Hydrodynamic interactions of colloidal droplets and their self-assembly in a microfluidic channel*

The recent experiment by Shen et al. (Adv. Sci. 3, 1600012, 2016) demonstrated the generation of micron-sized colloidal droplets and their subsequent self-assembly into dumbbells, triangles, etc., considered as building blocks of photonic materials, in a microfluidic channel. To understand the underlying hydrodynamic mechanism, hence better harnessing the process, we repeat the experiment numerically for 2-10 droplets, using the interface-correction level set/ghost fluid method (Ge et al. J. Comput. Phys. 353, 2018). As we vary the droplet initial position, the inflow condition, and the confinement, we find that their hydrodynamic interaction remains weak far from the channel inlet. Moreover, the dynamic rearrangement of the droplets is found to be mostly induced by the cross-stream migration, a 3D effect instead of the typical q2D dipolar flows. Our result is consistent with the theoretical analysis of Fouxon et al. (Phys. Rev. E. 96, 063110, 2017), suggesting that a highly non-uniform inflow condition is crucial for effective flow-assisted self-assemblies.