  Motion in a one-dimensional (1D) microfluidic array is simulated. Water
droplets, dragged by flowing oil, are arranged in a single row, and due to
their hydrodynamic interactions spacing between these droplets oscillates with
a wave-like motion that is longitudinal or transverse. The simulation yields
wave spectra that agree well with experiment. The wave-like motion has an
instability which is confirmed to arise from nonlinearities in the interaction
potential. The instability's growth is spatially localized. By selecting an
appropriate correlation function, the interaction between the longitudinal and
transverse waves is described.
