The dynamics of concentrated suspensions of non-colloidal, monodisperse particles in plane Poiseuille flows are investigated by fully three-dimensional numerical simulations for bulk volume fractions of 0.20–0.40 of neutrally-buoyant particles. The ensemble averages of the volume fraction and particle velocity profiles are consistent with previous experiments. A statistical analysis indicates that there is an intermediate region between particle layers near the wall and a plug region in the core, in which the behaviour of ensemble-averaged suspension field can be approximated by a continuum theory. In the intermediate region, the wall-normal and spanwise velocity fluctuations, angular velocity in the vorticity direction and particle shear stress are found to be linear functions of the distance from the wall. The particle normal stresses in the intermediate region are almost uniform, consistent with the concept of normal-stress-driven particle migration. The intermediate region decreases in extent and the width of the core region increases for larger bulk volume fractions. There is a remarkable similarity between the particle–phase pressure profiles scaled by the local shear rate for different bulk volume fractions. The particle pressure profiles in the intermediate region are compared with the rheological model proposed by Morris & Boulay (1999). The effective viscosity, evaluated from the ratio of the total shear stress to the fluid-phase shear stress, shows a good agreement with empirical viscosity relations in Couette-flow suspensions. In the present study, both non-local dynamics and finite-size effects of the particles are evident in the core of the channel. These effects are more pronounced at larger volume fractions.

The dynamics of a plane air sheet surrounded by a coflowing water film, discharging into stagnant air, is investigated by means of experiments and linear stability theory. For fixed values of the water-to-air thickness ratio, h = hw,0*/ha,0* ≃ 5.27, and of the air-to-water density ratio, S = ρa/ρw ≃ 0.0012, two different flow regimes are experimentally observed depending on the values of two control parameters, namely the Weber number, defined as We = ρwuw,0*2ha,0*/σ, and the velocity ratio, Λ = uw,0*/ua,0*, where uw,0* and ua,0* are the water velocity and the mean air velocity at the exit slit, respectively, and ha,0* and hw,0* are the half-thicknesses of the air and water sheets at the exit. The study focuses on the characterization of the transition between the two regimes found experimentally: a bubbling regime, leading to the periodic breakup of the air sheet, and a jetting regime, where both sheets evolve slowly downstream without breaking. With the aim of exploring whether the transition from the jetting to the bubbling regime is related to a convective/absolute instability transition, we perform a linear spatiotemporal stability analysis. The base flow is described by a simple model that incorporates the downstream evolution of the sheets, which shows excellent agreement with our experiments if the existence of a sufficiently long region of absolute instability, of the order of one absolute wavelength evaluated at the nozzle exit, is imposed as an additional requirement. Finally, we show that the transition is also properly captured by two-dimensional numerical simulations using the volume of fluid technique.

Algebraic topology (homology) is used to characterize quantitatively non-Oberbeck–Boussinesq (NOB) effects in chaotic Rayleigh–Bénard convection patterns from laboratory experiments. For fixed parameter values, homology analysis yields a set of Betti numbers that can be assigned to hot upflow and, separately, to cold downflow in a convection pattern. An analysis of data acquired under a range of experimental conditions where NOB effects are systematically varied indicates that the difference between time-averaged Betti numbers for hot and cold flows can be used as an order parameter to measure the strength of NOB-induced pattern asymmetries. This homology-based measure not only reveals NOB effects that Fourier methods and measurements of pattern curvature fail to detect, but also permits distinguishing pattern changes caused by modified lateral boundary conditions from NOB pattern changes. These results suggest a new approach to characterizing data from either experiments or simulations where NOB effects are expected to play an important role.

Understanding the cause of instability of viscoelastic liquid jets is of fundamental importance to realise practical applications such as ink-jet printing, fuel injection spraying, and fibre spinning. For common viscoelastic fluids, the elastic stresses caused by the stretching of entangled polymeric chains at the nozzle can persist along the jet for a long downstream distance far away from the exit. Unrelaxed elastic tension has been regarded as a factor responsible for the delay in the breakup of viscoelastic jets. The present study performs a complete linear stability analysis to obtain deeper insights into the response of unrelaxed elastic tension to the onset of three-dimensional instability in viscoelastic jets. Results show that the elastic effect is multidimensional. In the absence of the unrelaxed tension, the elastic force, characterised by a Deborah number, has a slightly destabilising influence on both axisymmetric and non-axisymmetric disturbances. However, when the unrelaxed tension arises, the elastic force begins to suppress the instabilities driven by surface tension and the wind-induced effect to a great extent. In particular, once the tension exceeds a threshold, some novel oscillating non-axisymmetric modes emerge because of stimulation by the relaxation of the elastic energy, causing a variety of asymmetrical deformations.

