The effect of particle aspect ratio and surface geometry on granular flows is assessed by performing numerical simulations of rod-like particles in simple shear flows using the discrete element method (DEM). The effect of particle surface geometry is explored by adopting two types of particles: glued-spheres particles and true cylindrical particles. The particle aspect ratio varies from one to six. Compared to frictionless spherical particles, smaller stresses are obtained for the glued-spheres and cylindrical particle systems in dilute and moderately dense flows due to the loss of translational energy, which is partially converted to rotational energy, for the non-spherical particles. For dilute granular flows of non-spherical particles, stresses are primarily affected by the particle aspect ratio rather than the surface geometry. As the particle aspect ratio increases, the effective particle projected area in the plane perpendicular to the flow direction increases, so that the probability of the occurrence of the particle collisions increases, leading to a reduction in particle velocity fluctuation and therefore a decrease in the stresses. Hence, a simple modification is made to the kinetic theory for granular flows to describe the stress tensors for dilute flows of non-spherical particles by incorporating a normalized effective particle projected area to account for the effect of particle collision probability. For dense granular flows, the stresses depend on both the particle aspect ratio and the surface geometry. Sharp stress increases at high solid volume fractions are observed for the glued-spheres particles with large aspect ratios due to the bumpy surfaces, which impede the flow. However, smaller stresses are obtained for the true cylindrical particles with large aspect ratios at high solid volume fractions. This trend is attributed to the combined effects of the smooth particle surfaces and the particle alignments such that the major/long axes of particles are aligned in the flow direction. In addition, the apparent friction coefficient, defined as the ratio of shear to normal stresses, is found to decrease as the particle aspect ratio increases and/or the particle surface becomes smoother at high solid volume fractions.

Lattice-Boltzmann simulations of fluid flow through sheared assemblies of monodisperse spherical particles have been performed. The friction coefficient tensor extracted from these simulations is found to become progressively more anisotropic with increasing Péclet number, $Pe= \dot {\gamma } {d}^{2} / D$, where $\dot {\gamma } $ is the shear rate, $d$ is the particle diameter, and $D$ is the particle self-diffusivity. A model is presented for the anisotropic friction coefficient, and the model constants are related to changes in the particle microstructure. Linear stability analysis of the two-fluid model equations including the anisotropic drag force model developed in the present study reveals that the uniformly fluidized state of low Reynolds number suspensions is most unstable to mixed mode disturbances that take the form of vertically travelling waves having both vertical and transverse structures. As the Stokes number increases, the transverse-to-vertical wavenumber ratio decreases towards zero; i.e. the transverse structure becomes progressively less prominent. Fully nonlinear two-fluid model simulations of moderate to high Stokes number suspensions reveal that the anisotropic drag model leads to coarser gas–particle flow structures than the isotropic drag model.

We present an experimental study of drop impact on a solid surface in the spreading regime with no splashing. Using the space–time-resolved Fourier transform profilometry technique, we can follow the evolution of the drop shape during the impact. We show that a self-similar dynamical regime drives the drop spreading until the growth of a viscous boundary layer from the substrate selects a residual minimal film thickness. Finally, we discuss the interplay between capillary and viscous effects in the spreading dynamics, which suggests a pertinent impact parameter.

We present an experimental study on the axisymmetric vortex ring generated by a thin circular disc. The velocity and vorticity fields are measured by digital particle image velocimetry (DPIV). The finite-time Lyapunov exponent fields and the Lagrangian coherent structures (LCSs) of the vortex flow are computed in order to analyse the transport of the fluid during its formation and identify the boundary of the vortex ring. The volume, circulation and energy of the vortex ring are calculated. It is found that the formation of the vortex ring basically includes three phases: a rapid growth phase, a stable growth phase and a non-axisymmetric phase. In the rapid growth phase (dimensionless time $0\lt {T}_{n} \lt 0. 2$) during which Taylor’s inviscid estimation is valid, the circulation of the vortex ring grows and the translational velocity of the vortex ring decreases. In the stable growth phase ($0. 2\lt {T}_{n} \lt 4$), the growth rate of the circulation decreases gradually. In the non-axisymmetric phase (${T}_{n} \gt 4$), the ring loses axisymmetry due to instability. Compared with the vortex ring generated by the laminar flow from an orifice, the one generated by a circular disc always moves with the disc, and the entrained fluid decreases and the saturated circulation increases. The temporal impulse exerted by the moving disc on the fluid is estimated by DPIV measurements and is calculated using the direct momentum conservation method. The momentum of the control volume enclosing the LCS is found to occupy 64–68 % of the entire impulse exerted by the disc on the fluid.

We investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number $Re= 28\hspace{0.167em} 000$ and a wide range of horizontal Froude number ${F}_{h} \in [0. 0225~0. 135] $ and buoyancy Reynolds number $\mathscr{R}= Re{{F}_{h} }^{2} \in [14~510] $. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale ${L}_{b} = U/ N$, where $U$ is the characteristic horizontal velocity of the dipole and $N$ the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a ${{\varepsilon }_{K} }^{2/ 3} { k}_{h}^{\ensuremath{-} 5/ 3} $ power law (where ${k}_{h} $ is the horizontal wavenumber and ${\varepsilon }_{K} $ is the dissipation rate of kinetic energy) from ${k}_{b} = 2\lrm{\pi} / {L}_{b} $ to the dissipative scales, with an energy deficit between the integral scale and ${k}_{b} $ and an excess around ${k}_{b} $. The vertical spectrum of kinetic energy can be expressed as $E({k}_{z} )= {C}_{N} {N}^{2} { k}_{z}^{\ensuremath{-} 3} + C{{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ where ${C}_{N} $ and $C$ are two constants of order unity and ${k}_{z} $ is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ shape and approaches the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum for ${k}_{z} \gt {k}_{o} $, ${k}_{o} $ being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ spectrum is associated with large horizontal scales $\vert {\mathbi{k}}_{h} \vert \lt {k}_{b} $ and the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum with the scales $\vert {\mathbi{k}}_{h} \vert \gt {k}_{b} $.

The influence of fluid droplet properties on the droplet-on-demand jetting of a Newtonian model fluid (water–isopropanol–ethylene glycol ternary system) has been studied. The composition of the fluid was adjusted to investigate how the Ohnesorge number ($\mathit{Oh}$) influences droplet formation (morphology and speed) by a microfabricated short-channel shear-mode piezoelectric transducer. The fluid space for satellite-free single droplet formation was indeed found to be bound by upper and lower $\mathit{Oh}$ limits, but these shift approximately linearly with the piezo pulse voltage amplitude ${V}_{o} $, which has a stronger influence on jetting characteristics than pulse length. Therefore the jettable fluid space can be depicted on a ${V}_{o} {{\ndash}}\mathit{Oh}$ diagram. Satellite-free droplets of the model fluid can be jetted over a wide $\mathit{Oh}$ range, at least 0.025 to 0.5 (corresponding to $Z= {\mathit{Oh}}^{\ensuremath{-} 1} $ of 40 to 2), by adjusting ${V}_{o} $ appropriately. Air drag was found to dominate droplet flight, as may be expected. This can be accurately modelled to yield droplet formation time, which turned out to be $20\text{{\ndash}} 30~\lrm{\ensuremath{\mu}} \mathrm{s} $ under a wide range of jetting conditions. The corresponding initial droplet speed was found to vary linearly with ${V}_{o} $, with a fluid-dependent threshold but a fluid-independent slope, and a minimum speed of about $2~\mathrm{m} ~{\mathrm{s} }^{\ensuremath{-} 1} $. This suggests the existence of iso-velocity lines that run substantially parallel to the lower jetting boundary in the ${V}_{o} {{\ndash}}\mathit{Oh}$ diagram.

The viscous spatiotemporal stability properties of low-density laminar round jets emerging from circular nozzles or tubes are investigated numerically providing, for the first time, a separate treatment of the two particular cases typically studied in experiments: a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture of two gases with different molecular weight, discharging into a stagnant ambient of the heavier species. To that end, use is made of a realistic representation for the base velocity and density profiles based on boundary-layer theory, with account taken of the effect of variable transport properties. Our results show significant quantitative differences with respect to previous parametric studies, and reveal that hot jets are generically more unstable than light jets, in the sense that they have larger associated critical density ratios for values of the Reynolds number and momentum thickness typically used in experiments. In addition, for several values of the jet-to-ambient density ratio, $S$, the downstream evolution of the local stability properties of the jet is computed as a function of the two main control parameters governing the jet, namely the Reynolds number, $\mathit{Re}$, and the momentum thickness of the initial velocity profile, ${\theta }_{0} / D$. It is shown that, for a given value of $S$, the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane can be divided in three regions. In the first region, defined by low values of $\mathit{Re}$ or very thick shear layers, the flow is locally convectively unstable everywhere. In the second region, with moderately large values of $\mathit{Re}$ and thin shear layers, the jet exhibits a localized pocket of absolute instability, away from boundaries. Finally, in the third region, that prevails in most of the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane, the absolutely unstable domain is bounded by the jet outlet. All the experiments available in the literature are shown to lie in the latter region, and the global transition observed in experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large. The marginal frequency of the resulting global self-excited oscillations is shown to be fairly well described by the absolute frequency evaluated at the jet outlet, in agreement with the numerical results obtained by Lesshafft et al. (J. Fluid Mech., vol. 554, 2006, pp. 393–409) for synthetic jets.

