresponding to the 2d jamming density, and suggest that this scaling
follows from the geometry of the deformed facets between bubbles in contact.
Overall, our work suggests a route to rationalize aspects of the ubiquitous
Herschel-Bulkley (power law) rheology observed in a wide range of disordered
materials.Comment: 16 pages, 14 figures, submitted to Phys. Rev. E. High quality version
available at: http://www.physics.leidenuniv.nl/sections/cm/gr