Impact of Weak Particle Inertia on a Dilute Suspension of Ellipsoids

ABSTRACT

In this paper, we investigate asymptotical models for the motion of small rigid ellipsoids suspended in a Newtonian fluid. The microscale models account for particle inertia and form the basis for dilute suspension modeling. They were derived from the description of first principles for a coupled particle-fluid problem by asymptotical analysis in the size ratio in Vibe and Marheineke (2015), where the effect of inertia was incorporated via different scalings of the particle momentum balances. We classify three different inertial regimes and analyze numerically their impact on the particle motion. We observe reasonable physical translational and rotational behavior.

KEYWORDS:

• asymptotic analysis
• macroscopic stress models
• fiber suspension flow

Notes

1 The parametrized rotation matrix reads as

2 To link the parameters considered in this paper with those in Einarsson et al. (2014), we scale the particle volume by the length of the small semi-axis (thus, d₂ = 1), choose the typical flow-gradient rate as the ratio of characteristic velocity with respect to the characteristic length , and use (2(2) ).