An experiment apparatus has been previously developed with the ability to independently control the instantaneous flow velocity in a water flume. This configuration, which uses two pitching hydrofoils to generate the flow fluctuations, allows the unsteady response of submerged structures to be studied over a wide range of driving frequencies and conditions. Linear unsteady lift theory has been used to calculate the instantaneous circulation about two pitching hydrofoils in uniform flow. A vortex model is then used to describe the circulation in the wakes that determine the velocity perturbations at the centreline between the foils. This paper introduces how the vortex model can be discretized to allow the inverse problem to be solved, such that the foil motions required to recreate a desired velocity time series can be determined. The results of this model are presented for the simplified cases of oscillatory velocity fluctuations in the vertical and stream-wise directions separately, and also simultaneously. The more general case of two-dimensional aperiodic velocity fluctuations is also presented, which demonstrates the capability of configuration between the suggested frequency limits of $0. 06\leq k\leq 1. 9$.

An experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same ‘surfing’ effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396–431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

For two-dimensional, creeping flow in a half-plane, we consider the singularity that arises at an abrupt transition in permeability from zero to a finite value along the wall, where the pressure is coupled to the seepage flux by Darcy’s law. This problem represents the junction between the impermeable wall of the inflow section and the porous membrane further downstream in a spiral-wound desalination module. On a macroscopic, outer length scale the singularity appears like a jump discontinuity in normal velocity, characterized by a non-integrable $1/ r$ divergence of the pressure. This far-field solution is imposed as the boundary condition along a semicircular arc of dimensionless radius 30 (referred to the microscopic, inner length scale). A preliminary numerical solution (using a least-squares variant of the method of fundamental solutions) indicates a continuous normal velocity along the wall coupled with a weaker $1/ \sqrt{r} $ singularity in the pressure. However, inconsistencies in the numerically imposed outer boundary condition indicate a very slow radial decay. We undertake asymptotic analysis to: (i) understand the radial decay behaviour; and (ii) find a more accurate far-field solution to impose as the outer boundary condition. Similarity solutions (involving a stream function that varies like some power of $r$) are insufficient to satisfy all boundary conditions along the wall, so we generalize these by introducing linear and quadratic terms in $\log r$. By iterating on the wall boundary conditions (analogous to the method of reflections), the outer asymptotic series is developed through second order. We then use a hybrid computational scheme in which the numerics are iteratively patched to the outer asymptotics, thereby determining two free coefficients in the latter. We also derive an inner asymptotic series and fit its free coefficient to the numerics at $r= 0. 01$. This enables evaluation of the singular flow field in the limit as $r\ensuremath{\rightarrow} 0$. Finally, a uniformly valid fit is obtained with analytical formulas. The singular flow field for a solid–porous abutment and the general Stokes flow solutions obtained in the asymptotic analysis are programmed in Fortran for future use as local basis functions in computational schemes. Numerics are required for the intermediate-$r$ regime because the inner and outer asymptotic expansions do not extend far enough toward each other to enable rigorous asymptotic matching. The logarithmic correction terms explain why the leading far-field solution (used in the preliminary numerics) was insufficient even at very large distances.

Three-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.

