Rhéologie des suspensions non Browniennes concentrées : une étude numérique

Abstract : Suspensions of rigid grains in a fluid constitute a class of complex fluids that present a rich rheology. Even simpler cases of non-Brownian, non-colloidal spherical grains suspended in a Newtonian fluid feature macroscopic behaviours that are still not completely understood, especially when the concentration of particles is high. In these materials, the complexity of the dynamic is the result of the subtle balance that occurs between hydrodynamic interactions mediated by the interstitial fluid, and contact forces between grains. In this work, we tackle those questions from the point of view of discrete numerical simulations, in the context of the simple shear of 2D concentrated suspensions. Hydrodynamic interactions are modelled by pair lubrication, coupled with a possibly frictional contact law. Grains inertia is not neglected. We have access to the whole stress tensor, allowing the measure of pressure, shear stress, and normal stress difference, as well as their associated viscosities. The study of constant volume simple shear shows the existence of a shear-thickening transition between a viscous regime at low shear rate (stress proportional to the shear rate) and an inertial regime at high shear rate (stress proportional to the shear rate squared), depending on whether the stress is dominated by lubrication interactions or grains inertia. The position of the measured transition shear rate is consistent with a scaling argument for the stress that takes its divergence with concentration into account. Constant pressure simple shear simulations then let us explore the behaviour of very concentrated suspensions (up to 1% to the theoretical jamming fraction) in their viscous flow domain. We show that the rheology of the mix can then be described by a flow law that is only function of the viscous number, constructed as the ratio of a typical time for the local rearrangement of grains subjected to viscous forces, and a convection time consistent with the imposed flow. This allows a precise characterization of the divergence of stress with particles concentration. At last, we measure the stationary microstructure that develops within the flow. We show an important anisotropy of contacts, and discuss the evolution of this distribution with the concentration of the suspension
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Michel Wone. Rhéologie des suspensions non Browniennes concentrées : une étude numérique. Autre [cond-mat.other]. Université Paris-Est, 2015. Français. ⟨NNT : 2015PEST1070⟩. ⟨tel-01223933⟩

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