1,140 research outputs found
Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow
We investigate the two-dimensional flow of a liquid foam around circular
obstacles by measuring all the local fields necessary to describe this flow:
velocity, pressure, bubble deformations and rearrangements. We show how our
experimental setup, a quasi-2D "liquid pool" system, is adapted to the
determination of these fields: the velocity and bubble deformations are easy to
measure from 2D movies, and the pressure can be measured by exploiting a
specific feature of this system, a 2D effective compressibility. To describe
accurately bubble rearrangements, we propose a new, tensorial descriptor. All
these quantities are evaluated via an averaging procedure that we justify
showing that the fluctuations of the fields are essentially random. The flow is
extensively studied in a reference experimental case; the velocity presents an
overshoot in the wake of the obstacle, the pressure is maximum at the leading
side and minimal at the trailing side. The study of the elastic deformations
and of the velocity gradients shows that the transition between plug flow and
yielded regions is smooth. Our tensorial description of T1s highlight their
correlation both with the bubble deformations and the velocity gradients. A
salient feature of the flow, notably on the velocity and T1 repartition, is a
marked asymmetry upstream/downstream, signature of the elastic behaviour of the
foam. We show that the results do not change qualitatively when various control
parameters vary, identifying a robust quasistatic regime. These results are
discussed in the frame of the actual foam rheology literature, and we argue
that they constitute a severe test for existing rheological models, since they
capture both the elastic, plastic and fluid behaviour of the foam.Comment: 41 pages, 25 figures, submitted to Journal of Fluid Mechanics (but
not in JFM style), short version of the abstrac
Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions
Discrete rearranging patterns include cellular patterns, for instance liquid
foams, biological tissues, grains in polycrystals; assemblies of particles such
as beads, granular materials, colloids, molecules, atoms; and interconnected
networks. Such a pattern can be described as a list of links between
neighbouring sites. Performing statistics on the links between neighbouring
sites yields average quantities (hereafter "tools") as the result of direct
measurements on images. These descriptive tools are flexible and suitable for
various problems where quantitative measurements are required, whether in two
or in three dimensions. Here, we present a coherent set of robust tools, in
three steps. First, we revisit the definitions of three existing tools based on
the texture matrix. Second, thanks to their more general definition, we embed
these three tools in a self-consistent formalism, which includes three
additional ones. Third, we show that the six tools together provide a direct
correspondence between a small scale, where they quantify the discrete
pattern's local distortion and rearrangements, and a large scale, where they
help describe a material as a continuous medium. This enables to formulate
elastic, plastic, fluid behaviours in a common, self-consistent modelling using
continuous mechanics. Experiments, simulations and models can be expressed in
the same language and directly compared. As an example, a companion paper
(Marmottant, Raufaste and Graner, joint paper) provides an application to foam
plasticity
- …