Many systems undergo dissipative processes in nature, and in the lab. Dissipation plays a critical part in many phenomena; two important examples are the growth of organisms, and self-organization in non-equilibrium processes. The growth of organisms involves a reduction in the entropy of the material being incorporated into the organism. To satisfy the second law of thermodynamics the organisms must dissipate energy into the environment. Self-organization proceeds differently in equilibrium and non-equilibrium processes. In the equilibrium case self-organization is driven by a transition towards the lowest energy state in the system; in non-equilibrium systems, a variable that would play the role of energy has not yet been found. We are interested in the self-organization of dissipative systems, and we aim to create simple dissipative systems that could give us insight into the self-organization process.
We studied the organization of spinning disks located at the interface between liquid and air . We drove the rotation of disks magnetically: each disk was filled with ferromagnetic powder, and we drove their rotation by spinning a permanent magnet under the dish that contained the disks (Figure 1). Single disk drifted to the axis of rotation of the magnet; multiple disks interacted repulsively and self-organized into ordered structures (Figure 2). As the disks rotated around their axis, they engaged the liquid near them and the resulting fluid flow generated hydrodynamic lift forces that led to an effective repulsion between the disks. The dissipation in this system was due the viscous flow and was critical to the formation of repulsive forces that stabilized the patterns of disks. Viscous friction enabled the engagement of the fluid near the disks, and ensured that the flow of fluid in the dish was laminar with a finite Reynolds number – condition under which hydrodynamic lift forces led to the repulsion between disks.
We are exploring 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 . 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). As one of the parameters is varied, however, the sizes of the bubbles produced become bi-disperse (Figure 4). Further 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.
Of all the complex systems that exist in our far-from-equilibrium universe, living organisms are probably the most inspiring in their abilities to survive, compete, and adapt through the continual degradation of useful energy. Building on this inspiration, we sought to develop simple experimental components that mimic some of the basic characteristics of living systems: dissipative, adaptive, interacting. The components we chose are based on flames – that is, the visible structures formed by the interplay between combustion and transport.
We have discovered that the most interesting dynamical behaviors occur for metastable flames – that is, for conditions intermediate between sustained combustion and complete extinction. We designed a multi-nozzle burner for oscillating flamelets inspired by the ‘rotating flame’ that circles the burner of a gas stove after the fuel is cut off (Figure 5). The burner has a reconfigurable design in which the nozzles are patterned in thin sheets of copper or aluminum. These exchangeable sheets form the top part of a 150-mm diameter burner that operates with a premixed combustible mixture of hydrocarbon gas and air.
For appropriately low rates of fuel flow, a single flamelet cannot be sustained indefinitely above its respective microburner. Instead, the extinguished flame may lay dormant as unburned fuel accumulates above the burner; ultimately, enough fuel accumulates to support ignition. When ignited (e.g., by a neighboring flamelet), the accumulated fuel is rapidly consumed, the flame burns out, and the cycle begins again. Importantly, the ignition of one flamelet may act to ignite a neighboring flamelet creating a chain reaction not unlike a sequence of falling dominoes. Figure 6 shows one oscillation of flamelets for nozzles patterned in a cross. In the centre of the cross there is enough fuel to sustain a ‘pilot’ flame, but along the arms of the cross the flames cannot burn continuously. Instead, flamelets travel down the arms of the cross periodically, and this oscillation is stable for hundreds of cycles.
1. Grzybowski, B.A., Stone, H. A., Whitesides, G. M. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface. Nature 405, 1033-1036 (2000).
2. Garstecki, P. and Whitesides, G. M. Flowing crystals: nonequilibrium structure of foam. Physical Review Letters 97, 024503 (2006).