Self-assembled dissipative structures
Self-assembly in dynamic could develop order in its final ‘structure’ only when energy dissipates. We have studied a dynamic, self-assembling system of millimeter-sized, magnetized disks floating on a liquid-air interface and spinning under the influence of a rotating external magnetic field (Figure 1). The rotation of the disks in the fluid gives rise to repulsive, hydrodynamic interactions between them and as a result, the disks organize into ordered structures (Figure 2). We found that the morphologies of these aggregates change in response to the changes in the local perturbations of the magnetic field .
|Figure 1: Schematic showing the study of dynamic self-assembly of spinning disks. A bar magnet rotates at angular velocity q below a dish filled with liquid (typically ethylene glycol/water or glycerine/water solutions). Magnetically doped disks are placed on the liquid-air interface and are fully immersed in the liquid except for their top surface. The disks spin at angular velocity q around their axes. A magnetic force Fm attracts the disks towards the center of the dish, and a hydrodynamic force Fh pushes them apart from each other.|
|Figure 2: Dynamic patterns formed by various numbers (n) of disks rotating at the ethylene glycol/water-air interface. This interface is 27mm above the plane of the external magnet. The disks are composed of a section of polyethylene tube (white) of outer diameter 1.27 mm, filled with poly(dimethylsiloxane), PDMS, doped with 25 wt% of magnetite (black center). All disks spin around their centers at q = 700 r.p.m., and the entire aggregate slowly (O < 2 r.p.m.) precesses around its center.|
Nonequilibrium structures in multiphase microfluidic flow
We have demonstrated a model system that produces a set of metastable, periodic lattices in a nonequilibrium process which provides a unique example of coupling between the dynamic stability of a limit cycle and an equilibrium property—minimization of energy—of the resulting structures. The system can be switched between different states with the use of steady-state external control. The self-guided, but externally controllable, growth of periodic structures can, we hope, bring a new perspective to the science of fabrication of regular structures. We have explored the formation of bubbles in a microfluidic flow-focusing device (Figure 3) in which the rate of flow of liquid and the pressure of gas are externally controllable (2). Over much of the flow rate/pressure phase space, the system produces monodisperse bubbles. We have shown that these bubbles can be used to generate flowing lattices and dynamically assembled foams (Figure 4). Variation of the parameter leads to periodic production of bubbles of four different sizes. The flow-focusing device can also be tuned to produce bubbles with a random size distribution. The system shows similar behavior to a dripping faucet, which also displays period-doubling bifurcations .
|Figure 3: Dynamic self-assembly of bubbles generated by multi-step flow focusing device. A single breakup event generated various combinations of multiple bubbles (artificially colored black using Photoshop for easier interpretation), ranging from bi-disperse bubbles (Fig. 1a – the larger bubble from one breakup associated with the smaller bubble from the previous break-up) to tri-disperse bubbles (Fig. 1b - bubbles of three different sizes from a single breakup associated together as the two smaller bubbles flowed around opposite sides of the largest bubble).|
|Figure 4: Optical micrographs showing the formation of droplets of water in hexadecane in coupled flow-focusing generators. The mutual interaction between droplets generated by multiple flow-focusing devices resulted in the in-phase mode of operation of the generators (marked with solid rectangles) or the out-of-phase mode of operation of the generators (marked with dashed rectangles). Water droplets were stabilized with surfactants (Span 80, 3% w/w).|