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Controlling the transport of particles in flowing suspensions at the micro-scale level is of immense interest in numerous contexts such as flow cytometry, single cell encapsulation and cell diagnostics. A commonly used technique for controlling particle positions in microchannel flows is so-called ‘hydrodynamic focusing'. It is based on cross-streamline migration of finite-size neutrally buoyant particles, towards specific equilibrium positions in the channel cross-section, due to finite flow inertia at the particle scale. Experiments in different channel geometries show that particles align in the streamwise direction. In this work we investigate this purely hydrodynamic streamwise self-assembly, using particle-resolved numerical simulations. We carefully explore relative particle trajectories during the phase of streamwise assembly, and show their dependence on the flow inertia, number of particles already assembled, and particle size.
The computed particle trajectories allow determining the equilibrium distance between aligned particles, which is comparable in average to available experimental data. We show how the origin of particle alignment is connected to the spiralling streamlines induced in the streamwise direction by a particle found at its equilibrium position. Given one (reference) particle at equilibrium, if another particle is for instance leading (in the flow direction) the reference one, it can be attracted back towards this spiralling region and reaches equilibrium (constant streamwise distance between the two particles). The range where this purely inertial attractive force occurs, depends on the Reynolds number. The striking result of this work is that the region where the pairwise attractive force applies can be very large compared to the particle size, and the way an ensemble of particles reaches equilibrium depends significantly on the number of particles trying to align.
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