This paper presents a linear stability analysis of plane Couette flow of a granular material using a kinetic-theory-based model for the rheology of the medium. The stability analysis, restricted to two-dimensional disturbances, is carried out for three illustrative sets of grain and wall properties which correspond to the walls being perfectly adiabatic, and sources and sinks of fluctuational energy. When the walls are not adiabatic and the Couette gap H is sufficiently large, the base state of steady fully developed flow consists of a slowly deforming ‘plug’ layer where the bulk density is close to that of maximum packing and a rapidly shearing layer where the bulk density is considerably lower. The plug is adjacent to the wall when the latter acts as a sink of energy and is centred at the symmetry axis when it acts as a source of energy. For each set of properties, stability is determined for a range of H and the mean solids fraction [barvee ]. For a given value of [barvee ], the flow is stable if H is sufficiently small; as H increases it is susceptible to instabilities in the form of cross-stream layering waves with no variation in the flow direction, and stationary and travelling waves with variation in the flow and gradient directions. The layering instability prevails over a substantial range of H and [barvee ] for all sets of wall properties. However, it grows far slower than the strong stationary and travelling wave instabilities which become active at larger H. When the walls act as energy sinks, the strong travelling wave instability is absent altogether, and instead there are relatively slow growing long-wave instabilities. For the case of adiabatic walls there is another stationary instability for dilute flows when the grain collisions are quasi-elastic; these modes become stable when grain collisions are perfectly elastic or very inelastic. Instability of all modes is driven by the inelasticity of grain collisions.

Flow visualization and particle image velocimetry (PIV) measurements are used to unravel the pattern transition and velocity field in the Taylor–Couette flow (TCF) of neutrally buoyant non-Brownian spheres immersed in a Newtonian fluid. With increasing Reynolds number ($Re$) or the rotation rate of the inner cylinder, the bifurcation sequence in suspension TCF remains same as in its Newtonian counterpart (i.e. from the circular Couette flow (CCF) to stationary Taylor vortex flow (TVF) and then to travelling wavy Taylor vortices (WTV) with increasing $Re$) for small particle volume fractions ($\unicode[STIX]{x1D719}<0.05$). However, at $\unicode[STIX]{x1D719}\geqslant 0.05$, non-axisymmetric patterns such as (i) the spiral vortex flow (SVF) and (ii) two mixed or co-existing states of stationary (TVF, axisymmetric) and travelling (WTV or SVF, non-axisymmetric) waves, namely (iia) the ‘TVF$+$WTV’ and (iib) the ‘TVF$+$SVF’ states, are found, with the former as a primary bifurcation from CCF. While the SVF state appears both in the ramp-up and ramp-down experiments as in the work of Majji et al. (J. Fluid Mech., vol. 835, 2018, pp. 936–969), new co-existing patterns are found only during the ramp-up protocol. The secondary bifurcation TVF $\leftrightarrow$ WTV is found to be hysteretic or sub-critical for $\unicode[STIX]{x1D719}\geqslant 0.1$. In general, there is a reduction in the value of the critical Reynolds number, i.e. $Re_{c}(\unicode[STIX]{x1D719}\neq 0)<Re_{c}(\unicode[STIX]{x1D719}=0)$, for both primary and secondary transitions. The wave speeds of both travelling waves (WTV and SVF) are approximately half of the rotational velocity of the inner cylinder, with negligible dependence on $\unicode[STIX]{x1D719}$. The analysis of the radial–axial velocity field reveals that the Taylor vortices in a suspension are asymmetric and become increasingly anharmonic, with enhanced radial transport, with increasing particle loading. Instantaneous streamline patterns on the axial–radial plane confirm that the stationary Taylor vortices can indeed co-exist either with axially propagating spiral vortices or azimuthally propagating wavy Taylor vortices – their long-time stability is demonstrated. It is shown that the azimuthal velocity is considerably altered for $\unicode[STIX]{x1D719}\geqslant 0.05$, resembling shear-band type profiles, even in the CCF regime (i.e. at sub-critical Reynolds numbers) of suspension TCF; its possible role on the genesis of observed patterns as well as on the torque scaling is discussed.

The development of optical fibers has revolutionized telecommunications by enabling longdistance broad-band transmission with minimal loss. In turn, the ubiquity of high-quality lowcost fibers enabled a number of additional applications, including fiber sensors, fiber lasers, and imaging fiber bundles. Recently, we showed that a multimode optical fiber can also function as a spectrometer by measuring the wavelength-dependent speckle pattern formed by interference between the guided modes. Here, we reach a record resolution of 1 pm at wavelength 1500 nm using a 100 meter long multimode fiber, outperforming the state-of-the-art grating spectrometers. We also achieved broad-band operation with a 4 cm long fiber, covering 400 nm -750 nm with 1 nm resolution. The fiber spectrometer, consisting of the fiber which can be coiled to a small volume and a monochrome camera that records the speckle pattern, is compact, lightweight, and low cost while providing ultrahigh resolution, broad bandwidth and low loss.

The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference.Numerical results for pressure, viscosity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance than an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equi-partition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartition, but mass disparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variations of the pressure, viscosity and granular energy with the mass ratio if the size ratio is held fixed, while the model predictions (with the equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the stress is defined in the compressive sense), and the effect of bidispersity is to increase the normal stress difference, thus enhancing the non-Newtonian character of the fluid.