The effect of pair interactions between charged macromolecules on the bulk stress is calculated for the Newtonian low-shear limit. Electrostatic force laws are derived for molecular conformations corresponding to the limits of weak and strong intramolecular repulsions and used to determine the equilibrium pair distribution function and the perturbation due to the flow. Intramolecular and near-field intermolecular hydrodynamic interactions are neglected as appropriate for so-called free draining macromolecules. The resulting bulk stress contains separate contributions from the far-field hydrodynamic interactions and the electrostatic forces. The coefficient of the O(c2) term in the viscosity which equals 0.4 in the purely hydrodynamic limit is predicted to increase dramatically with decreasing ionic strength for charged macromolecules in agreement with experimental data in the literature.

The distortion by a linear flow of the electric double layer around a small particle is studied for the case of a charge cloud which is thick in comparison with the particle radius and for arbitrary flow strengths, including those which are strong enough to produce a significant distortion of the cloud. For weak flows a second-order-fluid approximation is obtained for the stress contribution for a dilute suspension of such particles. For arbitrarily strong flows integral representations of the charge density and numerical calculations of the stress contribution are given for three representative flows: simple shear, axisymmetric strain and two-dimensional straining motion.

Using the principles of continuum mechanics, a theory is developed for describing quantitatively the sedimentation of small particles in vessels having walls that are inclined to the vertical. The theory assumes that the flow is laminar and that the particle Reynolds number is small, but c0, the concentration in the suspension, and the vessel geometry are left arbitrary. The settling rate S is shown to depend upon two dimensionless groups, in addition to the vessel geometry: a sedimentation Reynolds number R, typically O(1)-O(10); and Λ, the ratio of a sedimentation Grashof number to R, which is typically very large. By means of an asymptotic analysis it is then concluded that, as Λ → ∞ and for a given geometry, S can be predicted from the well-known Ponder-Nakamura-Kuroda formula which was obtained using only kinematic arguments. The present theory also gives an expression for the thickness of the clear-fluid slit that forms underneath the downward-facing segment of the vessel walls, as well as for the velocity profile both in this slit and in the adjoining suspension.

The sedimentation rate and thickness of the clear-fluid slit were also measured in a vessel consisting of two parallel plates under the following set of conditions: c0 ≤ 0·1, R ∼ O(1), O(10)5 ≤ Λ ≤ O(107) and 0° ≤ α ≤ 50°, where α is the angle of inclination. Excellent agreement was obtained with the theoretical predictions. This suggests that the deviations from the Ponder-Nakamura-Kuroda formula reported in the literature are probably due to a flow instability which causes the particles to resuspend and thereby reduces the efficiency of the process.

Interferometric data were obtained in the UTIAS 10 × 18 cm hypervelocity shock tube of oblique shock-wave reflexions in nitrogen at initial temperatures and pressures of about 300 K and 15 torr. The shock-Mach-number range covered was 2 ≤ Ms ≤ 8 over a series of wedge angles 2° ≤ θw ≤ 60°. Dual-wavelength laser interferograms were obtained by using a 23 cm diameter field of view Mach-Zehnder interferometer. In addition to our numerous results the available data for nitrogen, air and oxygen obtained over the last three decades were also utilized. It is shown analytically and experimentally that in non-stationary flows seven domains exist in the (Ms, θw) plane where regular reflexion (RR), single-Mach reflexion (SMR), complex-Mach reflexion (CMR) and double-Mach reflexion (DMR) can occur. In addition, the transition boundaries between these regions were established. The experimental results from many sources substantiate the present analysis, and areas of disagreement which existed in the literature are now clarified and resolved. It is shown that real-gas effects have a significant influence on the size of the regions and their boundaries. The comprehensive, accurate and sensitive isopycnic data will form a base for comparing existing and future numerical analyses of such complex flows.

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

Experimental investigations in the region following the passage of an isolated turbulent spot in a laminar boundary layer reveal the existence of a pair of oblique wave packets. These packets are swept at an angle of approximately 40°, and exhibit frequency and wave speed characteristics in agreement with predictions made for oblique Tollmien-Schlichting waves. No waves exist near the centreline of the spot.

Several observations of the breakdown of this ordered motion into a new turbulent spot are shown. This breakdown is accompanied by the appearance of an intense shear layer inclined to the wall.

The higher-order theory of the Weissenberg effect is developed as a perturbation of the state of rest. The perturbation is given in powers of the angular frequency Ω of the rod and the solution is carried out to O(Ω4). The perturbation induces a slow-motion expansion of the stress into Rivlin-Ericksen tensors in combinations which are completely characterized by five viscoelastic parameters. The effects of each of the material parameters may be computed separately and their overall effect by superposition. The values of the parameters may be determined by measurement of the torque, surface angular velocity and height of climb. Such measurements are reported here for several different sample fluids. Good agreement between the third-order theory and measured values of the velocity is reported. Secondary motions which appear at are computed using biorthogonal series. The analysis predicts the surprising fact that secondary motions run up the climbing bubble against gravity and intuition.

The equations for the rotation of non-axisymmetric ellipsoids in a simple shear flow at low Reynolds numbers are derived in terms of Euler angles. Numerical solutions of this third-order system of equations show a doubly periodic structure to the rotation, with a change in the general nature of the solutions when a certain planar rotation of the particle becomes unstable. Some analytic progress can be made for nearly spherical ellipsoids and for nearly axisymmetric ellipsoids. The near spheres show the same qualitative behaviour as the general ellipsoids. Quite small deviations from axial symmetry are found to produce large changes in the rotation.