A similarity solution is found which describes the flow impinging on a flat wall at an arbitrary angle of incidence. The technique is similar to a method used by Jeffery (1915) and discussed more recently by Peregrine (1981).

Brenner's general results for the force and torque experienced by an arbitrary particle simultaneously translating and rotating in a linear shear flow are applied to the spherical cap. The cap's five fundamental resistance tensors are determined and the corresponding tensors for the sphere and circular disk are recovered as special cases. The problem of a freely moving cap in a linear shear is considered and the resulting translational and rotational motions are analysed. The cap's centre of free rotation is found and trajectories of this point are plotted in a few instances. The cap is also found to possess a ‘point of planar motion’ which always moves in a plane perpendicular to the vorticity vector of the undisturbed shear regardless of the initial orientation of the cap. It is shown that the motion of the cap actually serves as a model for the motions of all ‘oblate’ asymmetric bodies of revolution which are moving freely in a linear shear.

In this paper, it is shown that if two spheres of equal radii areplaced axisymmetrically in a steady Stokes stream, separation of theflow from the spheres occurs if the distance between their centresis less than approximately 3-67 times the sphere radius. For sphereswhose spacing is less than this value, wakes form on both spheresand the fluid within the wakes moves in closed eddy type motion.When the distance between the centres of the spheres is less thanapproximately 3.22 times the sphere radius, a cylinder of fluidlinks both spheres, and within this cylinder the fluid rotates inone or more ring vortices, the number of vortices increasing as thedistance between the spheres is decreased. When the spheres are incontact, the fluid rotates in an infinite set of nested ringvortices.

The axisymmetric streaming Stokes flow past a body which contains a surface concave to the fluid is considered for the simplest geometry, namely, a spherical cap. It is found that a vortex ring is attached to the concave surface of the cap regardless of whether the oncoming flow is positive or negative. A stream surface ψ = 0 divides the vortex from the mainstream flow, and a detailed description of the flow is given for the hemispherical cup. The local velocity and stress in the vicinity of the rim are expressed in terms of local co-ordinates.

A study is made of Stokes flows in which a line rotlet or stokeslet is in the presence of a circular cylinder in a viscous fluid. In contrast to the Stokes Paradox for flow past an isolated cylinder, it is shown that if either type of singularity, with suitably chosen strength and location, is present, there can exist a flow which is uniform at infinity. A similar phenomenon can occur when two equal cylinders rotate with equal and opposite angular velocities, and the flow pattern is then such that there is a closed streamline enclosing both cylinders.