Taylor dispersion in concentrated suspensions of rotating cylinders

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Abstract
Laminar heat- or mass-transfer processes are theoretically investigated for two-dimensional spatially periodic suspensions of circular cylinders, each member of which rotates steadily about its own axis under the influence of an external couple. The novelty of the ensuing convective-diffusion phenomena derives from the absence of convective motion at the suspension lengthscale (the ‘macroscale’), despite its presence at the interstitial or particle lengthscale (the ‘microscale’). The latter fluid motion consists of a cellular vortex-like flow characterized by closed streamlines. These periodically closed streamlines give rise to a situation in which there exists no net flow at the macroscale. The resulting macroscale transport of heat or mass thus proceeds purely by conduction, the rate being characterized by a tensor diffusivity — dependent upon the angular velocity of the cylinders. Matched-asymptotic-expansion methods together with generalized Taylor dispersion theory are used to calculate this macroscale conductivity in the dual limit of large rotary Péclet numbers and small gap widths between adjacent cylinders. This prototype study illustrates the fact that the usual separation of transport processes into distinct convective and conductive contributions is not generally a scale-invariant concept; that is, microscale convec-tional contributions to the transport of heat or mass are not generally representable by corresponding macroscale convectipnal contributions to the transport. Possible applications of the analysis exist in the area of enhanced conduction rates in ferrofluids or other dipolar fluids rotating relative to a fixed external field (or conversely).

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