Paper Number
SC33 

Session
Suspensions & Colloids

Title
Micromechanical modeling of heterogeneous suspensions

Presentation Date and Time
October 17, 2018 (Wednesday) 1:55

Track / Room
Track 1 / Galleria I

Authors (Click on name to view author profile)

1. Dolata, Benjamin E. (Cornell University, School of Chemical and Biomolecular Engineering)
2. Zia, Roseanna N. (Stanford University, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Benjamin E. Dolata¹ and Roseanna N. Zia^2
1School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY; ²Chemical Engineering, Stanford University, Stanford, CA, CA 94305-4125

Speaker / Presenter 
Dolata, Benjamin E.

Text of Abstract
We present a theoretical study of the stress tensor in dilute heterogeneous suspensions. In such flows, the traditional volume averaging approach employed to compute the stress tensor in a statistically homogenous suspension is no longer generally valid; to overcome this limitation, we utilize a point-wise ensemble averaging method. In contrast with heterogeneous suspensions, where the particle stress depends only on the integral of the stress interior to the particle, i.e. the stresslet and torque, the stress in heterogeneous suspensions depends on the first, second, and all higher-order moments of the stress interior to the particle. Using tensor decomposition techniques, we derived differential identities that allow transformation of these volume moments of the stress into surface moments of the hydrodynamic traction and fluid velocity. We show that the stress tensor in heterogeneous suspensions is symmetric in the absence of externally applied torques on the particles, in contrast with prior work. We derive constitutive equations for dilute suspensions of spherical particles, showing that spatial heterogeneity in the suspension breaks the usual isotropy of the constitutive equations, leading to new couplings that are forbidden by symmetry in homogeneous suspensions.