The vibrational relaxation frequency measurements were made on mixtures of carbon dioxide and the light gases using a shock tube and a Mach-Zehnder interferometer. The temperature range covered was 350–1200 °K. It was discovered that in the case of helium the effectiveness of the carbon dioxide-helium collision increases with increasing temperature while in the case of hydrogen and deuterium the collision number displays an anomalous temperature behaviour. At about 1000 °K all the three light gases are almost equally efficient in exciting the vibrational modes of carbon dioxide.

The flow is examined in the neighbourhood of the trailing edge of slender aerodynamic shapes which terminate in either a cusp or a wedge. The manner in which the boundary layer reacts to the rapidly varying pressure field in such regions is analyzed using the method of matched asymptotic expansions. The case of a wedge is examined in greater detail and a criterion for separation to occur is established.

An electron beam technique was used to measure density profiles of strong shock waves in argon with high accuracy. The experimental results are compared with the results of theoretical models. Of the models that are available in enough detail for comparison, the best agreement with experiment is shown by the direct simulation Monte-Carlo method (Bird 1968), assuming an inverse 12th power molecular interaction force law. It is shown that the density maximum slope thickness is not sufficient for a detailed description of the shock wave structure.

A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophie flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.

A disturbance of finite amplitude λ, which is periodic in the direction of the axis of the channel, is superimposed on plane Poiseuille flow, and the subsequent development of the disturbance is studied. The disturbance is represented by an expansion in the eigenfunctions of the Orr-Sommerfeld equation with coefficients which are functions of the time, and an accurate numerical solution of the truncated system of non-linear ordinary differential equations for the coefficients is obtained.

It is found that even for Reynolds numbers R less than the critical value Rc, the flow breaks down when λ exceeds a critical value λc(R). This is shown in figure 11 for the case when the initial disturbance is represented by the first mode of the Orr-Sommerfeld equation. The development of this type of disturbance is illustrated in figures 1, 3 and 13 and, for the case of a higher-order mode initial disturbance, in figure 14. Near the time of breakdown, the curvature of the modified mean flow changes sign (figure 15), but a disturbance may die down even after a reversal in the sign of the curvature has taken place (see figure 2).

The stability of plane Poiseuille flow to disturbances of finite amplitude is affected by the characteristics of the higher-order modes of the Orr-Sommerfeld equation. As shown in figures 4, 10, and 12, and in figures 5, 6, and 7, these modes are either of a ‘boundary type’, characteristic of the region near the wall, or of an ‘interior type’, characteristic of the centre of the channel. The modes in the transition zone, where the two types merge, are easily amplified through mutual constructive interference, even though individually they have high damping coefficients. It is these transition modes which are mainly responsible for the breakdown through finite amplitude effects.

A Symposium on ‘The flow of fluid-solid mixtures’ was held at the University of Cambridge from 24 to 28 March 1969, under the auspices of the International Union of Theoretical and Applied Mechanics. There were 104 participants, representing 19 countries, and attendance was by invitation only. Since there will be no publication of the proceedings in full, the following condensed account of the developments described at the various sessions has been prepared for publication by three of the participants, all of whom were involved in the organization of the Symposium.

The development of reflected waves are studied when two shocks of unequal strength collide and when a shock collides with a constant temperature wall. Both these problems are examined using the Monte Carlo technique developed by Bird (1967). Some limitations upon this technique are suggested and a modified time advance parameter used.

Certain aspects of the transport of solid particles by a turbulent airstream are discussed, namely: the conveyance of particles in a horizontal pipe, including those carrying an appreciable electrostatic charge; the mechanism of deposition onto a solid wall; and the behaviour of fine particles in a shear flow, such as that in a round jet.

Rough estimates of the effect of the particles on the gaseous turbulence are made, and a primitive physical explanation is offered of the observed velocitylag and pressure drop associated with the transport of particles in a horizontal pipe, under conditions where the influence of the particles’ weight is significant.

Attention is drawn to the difficult problem of dynamically scaling a two-phase flow, and to the different types of interaction between the phases which can occur in a pipe according to its size, the gas velocity through it, and the physical characteristics of the particles.

The paper is an annotated version of a survey presented to the I.U.T.A.M. Symposium on ‘Flow of fluid-solid mixtures’ held in Cambridge during March 1969.

It is shown that there exist undamped solutions for perturbations of finite amplitude of plane Poiseuille flow, which are periodic in the direction of the axis of the channel. The shift in the ‘neutral curve’ as a function of the amplitude λ* of the disturbance is shown in figure 2. The solution is obtained by a perturbation method in which the eigenfunctions and the eigenvalue c are expanded in power series of the amplitude λ, as shown in (14), (15), (16) and (17). Near the neutral curve for a finite amplitude disturbance, the curvature of the mean flow shows a tendency to become negative (figure 5).