Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow

Abstract

We present the lubrication-corrected force-coupling method for the simulation of concentrated suspensions under finite inertia. Suspension dynamics are investigated as a function of the particle-scale Reynolds number \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇ and the bulk volume fraction ϕ in a homogeneous linear shear flow, in which \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇ is defined from the density ρf and dynamic viscosity μ of the fluid, particle radius a, and the shear rate \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }$\end{document}γ̇ as \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}= \rho _f \dot{\gamma } a^2 / \mu$\end{document}Reγ̇=ρfγ̇a2/μ. It is shown that the velocity fluctuations in the velocity-gradient and vorticity directions decrease at larger \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇. However, the particle self-diffusivity is found to be an increasing function of \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇ as the motion of the suspended particles develops a longer auto-correlation under finite fluid inertia. It is shown that finite-inertia suspension flows are shear-thickening and the particle stresses become highly intermittent as \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇ increases. To study the detailed changes in the suspension microstructure and rheology, we introduce a particle-stress-weighted pair-distribution function. The stress-weighted pair-distribution function clearly shows that the increase of the effective viscosity at high \documentclass[12pt]{minimal}\begin{document}$Re_{\dot{\gamma }}$\end{document}Reγ̇ is mostly related to the strong normal lubrication interaction in the compressive principal axis of the shear flow.