Numerical determination of the secondary acoustic radiation force on a small sphere in a plane standing wave field

Two numerical methods based on the Finite Element Method are presented for calculating the secondary acoustic radiation force between interacting spherical particles. The first model only considers the acoustic waves scattering off a single particle, while the second model includes re-scattering effects between the two interacting spheres. The 2D axisymmetric simplified model combines the Gor’kov potential approach with acoustic simulations to find the interacting forces between two small compressible spheres in an inviscid fluid. The second model is based on 3D simulations of the acoustic field and uses the tensor integral method for direct calculation of the force. The results obtained by both models are compared with analytical equations, showing good agreement between them. The 2D and 3D models take, respectively, seconds and tens of seconds to achieve a convergence error of less than 1%. In comparison with previous models, the numerical methods presented herein can be easily implemented in commercial Finite Element software packages, where surface integrals are available, making it a suitable tool for investigating interparticle forces in acoustic manipulation devices

Two interacting particles in an effective 2-3d random potential

We study the effect of coherent propagation of two interacting particles in an effective 2-3-d disordered potential. Our numerical data demonstrate that in dimension $d > 2$, interaction can lead to two--particles delocalization below one--particle delocalization border. We also find that the distance between the two delocalized particles (pair size) grows logarithmically with time. As a result pair propagation is subdiffusive.Comment: 15 Latex pages, + 15 figures compressed with uufile

Evidence of reverse and intermediate size segregation in dry granular flows down a rough incline

In a dry granular flow, size segregation behave differently for a mixture containing a few large beads with a size ratio (S) above 5 (Thomas, Phys.Rev.E 62,96(2000)). For moderate large S, large beads migrate to an intermediate depth in the bed: this is called intermediate segregation. For the largest S, large beads migrate to the bottom: this is called reverse segregation (in contrast with surface segregation). As the reversal and intermediate depth values depend on the bead fraction, this numerical study mainly uses a single large tracer. Small fractions are also computed showing the link between a tracer behavior and segregation process. For half-filled rotating drum and for rough incline, two and three (3D) dimensional cases are studied. In the tumbler, trajectories of a large tracer show that it reaches a constant depth during the flow. For large S, this depth is intermediate with a progressive sinking when S increases. Largest S correspond to tracers at the bottom of the flow. All 3D simulation are in quantitative agreement with the experiments. In the flow down an incline, a large tracer reaches an equilibrium depth during flow. For large S, its depth is intermediate, inside the bed. For the largest S, its depth is reverse, near the bottom. Results are slightly different for thin or thick flow. For 3D thick flows, the reversal between surface and bottom positions occurs within a short range of S: no tracer stabilizes near mid-height and two reachable intermediate depth layers exist, below the surface and above the bottom. For 3D thin flows, all intermediate depths are reachable, depending on S. The numerical study of larger tracer fractions (5-10%) shows the 3 segregation patterns (surface, intermediate, reverse) corresponding to the 3 types of equilibrium depth. The reversal is smoother than for a single tracer. It happens around S=4.5, in agreement with experiments.Comment: 18 pages, 27 figure

Thermodynamics and dynamics of two-dimensional systems with dipole-like repulsive interactions

Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical approximations. This interaction potential, which decays as an inverse cube of the interparticle distance, belongs to the class of very soft long-ranged interactions. As a result, the investigated system exhibits certain universal properties that are also shared by other related soft-interacting particle systems (like, for instance, the one-component plasma and weakly screened Coulomb systems). These universalities are explored in this article to construct a simple and reliable description of the system thermodynamics. In particular, Helmholtz free energies of the fluid and solid phases are derived, from which the location of the fluid-solid coexistence is determined. The quasi-crystalline approximation is applied to the description of collective modes in dipole fluids. Its simplification, previously validated on strongly coupled plasma fluids, is used to derive explicit analytic dispersion relations for the longitudinal and transverse wave modes, which compare satisfactory with those obtained from direct MD simulations in the long-wavelength regime. Sound velocities of the dipole fluids and solids are derived and analyzed.Comment: to be published in Phys. Rev.