The book provides an excellent compendium of modern approaches to the Boltzmann equation and to techniques for obtaining exact solutions to approximate forms of the equation, or approximate solutions to the complete equation. Primary emphasis in the book is on the application of classical kinetic theory to the flow of monatomic neutral gases. The problems considered span the range of Knudsen numbers from continuum flow to free molecule flow. The solution techniques discussed include analytical solutions to model equations, moment methods, perturbation methods, variational methods, discrete velocity methods, and Monte Carlo methods. Of necessity, most of the discussion pertains to problems capable of being represented by a linearized version of the Boltzmann equation or model equation. Of particular interest is a complete chapter devoted to gas surface interactions and the implications of such interactions relative to boundary conditions for the Boltzmann equation. The book ends with a presentation of existence and uniqueness results for the Boltzmann equation. The bibliography is extensive and references pertinent material through 1974. The book should be of interest to all involved in solution of flow problems requiring the use of kinetic theory methods.

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A model for the intermittent fine structure of high Reynolds number turbulence is proposed. The model consists of slender axially strained spiral vortex solutions of the Navier–Stokes equation. The tightening of the spiral turns by the differential rotation of the induced swirling velocity produces a cascade of velocity fluctuations to smaller scale. The Kolmogorov energy spectrum is a result of this model.

Stokes flow through a random, moderately dense bed of spheres is treated by a generalization of Brinkman's (1947) method, which is applicable to both stationary beds and suspensions. For stationary beds, Darcy's law with a permeability result similar to Brinkman's is derived. For suspensions an effective viscosity μ/(1–2·60ψ) is found, where ψ is the volume fraction of spheres. Also, an expression for the settling velocity is derived.

Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross-section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting and kissing and tumbling into stable cross-stream arrays. Drafting, kissing and tumbling are rearrangement mechanisms in which one sphere is captured in the wake of the other. The kissing spheres are aligned with the stream. The streamwise alignment is massively unstable and the kissing spheres tumble into more stable cross-stream pairs of doublets which can aggregate into larger relatively stable horizontal arrays. Cross-stream arrays in beds of spheres constrained to move in two dimensions are remarkable. These arrays may even coalesce into aggregations of close-packed spheres separated by regions of clear water. A somewhat weaker form of cooperative motion of cross-stream arrays of rising spheres is found in beds of square cross-section where the spheres may move freely in three dimensions. Horizontal arrays rise where drafting spheres fall because of greater drag. Aggregation of spheres seems to be associated with relatively stable cooperative motions of horizontal arrays of spheres rising in their own wakes.