We numerically assess the influence of non-uniform magnetic flux density and connected load resistance on turbulent duct flows in a liquid metal magnetohydrodynamic (MHD) electrical power generator. When increasing the magnetic flux density (or Hartmann number), an M-shaped velocity profile develops in the plane perpendicular to the magnetic field; the maximum velocity in the sidewall layer of the M-shaped profile increases to maintain the flow rate. Under the conditions of a relaminarized flow, the turbulence structures align along the magnetic field and flow repeatedly like a von Kármán vortex sheet. At higher Hartmann numbers, the wall-shear stress in the sidewall layer increases and the sidewall jets transit to turbulence. The sidewall jets in the MHD turbulent duct flows have profiles similar to the non-MHD wall jets, i.e. a mean velocity profile with outer scaling, Reynolds shear stress with the opposite sign in a sidewall jet, and two maxima for the turbulent intensities in a sidewall jet. The Lorentz force suppresses the vortices of the secondary mean flow near the Hartmann layer for low Hartmann numbers, whereas the secondary vortices remain near the Hartmann layer for high Hartmann numbers. An optimal load resistance (or load factor) to obtain a maximum electrical efficiency exists, because the strong Lorentz force for a low load factor and unextracted eddy currents for a high load factor reduce efficiency. When the value of the load factor is changed, the profiles of mean velocity and r.m.s. for the optimal load factor produce almost the same profiles as the high load factor near the open-circuit condition.

The flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes–Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green’s function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green’s function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An ‘indirect boundary integral method’ is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

This paper is concerned with the two-dimensional problem of nonlinear gravity waves travelling at the interface between a thin ice sheet and an ideal fluid of infinite depth. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff’s hypothesis, which yields a conservative and nonlinear expression for the bending force. A Hamiltonian formulation for this hydroelastic problem is proposed in terms of quantities evaluated at the fluid–ice interface. For small-amplitude waves, a nonlinear Schrödinger equation is derived and its analysis shows that no solitary wavepackets exist in this case. For larger amplitudes, both forced and free steady waves are computed by direct numerical simulations using a boundary-integral method. In the unforced case, solitary waves of depression as well as of elevation are found, including overhanging waves with a bubble-shaped profile for wave speeds $c$ much lower than the minimum phase speed ${c}_{\mathit{min}} $. It is also shown that the energy of depression solitary waves has a minimum at a wave speed ${c}_{m} $ slightly less than ${c}_{\mathit{min}} $, which suggests that such waves are stable for $c\lt {c}_{m} $ and unstable for $c\gt {c}_{m} $. This observation is verified by time-dependent computations using a high-order spectral method. These computations also indicate that solitary waves of elevation are likely to be unstable.

The instability of high-temperature jets is studied because of its importance to the analysis of gas-turbine engine exhaust flow, shock–shock interaction and bypass transition. The focus is on fluid–chemistry coupling, where the chemical time scales are supported by both reactive and inelastic molecular processes. The former are associated with dissociation/exchange reactions, while the latter are associated with transfers of vibrational quanta. The interaction affects both the instability growth rate and acoustic feedback by sustaining thermo-acoustic damping. Resonance conditions are identified as those that yield the maximum damping against the Damköhler number. The main results of the present study are the explanation of the dichotomy between vortical and acoustic modes in relation to the thermo-acoustic damping, and the analysis of the resonance condition as it depends on the physico-chemical properties of carbon/oxygen mixtures. The ability of a mode to support thermo-acoustic damping is related to the local convective Mach number of its most amplified frequency, and thus to the phenomenon of acoustic trapping in the jet core. Regarding the second issue, carbon dioxide acts as the best damper at low jet temperatures ${T}_{j} \approx 1000~\mathrm{K} $, where the vibrational relaxation is the main chemical scale, and up to ${T}_{j} = 3500~\mathrm{K} $ because its reactive chemistry resonates with the fluid fluctuation at a lower temperature than the dissociation of ${\mathrm{O} }_{2} $. At higher temperatures, oxygen is the best damper because of the larger endothermicity of the reactions it supports.

Applying the Floquet theory for linear motions (Howard & Yu, J. Fluid Mech., vol. 593, 2007, pp. 209–234) to the problem of wave propagation over a patch of periodic bottom corrugations in an otherwise flat seabed, we show that exact solutions to this scattering problem can be constructed without any constraint on the bottom amplitude and/or slope. These solutions are able to describe both the slowly and fast varying aspects of the flow, in contrast to the analyses based on the general ideas of slowly varying waves. We use as an example the well-studied Bragg scattering by a patch of bottom corrugations to present some quantitative results and comparisons with experimental data.

