Staggered and linear multi-particle trains constitute characteristic structures in inertial microfluidics. Using lattice-Boltzmann simulations, we investigate their properties and stability, when flowing through microfluidic channels. We confirm the stability of cross-streamline pairs by showing how they contract or expand to their equilibrium axial distance. In contrast, same-streamline pairs quickly expand to a characteristic separation but even at long times slowly drift apart. We reproduce the distribution of particle distances with its characteristic peak as measured in experiments. Staggered multi-particle trains initialized with an axial particle spacing larger than the equilibrium distance contract non-uniformly due to collective drag reduction. Linear particle trains, similar to pairs, rapidly expand towards a value about twice the equilibrium distance of staggered trains and then very slowly drift apart non-uniformly. Again, we reproduce the statistics of particle distances and the characteristic peak observed in experiments. Finally, we thoroughly analyze the damped displacement pulse traveling as a microfluidic phonon through a staggered train and show how a defect strongly damps its propagation.
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