The assembly of freely moving rigid fibres measures the flow velocity gradient tensor

The motion of an assembly of rigid fibres is investigated for different classes of closed streamline flows, steady or time dependent, two-dimensional or three-dimensional. In our study, the dynamics of the fibre assembly is fully coupled to the flow field by means of a state of the art immersed boundary method. We show that, for sufficiently small Stokes times of the assembly, the whole flow gradient tensor can be accurately reconstructed by simply tracking the fibre assembly and measuring suitable fibre velocity differences evaluated at the fibre ends. Our results strongly suggest the possibility of using rigid fibres (or assemblies of them) to perform multi-point flow measures, either in laboratory or in field: future experiments are therefore mandatory to inquire the feasibility of a new 'fibre tracking velocimetry' technique.