Theoretical predictions and experimental results for turbulent entrainment in inert and reacting, multiphase plumes are presented. It is shown that in an inert, pure plume, the entrainment coefficient is approximately constant with downstream distance. In a reacting plume, in which buoyancy is depleted by chemical reaction, the entrainment coefficient decreases strongly with distance from the source owing mainly to a decrease in the Richardson number. The effect on entrainment of the drift in the velocity and buoyancy distributions in the radial direction, i.e. the similarity drift introduced by Kaminski, Tait & Carazzo (J. Fluid Mech., vol. 526, 2005, pp. 361–76), is found to increase with downstream distance and with the reaction rate but, on laboratory-scale experiments, remains small compared to the contribution to entrainment from the turbulent stresses and buoyancy.

A constitutive model is developed for the complex rheology of rate-independent granular materials. The closures for the pressure and the macroscopic friction coefficient are linked to microstructure through evolution equations for coordination number and fabric. The material constants in the model are functions of particle-level properties and are calibrated using data generated through simulations of steady and unsteady simple shear using the discrete element method (DEM). This model is verified against DEM simulations at complex loading conditions.

The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional two-dimensional boundary-layer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the four-layer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Self-consistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the four-layer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U∞ θ/ν ≃ 780. The first-principles-based theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and four-layer regimes. As in channel flow, the transitional regime is marked by a non-negligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the four-layer regime. Empirical and theoretical evidence suggests that the formation of the four-layer structure also underlies the emergence of the mean dynamical properties characteristic of the high-Reynolds-number flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to .

We present an experimental study of a buoyancy-driven, low-Reynolds-number (Re < 1) exchange flow of two Newtonian fluids in a vertical cylindrical pipe (length 1 m and diameter 38.4 mm) connecting two fluid reservoirs. The denser, more viscous fluid was golden syrup and the less dense, less viscous fluid was a golden syrup–water solution; the ratio of the viscosities of the two fluids (β) ranged from 2 to 1180. Flows were initiated by removing a bung in the base of the upper reservoir or sliding out a gate positioned at the top, middle or bottom of the pipe. We observe the flows over long time durations (up to 356 h), and define the development of the flow with reference to a non-dimensional time (τ). The initial transient development of the flow was dependent on which of the two fluids initially filled the pipe, but this did not systematically affect the flow regime observed at τ ≫ 1. Two distinct flow regimes were observed: axisymmetric core-annular flow (CAF), in which the less viscous fluid occupies a cylindrical core and the denser fluid flows downwards in an annulus, and side-by-side (SBS) flow where both fluids are in contact with the pipe and there is a single interface between them. CAF formed at β ≥ 75 and SBS flow at β ≤ 117. In several experiments, for 5 ≤ β ≤ 59, a slowly developing transitional SBS (TSBS) flow was observed where SBS flow and CAF occurred simultaneously with SBS in the lower portion of the pipe; SBS existed throughout most of the pipe and in one case grew with time to entirely fill the pipe. Velocity profiles determined by tracking tracer particles show that the observed CAFs are adequately described by the formulation of Huppert & Hallworth (J. Fluid Mech., vol. 578, 2007, pp. 95–112). Experimental SBS velocity profiles are not well produced by the formulation of Kerswell (J. Fluid Mech., 10.1017/jfm.2011.190), possibly because the latter is restricted to flows whose cross-section has an interface of constant curvature. Despite the variations in flow regime, volume fluxes can be described by a power-law function of β, Q1 = 0.059 β−0.74. A comparison of experimental data with the theoretical approaches of Huppert Hallworth (2007) and Kerswell (2011) indicates that fluids are not arranged in the regime that maximises volume flux (e.g. SBS or CAF), nor do they adopt the geometry that maximises volume flux within that particular regime.