The lift on a solid sphere moving along a wall in a parabolic shear flow is obtained as a regular perturbation problem for low Reynolds number when the sphere is in the inner region of expansion. Comprehensive results are given for the 10 terms of the lift, which involve the sphere translation and rotation, the linear and quadratic parts of the shear flow and all binary couplings. Based on very accurate earlier results of a creeping flow in bispherical coordinates, precise results for these lift terms are obtained for a large range of sphere-to-wall distances, including the lubrication region for sphere-to-wall gaps down to 0.01 of a sphere radius. Fitting formulae are also provided in view of applications. The migration velocity of an inertialess spherical particle is given explicitly, for a non-rotating sphere with a prescribed translation velocity and for a freely moving sphere in a parabolic shear flow. Values of the lift and migration velocity are in good agreement with earlier results whenever available.

The linear stability of the plane Couette flow against thermoconvective rolls is studied. The case of a flow without a boundary-imposed temperature gradient is investigated. The non-uniform, possibly unstable, basic temperature distribution is caused by the effect of the internal viscous heating. Asymmetric thermal boundary conditions are considered: the bottom boundary is adiabatic, while the top boundary is isothermal. The focus is on a fluid with a large, mathematically infinite, Prandtl number, although the two-dimensional transverse roll instability is discussed also for a finite Prandtl number. The transition to the instability is described through the governing parameter GePe2, where Ge is the Gebhart number and Pe is the Péclet number. The response of the basic Couette flow to arbitrarily oriented oblique rolls is tested, so that a complete set of disturbance modes is taken into account. It is shown that the Couette flow is more unstable to longitudinal rolls than to any other oblique roll mode.

The characterization of electrosprayed droplets by means of retarding potential and time-of-flight techniques yields relevant information on the physics of the cone–jet itself. The experimental data reveal that a significant fraction of the electric power injected in the cone–jet is degraded by ohmic and viscous dissipations, as well as converted into surface energy. The degradation of energy can be cast in the form of a measurable voltage deficit that depends on the fluid's viscosity, electrical conductivity and dielectric constant, but is independent of its flow rate. These experimental facts require an identical scaling rt for both the characteristic radial and axial lengths of the cone-to-jet transition, the region where conduction current is transformed into convected surface charge. This fundamental scale is the geometric mean of the electrical relaxation length and the distance from the Taylor cone apex where the dynamic and capillary pressures become comparable. These two lengths are of the same order in a wide range of operational conditions, which further confirms the importance of the role played by electrical relaxation phenomena in the physics of cone–jets. The validity of rt is further supported by the numerical results of Higuera (J. Fluid Mech., vol. 484, 2003, pp. 303–327), whose profiles of the transition region non-dimensionalized with rt remain unchanged when the flow rate is varied. Finally, the dissipation of energy significantly increases the temperature of fluids with high conductivities, and future models for the cone–jets of these liquids will need to account for thermal effects.

Two aspects of small-scale turbulence are currently regarded universal, as they have been reported for a wide variety of turbulent flows. Firstly, the vorticity vector has been found to display a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain rate tensor; and secondly, the joint probability density function (p.d.f.) of the second and third invariant of the velocity gradient tensor, Q and R, has a characteristic teardrop shape. This paper provides an explanation for these universal aspects in terms of a spatial organization of coherent structures, which is based on an evaluation of the average flow pattern in the local coordinate system defined by the eigenvectors of the strain rate tensor. The approach contrasts with previous investigations, which have relied on assumed model flows. The present average flow patterns have been calculated for existing experimental (particle image velocimetry) or numerical (direct numerical simulation) datasets of a turbulent boundary layer (TBL), a turbulent channel flow and for homogeneous isotropic turbulence. All results show a shear-layer structure consisting of aligned vortical motions, separating two larger-scale regions of relatively uniform flow. Because the directions of maximum and minimum strain in a shear layer are in the plane normal to the vorticity vector, this vector aligns with the remaining strain direction, i.e. the intermediate eigenvector of the strain rate tensor. Further, the QR joint p.d.f. for these average flow patterns reveals a shape reminiscent of the teardrop, as seen in many turbulent flows. The above-mentioned organization of the small-scale motions is not only found in the average patterns, but is also frequently observed in the instantaneous velocity fields of the different turbulent flows. It may, therefore, be considered relevant and universal.