Nonlinear self-excited thermoacoustic oscillations appear in systems involving confined combustion in the form of coupled acoustic pressure oscillations and unsteady heat release rate. In this paper, we investigate the nonlinear transition undergone by thermoacoustic oscillations to flame blowout via intermittency, in response to variation in the location of the combustion source with respect to the acoustic field of the confinement. A ducted laminar premixed conical flame, stabilized on a circular jet exit with a fully developed exit velocity profile, was investigated. Transition to limit cycle oscillations from a non-oscillatory state was observed to occur via a subcritical Hopf bifurcation. Limit cycle oscillations underwent a further bifurcation to quasi-periodic oscillations characterized by the repeated formation of elongated necks in the flame that pinch off as pockets of unburned fuel–air mixture. The quasi-periodic state loses stability, resulting in an intermittent state identified as type II through recurrence analysis of phase space trajectories reconstructed from the acoustic pressure time trace. In this state, the flame undergoes repeated lift-off and reattachment. Instantaneous flame images suggest that the intermittent flame behaviour is influenced by jet flow dynamics.

It is demonstrated that a significant drag reduction for pressure-driven flows can be realized by applying spatially distributed heating. The heating creates separation bubbles that separate the stream from the bounding walls and, at the same time, alter the distribution of the Reynolds stress, thereby providing a propulsive force. The strength of this effect is of practical interest for heating with wavenumbers $\ensuremath{\alpha} = O(1)$ and for flows with small Reynolds numbers and, thus, it is of potential interest for applications in micro-channels. Explicit results given for a very simple sinusoidal heating demonstrate that the drag-reducing effect increases proportionally to the second power of the heating intensity. This increase saturates if the heating becomes too intense. Drag reduction decreases as ${\ensuremath{\alpha} }^{4} $ when the heating wavenumber becomes too small, and as ${\ensuremath{\alpha} }^{\ensuremath{-} 7} $ when the heating wavenumber becomes too large; this decrease is due to the reduction in the magnitude of the Reynolds stress. The drag reduction can reach up to 87 % for the heating intensities of interest and heating patterns corresponding to the most effective heating wavenumber.

A theory for the analytical prediction of microstructure of concentrated Brownian suspensions of spheres in simple-shear flow is developed. The computed microstructure is used in a prediction of the suspension rheology. A near-hard-sphere suspension is studied for solid volume fraction $\phi \leq 0. 55$ and Péclet number $Pe= 6\lrm{\pi} \eta \dot {\gamma } {a}^{3} / {k}_{b} T\leq 100$; $a$ is the particle radius, $\eta $ is the suspending Newtonian fluid viscosity, $\dot {\gamma } $ is the shear rate, ${k}_{b} $ is the Boltzmann constant and $T$ is absolute temperature. The method developed determines the steady pair distribution function $g(\mathbi{r})$, where $\mathbi{r}$ is the pair separation vector, from a solution of the Smoluchowski equation (SE) reduced to pair level. To account for the influence of the surrounding bath of particles on the interaction of a pair, an integro-differential form of the pair SE is developed; the integral portion represents the forces due to the bath which drive the pair interaction. Hydrodynamic interactions are accounted for in a pairwise fashion, based on the dominant influence of pair lubrication interactions for concentrated suspensions. The SE is modified to include the influence of shear-induced relative diffusion, and this is found to be crucial for success of the theory; a simple model based on understanding of the shear-induced self-diffusivity is used for this property. The computation of the microstructure is split into two parts, one specific to near-equilibrium ($Pe\ll 1$), where a regular perturbation expansion of $g$ in $Pe$ is applied, and a general-$Pe$ solution of the full SE. The predicted microstructure at low $Pe$ agrees with prior theory for dilute conditions, and becomes increasingly distorted from the equilibrium isotropic state as $\phi $ increases at fixed $Pe\lt 1$. Normal stress differences are predicted and the zero-shear viscosity predicted agrees with simulation results obtained using a Green–Kubo formulation (Foss & Brady, J. Fluid Mech., vol. 407, 2000, pp. 167–200). At $Pe\geq O(1)$, the influence of convection results in a progressively more anisotropic microstructure, with the contact values increasing with $Pe$ to yield a boundary layer and a wake. Agreement of the predicted microstructure with observations from simulations is generally good and discrepancies are clearly noted. The predicted rheology captures shear thinning and shear thickening as well as normal stress differences in good agreement with simulation; quantitative agreement is best at large $\phi $.

The effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.