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Article Dans Une Revue Physical Review Fluids Année : 2016

Taylor's experiment in a periodically sheared particulate suspension

Résumé

We revisit Taylor's experiment investigating the evolution of a blob of dye in a periodically sheared suspension of non-Brownian particles. Above a critical strain amplitude, particulate suspensions are subject to phase transition where reversibility is lost and particles fail to return to their original positions. We investigate the effect of this transition on the dispersion of a blob of dye. Beyond the critical strain, the dispersion of the blob is found to increase significantly. The dispersion coefficient of the blob of dye is measured and compared to the self-diffusivity coefficient of the particles. In 1966, Taylor illustrated in a now famous experiment the reversibility of Stokes flow [1]. A blob of dye is initially injected in a Couette cell filled with a very viscous and Newtonian fluid. When rotating one of the cylinder, the fluid is linearly sheared and the blob of dye stretches into a thin filament until almost disappearing. Then, upon reversing the rotation for the same number of turns, the drop astoundingly recovers its initial shape (except for slight blurring due to molecular diffusion). Inspired by Taylor's work, we performed the exact same experiment but in a suspension of non-Brownian particles to investigate how the presence of particles within the fluid breaks the reversibility of the flow and influences the dispersion process of the blob of dye. Under periodic shear, Pine et al. [2] demonstrated that non-Brownian suspensions undergo a dynamical phase transition. For a given particulate volume fraction and a small enough strain amplitude, the suspension relaxes to an absorbing reversible state in which particles return to their original position after every cycle of shear. However, when the strain amplitude exceeds a critical value γ c , which depends on the volume fraction and the particle roughness [3], the suspension transitions to a fluctuating state: the particles do not return to their original positions, and, when tracked stroboscopically at the end of each cycle of shear, the particles exhibit large fluctuations analogous to a random walk. In that fluctuating state, the loss of reversibility of the particles motion should also induce a loss of reversibility in the fluid motion. The goal in the present Rapid Communication is to perform Taylor's experiment in a particulate suspension to study the effect of this transition on the dispersion of the blob of dye. Under continuous shear, the phenomenon called " shear-induced diffusion " , which was widely investigated [3–10], was shown to significantly enhance the transfer of heat [9,11] or mass [12,13] across suspensions of non-Brownian particles. This enhancement occurs since under shear, particles within the fluid constantly collide with one another and change streamlines. The particles thus generate disturbances within the fluid which promote the dispersion of the scalar (temperature or concentration), prelude to its subsequent mixing. Particles also significantly affect transfers close to boundaries: the particle rotation was shown to disrupt the diffusive boundary layer by a " rolling-coating effect " (Souzy et al. [13]) which convects the scalar at a constant rate from the wall, where it is injected, to the bulk of the suspension. The dispersion enhancement of a scalar field has already been exensively studied in suspensions undergoing a continuous shear flow, but it has not yet been studied under periodic shear. Our motivation is that this latter flow configuration is particularly appealing since, after each cycle of shear, the affine part of the flow (the reversible part) cancels out. Therefore, by measuring the evolution of the blob of ink stroboscopically, i.e., at the end of each cycle of shear, one can investigate the blob's dispersion solely focusing on the effect of the fluctuations induced by the particles, not having to account for the background linear stretching as in a continuous shear.
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hal-01768667 , version 1 (17-04-2018)

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Mathieu Souzy, Phong Pham, Bloen Metzger. Taylor's experiment in a periodically sheared particulate suspension. Physical Review Fluids, 2016, 1 (4), pp.42001 - 42001. ⟨10.1103/PhysRevFluids.1.042001⟩. ⟨hal-01768667⟩
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