Many natural processes (e.g., fires, life) operate out of—and, often, far from—thermodynamic equilibrium. Often, these dissipative processes, and the systems in which they occur, spontaneously become more “complicated” while dissipating energy. That is, they develop patterns, structures, or behaviors that they did not have when first formed. We are interested in the self-organization of dissipative systems; we aim to create simple model systems that enable us to study the origin, structure, and stability of this organization.
We studied the organization of spinning disks located at the interface between liquid and air (1). 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). A 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 – a 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 (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). 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.
Our work in the area of flames has focused on (i) multistability and critical transitions in complex systems and (ii) the spread of signals through interconnected networks. Recently, we have constructed a model system to examine the eruption of small flames into intense, rapidly moving flames stabilized by feedback between wind and fire (i.e. “wind-fire coupling”—a mechanism of feedback particularly relevant to forest fires) (3). Using this model, we showed that slowly spreading flames can exhibit detectable symptoms of critical slowing down (i.e. the slowed recovery of multistable systems from perturbations as those systems approach tipping points) prior to such eruptions. This finding, which marks the first demonstration of critical slowing down in a combustion system of any kind, suggests that slowing responses of spreading flames to sudden changes in environment (e.g. wind, terrain, temperature) may anticipate the onset of intense, feedback-stabilized modes of propagation (e.g. “blowup” events in forest fires).
1. Grzybowski BA, Stone HA, Whitesides GM (2000) "Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface", Nature 405(6790):1033–1036.
2. Garstecki P, Whitesides GM (2006) "Flowing crystals: Nonequilibrium structure of foam", Phys Rev Lett 97(2).
3. Fox J, Whitesides G (2015) "Warning signals for eruptive events in spreading fires", Proc Natl Acad Sci 112(8):2378.