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Dynamics of the orientation behavior and its connection with rheology in sheared non-Brownian suspensions of anisotropic dicolloidal particlesThere is an obvious need for obtaining a closed set of equations describing multiphase flows and the complexity of their configurations. Despite their "frozen" interfaces, suspensions of rigid particles are also concerned by this issue. The description of the relative motion between the two phases is still controversial, in particular, concerning the forces acting on the particles and involving their concentration gradient or a shear rate gradient. It is our purpose here ͑a͒ to develop a two-fluid model especially designed for particles dispersed in a viscous liquid and ͑b͒ to close the model for rigid particles with the help of low-Reynolds-number hydrodynamics. Besides the obvious role of gravity forces, the migration of particles relative to the fluid is shown to result from two different physical phenomena: ͑a͒ the inhomogeneity of the stress resulting from direct interparticle forces and ͑b͒ Fick-like terms in the hydrodynamic force acting on the particles.

The cornerstone of multiphase flow applications in engineering practice is a scientific construct that translates the basic laws of fluid mechanics into a set of governing equations for effective interpenetrating continua, the effective-field (or two-fluid) model. Over more than half a century of development this model has taken many forms but all of them fail in a way that was known from the very beginning: mathematical ill-posedness. The aim of this paper is to refocus awareness of this problem from a unified fundamental perspective that clarifies the manner in which such failures took place and to suggest the means for a final closure.

We define a r-fractal as a self-similar structure built from N basic units, and with a maximum gyration radius scaling like Nr. We assume that r is a superuniversal exponent, independent of the space dimension d and verifying 1/d≤r≤1. We determine the equilibrium fractal dimension, the spectral and spreading dimensions, etc... as a function of r and d. These r-fractals seem to offer a simple picture of actual polymers, with r = 1 for chains and r = 3/4 for branched polymers. We reinterpret the Flory approximation as giving an oversimplified expression for the statistical distribution of the gyration radius of r-fractals. The correct expression leads to an improved version of the Flory model, whose success is (tentatively) explained by the rather unexpected behaviour of an exponent ratio which stays very close to its ideal value in a wide range of r and d

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent qualitative agreement with most of the experimental or numerical results concerning free-surface shear flows as well as confined shear flows.

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We measure the instantaneous velocity of particles sedimenting in a three-dimensional container at low particulate Reynolds numbers. We aim at characterizing the main specificities of the particle velocity fluctuations. We obtain the local and instantaneous Eulerian velocity field from particle image velocimetry: a thin Yag laser light sheet (about two diameters thick) illuminates the particles from one side of the cell to the other. Our measurements are therefore spatially localized and, together with the squared cross sections of the cells, these are the two main originalities of our instrumentation. Four different cells and three different particle sizes give access to aspect ratios (cell width W over particle radius a) ranging from about 50 up to 800. We confirm the existence of eddy-like structures for the velocity fluctuations. The structure size is found to be almost independent of the volume fraction Φ for 6.25×10−4<Φ<5×10−2 for a fixed aspect ratio W/a, in seeming contradiction with the results of Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)]. The velocity fluctuations’ profiles are close to parabolic for the smallest aspect ratios but display a plateau value in the central part of the cell for higher aspect ratios. The unexpected result of our experiments is the large distance of influence of the boundaries: in fact, the plateau values are observed to saturate for aspect ratios larger than a few hundreds for Φ=1×10−2, for example. Moreover, the saturated plateau values scale as φ0.45±0.05, in contrast with the φ1/3 scaling observed in most previous works.