Inertial effects on the rotational motion of a fibre in simple shear flow between two bounding walls

Abstract

The effects of fluid inertia on the rotational motion of a freely suspended fibre in shear flow have been investigated using the lattice Boltzmann method (LBM). Here, fluid inertia is characterized by the shear Reynolds number Rep based on the fibre length L. Data are reported for fibres with an aspect ratio of 10 in the interval of 0<Rep⩽20 for different flow confinement ratios κ, defined as the ratio of the channel height 2h to the fibre length L. For κ⩾3.0, the time-dependent orientation of the fibre at sufficiently small Reynolds numbers (Rep < 0.1) is shown to be in excellent agreement with Jeffery's theory. For κ = 3.0 and 2.0, the calculations reveal that the period of rotation increases rapidly with increasing Rep, and when Rep increases beyond a critical value Rec, the periodic rotation is stopped and the fibre remains in a stationary orientation ϕequ to the flow direction. This stationary orientation ϕequ is an increasing function of Rep. The results also show that Rec increases and ϕequ decreases with decrease in κ from 3.0 to 2.0. For the highly confined domain (κ = 1.2), there is no periodic rotation and the fibre has a stationary orientation through the range of Rep studied (0<Rep⩽20).