Pairwise interactions in inertially driven one-dimensional microfluidic crystals

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 one-dimensional crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. The damping of the spring is due to inertial focusing forces, and the spring force arises from the interplay of viscous particle-particle and particle-wall interactions. The equilibrium spacing can be represented by a quadratic function in the particle size and therefore can be controlled by tuning the particle radius.