  Finite-size neutrally buoyant particles in a channel flow are known to
accumulate at specific equilibrium positions or spots in the channel
cross-section if the flow inertia is finite at the particle scale. Experiments
in different conduit geometries have shown that while reaching equilibrium
locations, particles tend also to align regularly in the streamwise direction.
In this paper, the Force Coupling Method was used to numerically investigate
the inertia-induced particle alignment, using square channel geometry. The
method was first shown to be suitable to capture the quasi-steady lift force
that leads to particle cross-streamline migration in channel flow. Then the
particle alignment in the flow direction was investigated by calculating the
particle relative trajectories as a function of flow inertia and of the ratio
between the particle size and channel hydraulic diameter. The flow streamlines
were examined around the freely rotating particles at equilibrium, revealing
stable small-scale vortices between aligned particles. The streamwise
inter-particle spacing between aligned particles at equilibrium was calculated
and compared to available experimental data in square channel flow (Gao {\it et
al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017)). The new result
highlighted by our numerical simulations is that the inter-particle spacing is
unconditionally stable only for a limited number of aligned particles in a
single train, the threshold number being dependent on the confinement
(particle-to-channel size ratio) and on the Reynolds number. For instance, when
the particle Reynolds number is $\approx1$ and the particle-to-channel height
size ratio is $\approx0.1$, the maximum number of stable aligned particles per
train is equal to 3. This agrees with statistics realized on the experiments of
(Gao {\it et al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017)).
