Emergence and Complexity

1. Bubbles in MazesGeorge WhitesidesDepartment of Chemistry and Chemical BiologyHarvard Universitygwhitesides@gmwgroup.harvard.edu

3. Emergence and Complexity • Complex systems are composed of: • Components… • …that interact with one another (non-linearly) • These systems may show behavior that is unexpected (i.e., emergent) based on knowledge of the properties of the components

4. Our Approach: “Synthetic Complexity” • Design and fabricate “simple” components—as well understood as possible • Allow dynamic self-assembly: self-assembly occurs only when the system dissipates energy • Examine systems having small numbers of these components • Look for the onset of unpredicted (emergent) behavior • Try to understand this behavior

5. The Strategy: • Design/build systems of physical components • Interactions (“attraction”/”repulsion”) • One/another, environment • Dissipation • Interactions (Dissipation; Out-of-equilibrium) • How to generate: • Movement, reproduction, interaction, death…trading, recruiting, joining,…politics, love, … • Enthalpy and Entropy G = H – TS • Molecules (H ~ TS); Components (H>TS); Agents, Organisms • A Form of Analog Computation • The incursion of reality into simplicity

6. Microcontact Printing and Micromolding, and Microfluidic Systems

7. Microcontact Printing 1 cm

8. Microcontact printing (mCP) Micromolding in capillaries (MIMIC) Microtransfer molding (mTM) Near field lithography Soft Lithography: Basic Techniques hu Mask Resist Si Master Pour prepolymer and cure Remove stamp

9. Laminar Flow Flow

10. Flows at Small Scales... Laminar Flow Reynolds number (Re) < 2000 Multi-stream laminar flows L L = channel diameter v = flow velocity r = density h = viscosity Controllable Fine Structure and Optically Smooth Interfaces

11. Quake’s PET Synthesizer

13. Microfluidic Laser Light Sources Microcavity laser Microfluidic waveguide laser (Helbo, Tech.University, Denmark, 2003)

14. Generation of sequence of dye droplets 2x FF device 3x FF device Oxazine 720 R590 R640 Oxazine 720 R590

15. Synthetic approach: Bubbles and Droplets T – junction flow focusing shear rupturing Rayleigh-Plateau instability Anna etal, APL 82, 364, 2003 Thorsen etal, PRL 86, 4163, 2001

16. Flow-focusing * 200 µm, 150 times slower Than real time

17. Flow-focusing * liquid (Q) gas (p) liquid (Q) volume of the bubble: frequency of bubbling: independent control of size and volume fraction Vb p/Q f  pQ Garstecki, APL, 2004, 85

18. Complicated Networks (Mazes) Dijkstra’s Algorithm Chemical Wave Propagation1 Ameboid Organism2 Glow Discharge3 Fluids in Microchannels4 1. Steinbock, O., et al.; Science1995, 267, 868 2. Nagakaki, T., et al.; Nature2000, 407, 470. 3. Reyes, D. R., et al.; Lab on a Chip 2002, 2, 113 4. Fuerstman, M. J., et al.; Langmuir2003, 19, 4714

19. 5 mm Solving a One-Solution Maze Using Two Miscible Fluids

20. Why solving mazes using bubbles/droplets? • Discrete elements and interaction between elements  Nonlinearity • Real network problems • distribution networks, traffic systems, shipping • the number of objects on a particular route influence the paths of objects that enter the network afterward.

21. Bubbles and Droplets in Microchannel • Bubble/droplet follows path of least fluidic resistance at the time the bubble reaches a junction (it’s pulled in both directions and follows the direction of greater pull) • Bubbles/droplets inside a square channel increase the resistance of the channel1 Rapid Flow in Regions Around Bubbles Fluid Film 1. Wong, H., et al.; J. Fluid Mech.1995, 292, 71

22. R 2 R 1 R 4 R 3 Fluidic Resistance – How a Bubbles Chooses Its Path • Approximation for the velocity of flow in a rectangular channel: h w L • Analogy to Ohm’s Law for resistors  V = I R

23. resistance to flow R ≈ L/ma2 = Lr0 R ≈ Lr0 + nl(rb-r0) = Lr0 + na

24. simple fluid will split as q1/q2=R2/R1 • a bubble has to make a decision • once a bubble enters a channel it increases the channel’s resistance resistance to flow R1 R2

