Application limits of Jeffery’s theory for elongated particle torques in turbulence: a DNS assessment

Abstract

Non-spherical particles suspended in fluid flows are subject to hydrodynamic torques generated by fluid velocity gradients. For small axisymmetric particles, the most popular formulation of hydrodynamic torques is that given by Jeffery (Proc R Soc Lond A 102:161–179, 1922), which is valid for uniform shear flow in the viscous Stokes regime. In the lack of simple alternative formulations outside the Stokes regime, the Jeffery formulation has been widely applied to inertial particles in turbulent flows, where it is bound to produce inaccurate results. In this paper we quantify the statistical error incurred when the Jeffery formulation is used to study the motion of elongated axisymmetric particles under nonlinear shear flow conditions. Considering the archetypical case of prolate ellipsoidal particles in turbulent channel flow, we show that error for ellipsoids of the same length, l, as the Kolmogorov scale of the flow, $$\eta _K$$ , is indeed small (order $$1\%$$ ) but increases exponentially up to $$l \simeq 10 \eta _K$$ before becoming almost independent of elongation.