Arshad Kudrolli

Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio

A multi-layered skylight having an outer element with a central domed portion and a downwardly extending circumferential skirt portion, said outer element comprising a monolayer of a synthetic resin which transmits light, and an inner element of one-piece construction with a central domed portion and a substantially planar circumferential edge portion, said inner element comprising at least two sheets of a synthetic resin which transmits light, said sheets being substantially parallel to one another and having a plurality of supporting elements extending therebetween, said elements being arranged with the planar edge portion of said inner element being within and surrounded by the circumferential skirt portion of said outer element and with the central domed portions of said inner and outer elements being in a substantially parallel spaced relationship to one another.

Swarming and Swirling in Self-Propelled Polar Granular Rods

Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering, aggregation at the side walls, and clustering absent in round SP particles. Furthermore, we find that at sufficiently strong excitation SP rods engage in a persistent swirling motion in which the velocity is strongly correlated with particle orientation.

Superlattice patterns in surface waves

Abstract We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio is utilized in this work. A superlattice pattern (“superlattice-I”) consisting of two hexagonal lattices oriented at a relative angle of 22° is obtained with a 6:7 ratio of forcing frequencies. Several theoretical approaches that may be useful in understanding this pattern have been proposed. In another example, the waves are fully described by two superimposed hexagonal lattices with a wavelength ratio of 3 , oriented at a relative angle 30°. The time dependence of this “suoerlattice-II” wave pattern is unusual. The instantaneous patterns reveal a time-periodic stripe modulation that breaks the sixfold symmetry at any instant, but the stripes are absent in the time average. The instantaneous patterns are not simply amplitude modulations of the primary standing wave. A transition from the superlattice-II state to a 12-fold quasi-crystalline pattern is observed by changing the relative phase of the two forcing frequencies. Phase diagrams of the observed patterns (including superlattices, quasicrystalline patterns, ordinary hexagons, and squares) are obtained as a function of the amplitudes and relative phases of the driving accelerations.

Angle of repose and segregation in cohesive granular matter.

We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid (liquid) is small and it forms liquid bridges between particles thus giving rise to cohesive forces, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two-dimensional silo through the transparent glass side walls and using color-coded particles. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value that depends on the size of the particles. We systematically study the effect of viscosity by using water-glycerol mixtures to vary it over at least three orders of magnitude while keeping the surface tension almost constant. Besides surface tension, the viscosity of the fluid is observed to have an effect on the angle of repose and the extent of segregation. In case of bidisperse particles, segregation is observed to decrease and finally saturate depending on the size ratio of the particles and the viscosity of the fluid. The sharp initial change and the subsequent saturation in the extent of segregation and angle of repose occurs over similar volume fraction of the fluid. Preferential clumping of small particles causes layering to occur when the size of the clumps of small particles exceeds the size of large particles. We calculate the azimuthal correlation function of particle density inside the pile to characterize the extent of layering. In the second series of experiments, particles are poured into a container filled with a fluid. Although the angle of repose is observed to be unchanged, segregation is observed to decrease with an increase in the viscosity of the fluid. The viscosity at which segregation decreases to zero depends on the size ratio of the particles.

Velocity statistics in excited granular media

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) approximately exp(-mid R:v/v(c)mid R:(1.5)), in agreement with a recent theory. The characteristic velocity v(c) is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. (c) 1999 American Institute of Physics.

Maximum angle of stability of a wet granular pile

Anyone who has built a sandcastle recognizes that adding liquid to the sand grains increases the overall stability. However, measurements of the stability in wet granular materials often conflict with theory and with each other1,2,3,4,5,6,7. The friction-based Mohr–Coulomb model3,8 distinguishes between granular friction and interparticle friction, but uses the former without providing a physical mechanism. A frictionless model for the geometric stability of dry particles on the surface of a pile2 is in excellent agreement with experiment. However, the same model applied to wet grains overestimates the stability and predicts no dependence on system size. Here we take a frictionless liquid-bridge model and perform a stability analysis within the pile. We reproduce our experimentally observed dependence of the stability angle on system size, particle size and surface tension. Furthermore, we account for past discrepancies in experimental reports by showing that sidewalls can significantly increase the stability of granular material.

Size segregation of granular matter in silo discharges.

We present an experimental study of segregation of granular matter in a quasi-two-dimensional silo emptying out of an orifice. Size separation is observed when multisized particles are used with the larger particles found in the center of the silo in the region of fastest flow. We use imaging to study the flow inside the silo and quantitatively measure the concentration profiles of bidisperse beads as a function of position and time. The angle of the surface is given by the angle of repose of the particles, and the flow occurs in a few layers only near the top of this inclined surface. The flowing region becomes deeper near the center of the silo and is confined to a parabolic region centered at the orifice which is approximately described by the kinematic model. The experimental evidence suggests that the segregation occurs on the surface and not in the flow deep inside the silo where velocity gradients also are present. We report the time development of the concentrations of the bidisperse particles as a function of size ratios, flow rate, and the ratio of initial mixture. The qualitative aspects of the observed phenomena may be explained by a void filling model of segregation.

Diffusion and mixing in gravity-driven dense granular flows

We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with long-lasting contacts but not thermal collisions, as in normal fluids.

Segregation transitions in wet granular matter

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid V(f) is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation s and the angle of repose straight theta. We show that the sharp initial change and the subsequent saturation in s and straight theta occurs over similar V(f). We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.

Maximum and minimum stable random packings of Platonic solids.

Motivated by the relation between particle shape and packing, we measure the volume fraction ϕ occupied by the Platonic solids which are a class of polyhedrons with congruent sides, vertices, and dihedral angles. Tetrahedron-, cube-, octahedron-, dodecahedron-, and icosahedron-shaped plastic dice were fluidized or mechanically vibrated to find stable random loose packing ϕ(rlp)=0.51,0.54,0.52,0.51,0.50 and densest packing ϕ(rcp)=0.64,0.67,0.64,0.63,0.59, respectively, with standard deviation of ≃ ± 0.01. We find that ϕ obtained by all protocols peak at the cube, which is the only Platonic solid that can tessellate space, and then monotonically decrease with number of sides. This overall trend is similar but systematically lower than the maximum ϕ reported for frictionless Platonic solids and below ϕ(rlp) of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower ϕ.