Dissipative Systems

Chemistry tends to study systems at, or moving toward, thermodynamic equilibrium. But the most interesting systems in the world around us—life, thought, combustion, ecosystems, traffic, epidemics, the stock market, the planetary environment, weather, cities—are “dissipative;” that is, their characteristic features only emerge spontaneously in presence of a flux of energy. Dissipative systems have a tendency to become more “complicated” while dissipating energy. That is, they develop patterns, structures, or behaviors that they did not have when first formed. Advances have been made in chemistry and in various other disciplines (such as physics, biology, and ecology), but, unlike in equilibrium systems, we are still at the very beginning of understanding the principles governing dissipative systems— both theoretically and empirically [1]. We aim to create simple model systems which enable us to study the origin, structure, and stability of this organization.

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 [2].

Dissipative Systems-Fig1 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.


Dissipative Systems-Fig2 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.


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 [3].

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 [4].

Dissipative Systems-Fig3 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).
Dissipative Systems-Fig4 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).
Our work in the area of dissipative systems includes the study of dissipative phenomena such as flames, swarming, and autocatalytic reaction network. These are all examples of far-from-equilibrium dissipative structures which exhibit coherent behavior that arise from an energy flux (i.e., heat, friction, matter, respectively) [5].



1. Whitesides GM (2015) "Reinventing Chemistry", Angew. Chem. Int. Ed. 54, 3196–3209.
2. 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.
3. Grzybowski, B.A., Whitesides GM (2001) "Macroscopic Synthesis of Self-Assembled Dissipative Structures", J. Phys. Chem. B, 105, 8770-8775.
4. Garstecki P, Whitesides GM (2006) "Flowing crystals: Nonequilibrium structure of foam", Phys Rev Lett 97, 024503-024506.
5. Fox J, Whitesides G (2015) "Warning signals for eruptive events in spreading fires", Proc Natl Acad Sci 112(8):2378-2383.