Self-diffusion of particles in shear flow of a suspension

Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficient D was calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values of D are not of high accuracy, but are correct to within a factor of two. In the range 0 D/a 2 ω increases from zero linearly with ϕ up to D/a 2 ω ≅ 0·02 (where ϕ = volumetric concentration of particles, a = particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 D/a 2 ω is not clear because of experimental scatter, but in this range D/a 2 ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value of D/a 2 ω.

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