George Keith Batchelor. 8 March 1920 – 30 March 2000

George Batchelor was a pioneering figure in two branches of fluid dynamics: turbulence, in which he became a world leader over the 15 years from 1945 to 1960; and suspension mechanics (or ‘microhydrodynamics’), which developed under his initial impetus and continuing guidance throughout the 1970s and 1980s. He also exerted great influence in establishing a universally admired standard of publication in fluid dynamics through his role as founder Editor of the Journal of Fluid Mechanics , the leading journal of the subject, which he edited continuously over four decades. His famous textbook, An introduction to fluid dynamics , first published in 1967, showed the hand of a great master of the subject. Together with D. Küchemann, F.R.S., he established in 1964 the European Mechanics Committee (forerunner of the present European Society for Mechanics), which over the 24-year period of his chairmanship supervised the organization of no fewer than 230 European Mechanics Colloquia spanning the whole field of fluid and solid mechanics; while within Cambridge, where he was a Fellow of Trinity College and successively Lecturer, Reader and Professor of Applied Mathematics, he was an extraordinarily effective Head of the Department of Applied Mathematics and Theoretical Physics from its foundation in 1959 until his retirement in 1983.

Hydrodynamic diffusion of suspended particles: a symposium

Hydrodynamic diffusion refers to the fluctuating motion of non-Brownian particles (or droplets or bubbles) in a dispersion, which occurs due to multiparticle interactions. For example, in a concentrated sheared suspension, particles do not move along streamlines but instead exhibit fluctuating motions as they tumble around each other (figure 1a). This leads to a net migration of particles down gradients in particle concentration and in shear rate, due to the higher frequency of encounters of a test particle with other particles on the side of the test particle which has higher concentration or shear rate. As another example, suspended particles subject to sedimentation or fluidization do not generally move relative to the fluid with a constant velocity, but instead experience diffusion-like fluctuations in velocity due to interactions with neighbouring particles and the resulting variation in the microstructure or configuration of the suspended particles (figure 1b). In flowing granular materials, the particles interact through direct collisions or contacts; these collisions also cause the particles to undergo fluctuating motions characteristic of diffusion processes. Although the existence and importance of hydrodynamic diffusion of particles have been embraced only in the past several years, the subject has already captured the attention of a growing number of researchers in several diverse fields (e.g. suspension mechanics, fluidization, materials processing, and granular flows).

Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

Constitutive equations in suspension mechanics. Part 1. General formulation

Neither the phenomenological nor the structural approach to the determination of constitutive equations has yet shown itself to be capable of producing useful and predictive descriptions of the majority of technologically important complex fluids. In the present paper we explore the suggestion that significant progresscanbe made when these two complementary approaches to rheology are combined. For this initial study we restrict our attention to materials which can be modelled as a suspension of particles in a Newtonian fluid, thereby including most polymer solutions while excluding polymer melts. By applying phenomenological techniques to the basic formulation of suspension mechanics we are able to deduce a common simplified constitutive model for all suspension-like materials and to reveal its physical origin. The present analysis demonstrates that the constitutive model of Hand (1962), involving a single second-order tensor, is not sufficiently general for a rigorous description of the majority of suspension-like materials. Consideration of the constitutive forms for the limiting cases of near-equilibrium and strongly non-equilibrium microstructure suggests, however, that Hand's model may provide a reasonable approximation to the exact constitutive behaviour which is useful over the whole range of flow strengths.