Tetrahedral colloidal clusters from random parking of bidisperse spheres.

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to--or "park" on--smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio α of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at α = 2.45. The high yield of tetrahedra, which reaches 100% in simulations at α = 2.41, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the "minimum parking" number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio α(c) = (1 + sqrt[2]) ≈ 2.41, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.

Synchronized reinjection and coalescence of droplets in microfluidics.

Coalescence of two kinds of pre-processed droplets is necessary to perform chemical and biological assays in droplet-based microfluidics. However, a robust technique to accomplish this does not exist. Here we present a microfluidic device to synchronize the reinjection of two different kinds of droplets and coalesce them, using hydrostatic pressure in conjunction with a conventional syringe pump. We use a device consisting of two opposing T-junctions for reinjecting two kinds of droplets and control the flows of the droplets by applying gravity-driven hydrostatic pressure. The hydrostatic-pressure operation facilitates balancing the droplet reinjection rates and allows us to synchronize the reinjection. Furthermore, we present a simple but robust module to coalesce two droplets that sequentially come into the module, regardless of their arrival times. These re-injection and coalescence techniques might be used in lab-on-chip applications requiring droplets with controlled numbers of solid materials, which can be made by coalescing two pre-processed droplets that are formed and sorted in devices.