We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.
We report experiments on the equipartition of kinetic energy in a mixture of pairs of different types of grains vibrated in two dimensions. In general, the two types of grains do not attain the same granular temperature, T(g) = 1/2m
We present new data for the electrical conductivity of foams in which the liquid fraction ranges from two to eighty percent. We compare with a comprehensive collection of prior data, and we model all results with simple empirical formulae. We achieve a unified description that applies equally to dry foams and emulsions, where the droplets are highly compressed, as well as to dilute suspensions of spherical particles, where the particle separation is large. In the former limit, Lemlich's result is recovered; in the latter limit, Maxwell's result is recovered.
Experiments are performed on the transport of gas and liquid in a column of aqueous foam maintained in steady state by a constant gas flux at the bottom. We measure vertical profiles of the bubble velocities, the bubble radii, and the liquid fraction, for four different gas fluxes. In steady state the bubbles move upwards with constant speed equal to the measured gas flux, which accounts for all transport of gas. The bubbles also coarsen by gas diffusion at a rate that depends on liquid fraction. Away from the bottom, the Plateau border radii are constant. Therefore capillary effects are negligible and the steady-state liquid-fraction profile is set chiefly by the balance of viscous forces and gravity. The flow within the Plateau borders may be modeled with a no-slip boundary condition for our system. These findings provide a simple description of steady-state foams via the coarsening and drainage equations, which can be combined and solved analytically for bubble radius and liquid-fraction profiles.
We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.Aqueous foam is a quintessential non-equilibrium system, even in absence of film rupture. An initially homogeneous foam will drain due to gravity, and will coarsen due to gas diffusion, en route to an equilibrium state of total phase separation where the foam vanishes. The beautiful topology and microstructure of soap films and their junctions into Plateau borders and vertices have inspired wide-ranging studies of coarsening and drainage as fundamental evolution mechanisms [1,2]. However, drier foams coarsen more rapidly, and coarser foams drain more rapidly, and this interplay enhances temporal evolution and spatial inhomogeneity in situations such as free [3] and forced drainage [4]. In spite of good progress, several open questions remain. For example there is no consensus on how the coarsening rate depends on liquid content [4][5][6]. And there is little understanding of how drainage is affected by a distribution of bubble sizes.To advance the understanding of such issues we examine a geometry in which a vertical column of foam is created by a continuous stream of small bubbles into a pool of surfactant solution. Here the foam reaches a state where the bubbles rise at constant speed, and the liquid remains at rest, in the laboratory frame. Prior studies of such steady-state foams focus mainly on the height of the foam as the key observable quantity [7,8], though recently the liquid fraction profile was predicted under the assumption of constant bubble size [9]. Here the liquid content, the bubble speed, and the bubble size distribution, are all independent of time and are hence measured at our leisure as a function of height. This is a simplification over free and forced drainage, which require study as a function of both position and time. Furthermore, the steady-state condition allows for a different and unexplored type of interplay c EDP Sciences
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