The multipole representation technique of Gluckman, Pfeffer & Weinbaum for slow, viscous, axisymmetric motion has been applied to a system of two spheroids. The two particles may have different shapes and volumes. The limitations of this method have been studied through calculations of the drag forces and velocities of particles with aspect ratios from 0·1 to 10 and relative volumes V from 1 to 103. The multipole-expansion convergence is quite slow for large relative volumes and requires on the order of $4 \times V^{\frac{1}{3}}$ multipoles. Wild fluctuations in the drag as the number of multipoles increases were found for large oblate spheroids. Relative velocities are given quite accurately for separations of the centres greater than 1·02 times the minimum separation. Comparisons are made with previous results and approximate theories for two spheres, for non-identical particles at large separation, and for a sphere near a large spheroid.

A general class of solutions is studied describing three-dimensional steady convection flows in a fluid layer heated from below with boundaries of low thermal conductivity. Non-linear properties of the solutions are analysed and the physically realizable convection flow is determined by a stability analysis with respect to arbitrary three-dimensional disturbances. The most surprising result is that square-pattern convection is preferred in contrast to two-dimensional rolls that represent the only form of stable convection in a symmetric layer with highly conducting boundaries. The analysis is carried out in the limit of infinite Prandtl number and for a particular boundary configuration. But it is shown that the results hold for arbitrary Prandtl number to the order to which they have been derived and that other assumptions about the boundaries require only minor modifications as long as their thermal conductance remains low.

Nonlinear capillary instability of an axisymmetric infinite liquid column is investigated with an initial velocity disturbance consisting of a fundamental and one harmonic component. A third-order solution is developed using the method of strained co-ordinates. For the fundamental disturbance alone, the solution shows that a cut-off zone of wavenumbers (k) exists such that the surface waves grow exponentially below the cut-off zone, linearly in the middle of the zone (near k = 1), and an oscillatory solution exists for wavenumbers above the boundary of the zone. For an input including both the fundamental and a harmonic, all wave components grow exponentially when the fundamental is below the cut-off zone. Using a Galilean transformation, the solution is applied to a progressive jet issuing from a nozzle. The jet breaks into drops interspersed with smaller (satellite) drops for k < 0·65; no satellites exist for k > 0·65. It is shown theoretically that the formation of satellites can be controlled by forcing the jet with a suitable harmonic added to the fundamental.

The behaviour of a perturbed capillary jet is experimentally determined by studying the jet from the time it emerges from a small hole to the point at which individual droplets of fluid begin to form. Under any particular set of externally applied experimental parameters, i.e. jet velocity, disturbance wavenumber and amplitude, there is a unique, minimum time to this breakup into drops. This characteristic is needed to relate the magnitude of the input voltage to the modulating device and the output velocity perturbation that it produces. Using this relationship we then compare the experimentally produced profiles of jet shape to corresponding ones calculated by using the theory of Chaudhary & Redekopp (1980). The agreement is satisfactory, especially for small values of input voltage. Then, in the neighbourhood of the cutoff wavenumber, we show that the predicted linear growth of the jet profile is also reproduced in the experimental model.

We continue the experiments of Chaudhary & Maxworthy (1980) to include the behaviour at and beyond the point along the jet at which individual drops interspersed with small satellite drops begin to form. In particular, we show how the perturbation wavenumber and amplitude for a fundamental disturbance alone combine to give a variety of modes of breakup into drops and a variety of patterns of drop recombination further downstream. We then show how the addition of a third harmonic to this fundamental can be used in a variety of parameter combinations to control the behaviour of the satellite drops and in some cases eliminate them completely.

Two problems exhibiting breakdown in local similarity solutions are discussed, and the appropriate asymptotic form of the exact solution is determined in each case. The first problem is the very elementary problem of pressure driven flow along a duct whose cross-section has a sharp corner of angle 2α. When 2α < ½π, a local similarity solution is valid, whereas, when 2α > ½π, the solution near the corner depends on the global geometry of the cross-section. The transitional behaviour when 2α = ½π is determined.

The second problem concerns low-Reynolds-number flow in the wedge-shaped region |θ| < α when either a normal velocity proportional to distance from the vertex is imposed on both boundaries, or a finite flux 2Q is introduced or extracted at the vertex (the Jeffery–Hamel problem). It is shown that the similarity solution in either case is valid only when 2α < 2αc ≈ 257·5°; a modified problem is solved exactly revealing the behaviour when α > αc, and the transitional behaviour when α = αc (when the similarity solutions become infinite everywhere). An interesting conclusion for the Jeffery–Hamel problem is that when α > αc, inertia forces are of dominant importance throughout the flow field no matter how small the source Reynolds number 2Q/ν may be.

The streamline patterns of some simple two-dimensional Stokes flows are studied and the results used both to understand and to predict the streamlines of flows in more complicated geometries, in particular the streamlines of flows that contain eddies or regions of closed streamlines. Initially, streamline patterns are studied locally, either around some special point, such as a stagnation point or a point where a streamline meets a wall, or in a special region, such as a corner. The use of these local analyses is illustrated by finding the streamlines for shear flow around a rotating cylinder; the illustration also shows how fluid in Stokes flow can be turned back on itself (‘blocked’). The local analyses of flow in a corner are used to understand the eddy patterns that have been discovered in a variety of flows. The eddies occur in corner-like regions and in these regions the flow can be regarded as the superposition of two components. One component, the eddy flow, is the result of flow outside the corner stirring the fluid in the corner, while the other is the direct result of local conditions in the corner. The competition between these two components determines whether eddies actually appear in a given flow. Finally, the approach developed here is applied to a new flow situation, namely a shear flow which is bounded by a moving wall and which contains a stationary cylinder touching the wall. The streamlines deduced for different ratios of the shear strength to the wall velocity show both new eddy patterns and unexpected regions of blocked flow.

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann number M and interaction parameter N have very large values and the magnetic Reynolds number is extremely small.

The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.

Results from experiments with four different ducts are reported when magnitudes of the field strength and mean velocity are such that the Hartmann number and interaction parameter are large. The first is a straight, circular, highly conducting wall duct situated in a non-uniform transverse magnetic field. Results suggest that as a first approximation the flow may be regarded as being fully developed throughout. In fact there is a slight distortion of the flow in the non-uniform field region revealed by hot-film probe measurements of the streamwise velocity which varies in a novel but readily explicable manner. The second duct is similar except that its wall is weakly conducting. A pressure drop across the non-uniform field region suggests that the behaviour of the flow is weakly reminiscent of that in a non-conducting duct. The two other ducts also have weakly conducting walls but contain either one or two 90° bends and are situated in a uniform field. Symmetry of each duct about its mid-point leads to symmetric potential distributions which indicate the existence of two symmetrically arranged recirculating current flows and these lead to pressure drops across the bends. In the duct with two bends, part of it, the offset, lies parallel to the field lines and a surprising prediction relating the pressure drop across the offset to N finds some support.

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.

The idea behind the general theory of ‘hydraulic’-type problems as described by Gill (1977) is applied to an inertial boundary current. The flow considered is a single-layer inviscid fluid flowing under gravity along a rotating, irregular wall. It is shown that owing to variations in the curvature of the wall the boundary current may be controlled in the hydraulic sense at sections along the wall classified as ‘bays’. It is also shown that because of such variations in geometry the flow can be ‘blocked’. The behaviour of the flow in response to variations in the bottom topography, such as a varying lateral slope or a broad-crested weir, is discussed with particular reference to conditions under which the flow is either controlled or blocked.