Narayanan Menon

Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets

Significance Thin elastic sheets buckle and wrinkle to relax compressive stresses. Wrinkling metrologies have recently been developed as noninvasive probes of mechanical environment or film properties, for instance in biological tissues or textiles. This work proposes and experimentally tests a prediction for the local wavelength of wrinkles in nonuniform curved topographies. Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles—their wavelength—is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.

Indentation of ultrathin elastic films and the emergence of asymptotic isometry.

We study the indentation of a thin elastic film floating at the surface of a liquid. We focus on the onset of radial wrinkles at a threshold indentation depth and the evolution of the wrinkle pattern as indentation progresses far beyond this threshold. Comparison between experiments on thin polymer films and theoretical calculations shows that the system very quickly reaches the far from threshold regime, in which wrinkles lead to the relaxation of azimuthal compression. Furthermore, when the indentation depth is sufficiently large that the wrinkles cover most of the film, we recognize a novel mechanical response in which the work of indentation is transmitted almost solely to the liquid, rather than to the floating film. We attribute this unique response to a nontrivial isometry attained by the deformed film, and we discuss the scaling laws and the relevance of similar isometries to other systems in which a confined sheet is subjected to weak tensile loads.

Breakdown of Energy Equipartition in a 2D Binary Vibrated Granular Gas

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. However, the temperature ratio is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but not on their inelasticity. Also, the temperature ratio is insensitive to compositional variables such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multicomponent mixture.

Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities.

Smooth wrinkles and sharply crumpled regions are familiar motifs in biological or synthetic sheets, such as rapidly growing plant leaves and crushed foils. Previous studies have addressed both morphological types, but the generic route whereby a featureless sheet develops a complex shape remains elusive. Here we show that this route proceeds through an unusual sequence of distinct symmetry-breaking instabilities. The object of our study is an ultrathin circular sheet stretched over a liquid drop. As the curvature is gradually increased, the surface tension stretching the sheet over the drop causes compression along circles of latitude. The compression is relieved first by a transition into a wrinkle pattern, and then into a crumpled state via a continuous transition. Our data provide conclusive evidence that wrinkle patterns in highly bendable sheets are not described by classical buckling methods, but rather by a theory which assumes that wrinkles completely relax the compressive stress. With this understanding we recognize the observed sequence of transitions as distinct symmetry breakings of the shape and the stress field. The axial symmetry of the shape is broken upon wrinkling but the underlying stress field preserves this symmetry. Thus, the wrinkle-to-crumple transition marks symmetry-breaking of the stress in highly bendable sheets. By contrast, other instabilities of sheets, such as blistering and cracking, break the homogeneity of shape and stress simultaneously. The onset of crumpling occurs when the wrinkle pattern grows to half the sheet’s radius, suggesting a geometric, material-independent origin for this transition.

STRUCTURAL STUDIES OF AN ORGANIC LIQUID THROUGH THE GLASS TRANSITION

We have performed neutron diffraction experiments on deuterated propylene glycol, an organic glass former, at temperatures ranging from where its dynamical response approaches that of normal liquids to below the point where relaxation times appear to diverge. Our studies extend over a very broad range of scattering wave vector (0.01<Q<30 A−1). In contrast to models which predict clustering, we find no evidence in the liquid at any temperature for heterogeneities large on molecular scales. However, we do note subtle changes at shorter lengths. Using molecular dynamics simulations to model our results, we identify these changes with increasing density and increasing orientational order induced by hydrogen bonding in the liquid as it cools. Analysis of the orientational correlations between molecules reveals a strong dependence on their relative positions.

Fluidized Granular Medium as an Instance of the Fluctuation Theorem

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.

Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic, and smectic correlations

We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. In addition to varying packing fraction and aspect ratio as in most studies on hard-particle systems, we take advantage of our ability to vary the precise shape of these macroscopic particles to investigate the effect of shape on their nonequilibrium steady states. We find that the shape plays an important role in determining the nature of the orientational ordering at high packing fraction. Cylindrical particles show substantial tetratic correlations over a range of aspect ratios where spherocylinders have previously been shown to undergo transitions between isotropic and nematic phases. Particles that are thinner at the ends (rolling pins or bails) show nematic ordering over the same range of aspect ratios, with a well established nematic phase at large aspect ratio and a defect-ridden nematic state with large-scale swirling motion at small aspect ratios. Finally, long-grain, basmati rice, whose geometry is intermediate between the two shapes above, shows phases with strong indications of smectic order.

Wide-frequency dielectric susceptibility measurements in glycerol

Data are presented on the dielectric relaxation in supercooled liquid glycerol. These data span over 14 decades in frequency from 10 −4 Hz to 2×10 10 Hz. It is found that the peak in the imaginary part of the dielectric susceptibility has a temperature dependence that can be fit with a Vogel-Fulcher form: v = v 0 exp[− A /( T − T 0 )]. The shape of the response function in the high frequency tail cannot be fit with a stretched-exponential form. However the data can be scaled onto a single master curve which has previously been shown to fit a number of other glass-forming liquids.

Specific heat spectroscopy: Origins, status and applications of the 3ω method

Abstract We review the technique of ‘specific heat spectroscopy,’ of Birge and Nagel. The technique, also called the ‘3ω method’ in the literature, is nonadiabatic; it is based on thermal diffusion into a thick sample from a thin metallic film that serves simultaneously as heater and thermometer. Specific heat spectroscopy allows one to measure the dynamic specific heat of a liquid or solid over a frequency range exceeding 6 decades, and simultaneously the thermal conductivity over a more limited frequency range. Designed to study supercooled liquids near the glass transition, specific heat spectroscopy has also been used to study phase transitions and biological systems.

Loose packings of frictional spheres

We have produced loose packings of cohesionless, frictional spheres by sequential deposition of highly-spherical, monodisperse particles through a fluid. By varying the properties of the fluid and the particles, we have identified the Stokes number (St)—rather than the buoyancy of the particles in the fluid—as the parameter controlling the approach to the loose packing limit. The loose packing limit is attained at a threshold value of St at which the kinetic energy of a particle impinging on the packing is fully dissipated by the fluid. Thus, for cohesionless particles, the dynamics of the deposition process, rather than the stability of the static packing, defines the random loose packing limit. We have made direct measurements of the interparticle friction in the fluid, and present an experimental measurement of the loose packing volume fraction, ϕRLP, as a function of the friction coefficient μs.