  In microfluidic devices, inertia drives particles to focus on a finite number
of inertial focusing streamlines. Particles on the same streamline interact to
form one-dimensional microfluidic crystals (or "particle trains"). Here we
develop an asymptotic theory to describe the pairwise interactions underlying
the formation of a 1D crystal. Surprisingly, we show that particles assemble
into stable equilibria, analogous to the motion of a damped spring. Although
previously it has been assumed that particle spacings scale with particle
diameters, we show that the equilibrium spacing of particles depends on the
distance between the inertial focusing streamline and the nearest channel wall,
and therefore can be controlled by tuning the particle radius.
