Microstructure and rheology of finite inertia neutrally buoyant suspensions. (25th June 2014)

• Record Type: Journal Article
• Authors: Haddadi, Hamed; Morris, Jeffrey F.
• Is Part Of: Journal of fluid mechanics. Volume 749(2014:Jun.)
• Page Start: 431
• Page End: 459
• Publication Date: 2014-06-25
• Subjects: Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2014.238
• Languages: English
• ISSNs: 0022-1120

Abstract

<abstract> <title>Abstract</title> <p>The microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6nd4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\phi $]]></tex-math></alternatives></inline-formula>. The inertia is characterized by the particle-scale shear flow Reynolds number <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6nq3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$]]></tex-math></alternatives></inline-formula>, where <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6mgq" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$a$]]></tex-math></alternatives></inline-formula> is the particle radius, <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6kb0" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\dot{\gamma }$]]></tex-math></alternatives></inline-formula> is the shear rate and <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6n9g" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\rho $]]></tex-math></alternatives></inline-formula> and <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6m23" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\mu $]]></tex-math></alternatives></inline-formula> are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6jt6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$0.005\leqslant \mathit{Re}\leqslant 5$]]></tex-math></alternatives></inline-formula> and<inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6m46" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$0.1\leqslant \phi \leqslant 0.35$]]></tex-math></alternatives></inline-formula>. The flow-induced microstructure is studied using the pair distribution function <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh11pb6m69" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$g(\boldsymbol {r})$]]></tex-math></alternatives></inline-formula>. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions (PDFs) of linear and angular accelerations are also presented.</p> </abstract>