We present conceptual designs of viscometers corresponding to our new exact molecular simulation method (Dayal & James, J. Mech. Phys. Solids, vol. 58 (2), 2010, pp. 145–163). The molecular simulation method is a generalization of the method of Lees & Edwards (J. Phys. C: Solid State Phys., vol. 5, 1972, p. 1921), and includes a three-parameter family of incompressible flows, as well as compressible flows and unsteady flows exhibiting vortex stretching. All fluids are allowed. The method gives a way to simulate these flows using relatively few molecules, in the absence of a constitutive relation describing the fluid. This paper presents conceptual designs for viscometers that produce large families of these flows. The basic theme of this paper is that the flows discussed here are a better way to characterize the properties of complex fluids than the currently available methods, such as those based on viscometric flows.

This paper theoretically investigates the initial up-flow of a vertical turbulent fountain (round or plane) in a linearly stratified environment. Conservation equations (volume, momentum and buoyancy) are written under the Boussinesq approximation assuming an entrainment proportional to the vertical velocity of the fountain. Analytical integration leads to exact values of both density and flow rate at the maximal height reached by the fountain. This maximal height is expressed as a function of the release conditions and the stratification strength and plotted from a numerical integration in order to exhibit overall behaviour. Then, analytical expressions for the maximal height are derived from asymptotic analysis and compared to experimental correlations available for forced fountains. For weak fountains, these analytical expressions constitute a new theoretical model. Finally, modified expressions are also proposed in the singular case of an initially non-buoyant vertical release.

We extend previous work of Boyer, Davies & Guo (Fluid Dyn. Res., vol. 21, 1997, pp. 381–401) to consider the evolution of an initially two-layer stratified fluid in a cylindrical tank which is driven by a horizontal rotating disk. The turbulent motions induced by the disk drive entrainment at the interface, and similarly to the results of Boyer et al. (1997), the layer nearer to the disk deepens. Through high-frequency conductivity probe measurements, we establish that the deepening layer is very well-mixed, and the thickness of the interface between the two evolving layers appears to be approximately constant. Under certain circumstances, we find that the rate of increase in depth of the deepening layer decreases with time, at variance with the results of Boyer et al. (1997), and implying that the characteristic velocity in the deepening layer decreases as the upper layer deepens. We propose that such time-dependent deepening, and the associated weakening of the upper-layer velocities, occurs naturally because of the combined power requirements of entrainment and layer homogenization which inhibit, when the stratification is very strong, the characteristic velocities of the deepening layer approaching the (constant) velocities of the driving disk, as assumed by Boyer et al. (1997).

The flow structure on low-aspect-ratio wings arising from pitch-up motion is addressed via a technique of particle image velocimetry. The objectives are to: determine the onset and evolution of the three-dimensional leading-edge vortex; provide complementary interpretations of the vortex structure in terms of streamlines, projections of spanwise and surface-normal vorticity, and surfaces of constant values of the second invariant of the velocity gradient tensor (iso- surfaces); and to characterize the effect of wing planform (rectangular versus elliptical) on this vortex structure. The pitch-up motion of the wing (plate) is from 0 to over a time span corresponding to four convective time scales, and the Reynolds number based on chord is 10 000. Volumes of constant magnitude of the second invariant of the velocity gradient tensor are interpreted in conjunction with three-dimensional streamline patterns and vorticity projections in orthogonal directions. The wing motion gives rise to ordered vortical structures along its wing surface. In contrast to development of the classical two-dimensional leading-edge vortex, the flow pattern evolves to a strongly three-dimensional form at high angle of attack. The state of the vortex system, after attainment of maximum angle of attack, has a similar form for extreme configurations of wing planform. Near the plane of symmetry, a large-scale region of predominantly spanwise vorticity dominates. Away from the plane of symmetry, the flow is dominated by two extensive regions of surface-normal vorticity, i.e. swirl patterns parallel to the wing surface. This similar state of the vortex structure is, however, preceded by different sequences of events that depend on the magnitude of the spanwise velocity within the developing vortex from the leading edge of the wing. Spanwise velocity of the order of one-half the free stream velocity, which is oriented towards the plane of symmetry of the wing, results in regions of surface-normal vorticity. In contrast, if negligible spanwise velocity occurs within the developing leading-edge vortex, onset of the regions of surface-normal vorticity occurs near the tips of the wing. These extremes of large and insignificant spanwise velocity within the leading-edge vortex are induced respectively on rectangular and elliptical planforms.

Axisymmetric droplet impact on a hydrophilic substrate with one pore of relatively large radius is numerically studied using diffuse-interface methods. The flows above the substrate and in the capillary are fully resolved by a Navier–Stokes solver that accounts for contact-angle hysteresis. Upon impact, the infiltration of the drop into the capillary is seen to follow one or more of the three regimes identified in recent experiments (Delbos, Lorenceau & Pitois, J. Colloid Interface Sci., vol. 341, 2010, p. 171): complete penetration, partial penetration as a slug, and re-entry with bubble entrapment. The agreement on experimentally measured quantities, such as transition criteria and slug lengths, is quantitative. On this basis we reveal previously unidentified flow phenomena, investigate flow details that are not accessible experimentally, expand the parameter space considered previously, identify the key asymptotic regimes in the penetration transient, generalize the results in terms of relevant dimensionless groups, and provide a further step (using a multi-capillary arrangement as an idealization of a porous substrate) towards the ultimate purpose of such work, which is the understanding of inertial effects with porous substrates, including eccentric impacts. The significant effect of impact inertia is revealed as a spatial anchoring of a stagnation region, formed and persisting for most of the transient. As a consequence, fluid within an upright cylinder is destined to enter the capillary, and this is in agreement with the hypothesis of Delbos et al. in interpreting the amounts of liquid found inside the capillary, except that the radius of the cylinder is 30 % greater than the capillary radius. The remainder of the liquid spreads laterally on the substrate surface, and the slug regime is a consequence of this partition. Numerical experiments also indicate that after reaching the maximum-spread area, the lamella on the substrate tends to refill the capillary and entrap a bubble, unless contact-angle hysteresis hinders the radially inward motion of the lamella.

Turbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an exact scaling law for heat transfer by geostrophic convection, , by considering the stability of the thermal boundary layers, where , and are the Nusselt, Rayleigh and Ekman numbers, respectively, and is the critical Rayleigh number for the onset of convection. Furthermore, we use the scaling behaviour of the thermal and Ekman boundary layer thicknesses to quantify the necessary conditions for geostrophic convection: . Interestingly, the predictions of both heat flux and regime transition do not depend on the total height of the fluid layer. We test these scaling arguments with data from laboratory and numerical experiments. Adequate agreement is found between theory and experiment, although there is a paucity of convection data for low .

The flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, the discrepancy is addressed. First, weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and, second, new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

The aerodynamically driven annular liquid sheet exhibits a complex nonlinear instability. Novel interfacial velocimetry experiments suggest that two distinct physical sources of instability may be present. The first is the well-known free shear layer instability, which is quasi-sinusoidal and nonlinear. The second is a distinct nonlinear rupturing instability, modulated on the previous one. It may be directly driving primary atomization. This instability has not been previously observed in isolation and is inherently nonlinear and non-sinusoidal. Novel application of Koopman analysis and the Hilbert transform permit investigation of these distinct instabilities. A greater understanding of the rupturing instability may lead to a better understanding of atomization phenomena.