25. Fluidic Resistance – Surfactants Fuerstman 2007, submitted

26. Finding the Shortest Path through a Network that Contains Two Open Paths * * 1) 2) One bubble at a time Two bubbles at a time Bubble takes shorter path Second bubble takes longer path Presence of a bubble makes a path less favorable for other bubbles

27. A Network with Three Open Paths – Best Path is Not Necessarily the Shortest * * 1) 2) Increasing frequency of bubbling “turns on” second path Bubbles traverse path of least resistance * 3) At even higher frequency, bubbles finally choose shortest path

28. RRed RBlue RGreen Why Does the Bubble Sometimes Choose a Longer Path? • A path has a characteristic resistance R • Bubbles choose path of least resistance •R of a path ∝ length of the path L < < LGreen LRed LBlue •Resistances add as in electronic circuits Large segments of a path in parallel with another path decrease effective resistances of both paths RGreen < RBlue < RRed

29. Path selection: Length • Fluidic resistance of rectangular channel is proportional to the length of the path. As L increases, resistance increases.

30. Two-solution Maze: Length 6 droplets per network 4 droplets per network * *  Shorter path – lower resistance

31. Path selection: Turn • The length of the two-path is the same • The droplet entering the network takes the path with the higher number of turns • Turns decrease the fluidic resistance of the path • Turns effectively make the length of the path short : a droplet just entering the network The same number of droplets are present in each path when the droplet just reaches the branch

32. Two-solution Maze: Turn 2 droplets per network (Red:Blue = 1:1) 3 droplets per network (Red:Blue = 2:1) 1 droplets per network (All Red) * * *  Turns decrease the fluidic resistance of the path

33. Path selection: Dead-end • The length of the two-path is the same • The droplet entering the network takes the path with the higher number of dead-ends • Dead-ends decrease the fluidic resistance of the path • Dead-ends effectively make the width of the path wide • Droplets experience lower shear force at a branch of the path : a droplet just entering the network The same number of droplets are present in each path when the droplet just reaches the branch

34. Two-solution Maze: Dead-end 2 droplets per network (All Red) 3 droplets per network (Red:Blue = 2:1) * *  Dead-ends decrease the fluidic resistance of the path

35. Path selection: Width • Fluidic resistance of rectangular channel depends on the width of the channel. w2 (mm) = 100 for i) – iv) As w or h decreases, resistance increases.

36. Two-solution Maze: Width 2 droplets per network (All Red) 3 droplets per network (Red:Blue = 2:1) * *

37. Three-solution Maze: three way branch Total rate of flow (continuous phase) 2700 mm/hr 700 mm/hr 200 mm/hr * * * • Middle path is not the shortest path • Droplets slow down or even stop the flow in the channel they flow

38. Single droplet blocks the channel * • A droplet stays at the trap on the red path • All subsequent droplets take the blue path

39. Synthetic complexity is a new type of engine for discovery of processes • Systems of simple components provide a tractable (for experimentalists) entry into dissipative/out-of-equilibrium systems • The droplet entering a maze “sees” all the possible solutions to the maze at the moment, and take the path with the lowest resistance. • The stream of droplets can solve and distinguish the paths of the mazes with different (1) length of path, (2) width of path, (3) number of turns, and (4) number of dead-ends Conclusions

40. Acknowledgements • Bubbles in mazes • Piotr Garstecki (fundamentals) • Michinao Hashimoto (mazes) • Mike Fuerstman (details of bubble movement) • Howard Stone (DEAS) theory; FF generator • Department of Energy

42. Emergence

43. Emergence • New physics/chemistry, or simply “we don’t understand”? • Does it make a difference? • Is understanding in principle, but not understanding in practice, understanding? • Does the Schroedinger equation predict true love? What are the limits to reductionism?

44. What Works? Best? • Cellular atomata; Control theory; Systems engineering; Operations Research; Logical Networks; Catalytic Networks; Mathematical structures • What are the metrics for success? • Life. • To order is not to live. • Reality always introduces unanticipated perturbations. -------------- Theory always claims too much; Experiment always asks too much.