Algorithm for a Microfluidic Assembly Line

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical constituents. We illustrate the algorithm by showing that a modified Hele-Shaw cell with 7 controlled flow rates can be designed to construct the entire English alphabet from particles that irreversibly stick to each other.

Figure 1

(a) Schematic: Five particles are advected by the flow field in a circular cell. The flow field, visualized by its streamlines, is set up by 11 flow rates imposed on the boundary (arrows indicating the strength and direction). (b),(c) Two trajectories transporting particles from a fixed initial position to their desired final position with the required flow rates. The linear trajectory (b) requires flow rates almost 2 orders of magnitude higher than the trajectory in (c). This optimized trajectory minimizes dissipation.

Figure 2

Sequentially particles are added to form aggregates of arbitrary shape. The three columns present snapshots along the assembly of three example structures presented in the last row. The required time variations of the 7 controlled flow rates are computed a priori (e.g., Fig. 3). See movie M1 in Ref. 14 for an animation.

Figure 3

Flow rates $f_k/\pi aH\delta {\tau }^{-1}$ for the 7 inlets as a function of time $t/\tau$. These allow us to spell the letter “$B$.” At each integer time a new particles enters the cell.