Ballistic deflection of fibres in decelerating flow
Journal article, 2016
We investigate the motion of inertial, rod-like fibres in the decelerating flow of a wedge-shaped channel with non-creeping fibre-flow interactions. We consider the trajectories of isolated fibres to identify the conditions for which these trajectories deflect from the streamlines of the flow as well as a rectilinear path. We carry out analytical and numerical studies under the assumption of an infinite fibre hydrodynamic resistance to transverse flow, and we expand the numerical study by taking into account a finite transverse hydrodynamic resistance. The analytical analysis identifies a longitudinal ballistic number Bℓ and a transverse ballistic number Bt as two dimensionless parameters that govern the fibre dynamics. It is found that Bℓ is the product of the Stokes number Stℓ in the longitudinal direction of the fibre and the channel opening angle β. As anticipated, a fibre moves along the streamlines in the viscosity-dominated regime (Bℓ « 1, Bt « 1), while it moves in a straight line without being rotated in the inertia-dominated regime (Bt » 1). The focus of the present study is on the intermediate regime (Bℓ » 1, Bt < 1), in which we identify and analyse a fibre trajectory that significantly deviates from the streamlines of the flow. This behaviour is observed for both infinite and finite resistances to transverse flow, and it is referred to as ballistic deflection. We argue that ballistic deflection may increase the rate of collisions between suspended fibres, and thus potentially affects the rate of fibre aggregation in flowing suspensions. An order of magnitude estimate of the ballistic numbers identifies dry-forming of pulp mats, which includes an air-wood fibre flowing suspension, to operate in the regime of ballistic deflection.