Oscillations with Uniquely Long Periods in a Microfluidic Bubble Generator.
Original entry: Sorell Massenburg, APPHY 226, Spring 2009
PIOTR GARSTECKI, MICHAEL J. FUERSTMAN AND GEORGE M. WHITESIDES. Nature Physics, 2005, 1, 168-171.
Bubbles, capillary, microfluidics
Understanding spatiotemporal complexity is important to many disciplines, from biology to finance. However, because it is seldom possible to achieve complete control over the parameters that determine the behaviour of real complex systems, it has been difficult to study such behaviour experimentally. Here we demonstrate a simple microfluidic bubble generator that shows stable oscillatory patterns (both in space and time) of unanticipated complexity and uniquely long repetition periods. At low flow rates, the device produces a regular stream of bubbles of uniform size. As the flow increases, the system shows intricate dynamic behaviour typified by a stable limit cycle of order 29 bubbles per period, which repeats without change over intervals of up to 100 periods and more. As well as providing an example of a well-characterized and experimentally tractable model system with which to study complex, nonlinear dynamics, such behaviour demonstrates that it is possible to observe complex and stable limit cycles without active external control.
The authors here compare the bubble production of two different types of flow-focusing devices. One device is more a more typical device with a a single inlet for the inner phase a two for the continuous phase. The other is a flow focusing geometry that still uses just one inlet channel but now has five ten inlets for the continuous phase, which means that there are now five opportunities for the inner phase (<math>N_2</math>) to split.
The principle finding is that the behavior of bubbles being created is periodic, beginning as simple (relatively monodisperse) and becoming more complex and monodisperse by the end of the period. This is significant because is the demonstration of a rare system that is dynamically complex, yet periodically stable that does not need active external control. By adjusting the pressure, the periodicity can be varied from less than 10 bubbles per period up to about 40 bubbles per period.
In general the periodicity increases with pressure until about 80kPa.
To on effectively illustrate the periodicity, the authors construct a binary function to explain the, <math>\rho=1</math> when the gas is in the final outlet and <math>/rho=-1</math> when water is there instead. By tracking this quantity over the course of 4.3s, the authors develop traces and an autocorrelation function of periods contained in the 4.3s interval.
To look at the stability of the periodic behavior, several Poincare maps are developed. The maps of c) and e) are for relatively short intervals. However, the maps in d) and f) are large data series, 25,257 bubbles in all. The clustering in map d) and f) around points shown in c) and e), respectively, show that this behavior is periodic, not chaotic. Errors (deviations from the single point) are caused by limitations in data collection speed and slight variations in bubble interval. Interestingly, these variations decay with time, which stands in contrast with other non-linear systems. Multiperiodic trajectories are usually associated with strange attractors.
The authors suggest that this finding could pave the way to space-filling emulsion droplets that that have a controlled and reproducible polydispersion. This work may also assist in synthesis and production processes that are non-linear.