Difference between revisions of "Non-Linear Dynamics of a Flow-Focusing Bubble Generator: An Inverted Dripping Faucet"
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*<math>Re=\rho u L / \mu</math> | *<math>Re=\rho u L / \mu</math> | ||
| + | *<math>Ca_{flow}=u\mu / \gamma</math> | ||
| + | *<math>We_{flow}=\rho u^2 L/ \gamma</math> | ||
Revision as of 05:50, 24 February 2009
Physical Review Letters [0031-9007] P. Garstecki, M.J. Fuerstman, G. M. Whitesides (2005) vol:94 iss:23 pg:234502[1]
Brief Summary
This letter deals with the chaotic behaviour of a microfluidic bubble generator (the device reported in [2]). Briefly, a gaseous thread is forced through a small orifice while being squeezed by an outer liquid flow; the thread then becomes energetically unstable which results in a bubble being pinched off. Upon varying various parameters of the system such as the gas pressure and liquid flow rate, several bifurcations in the bubble producing behaviour are observed. The deviced is pictured in micrographs in figures 1 and 2. Figure 2 shows different higher-order regimes of bubble production; the figure letter corresponds to the flow rates demarcated in figure 3. The study of the chaotic behaviour of these types of devices is crucial in order to implement them as emulsion makers, for colloid production and in droplet-based microfluidics among many other applications.
Capillarity Phenomena
The main aim of this letter is to pinpoint the physical reason for the bifurcations observed in a microfluidic bubble generator (see [3] for a description of the operation of the device and the initial report of chaotic behaviour). Figure 3 shows the main result: as the fluid flow rate is increased, the diameter of the bubbles decreases until a first bifurcation at <math>Q=1.06 \mu L/s</math>. At this point, the device produces bubbles of two distinct radii sequentially so that one cycle results in the production of both sizes of bubbles. This weak "period-2" behaviour quickly disappears in what is termed a "frequency halving" - the two radii converge and the bubble generation returns to "period-1" behaviour. Another bifurcation occurs at <math>Q=2.8 \mu L/s</math>, which begins a series of further period-doublings. Above the seemingly chaotic branching region just below<math>Q=3.45 \mu L/s</math>, the device appears to stabilize into period-3 oscillations. In order to explain these non-linear behaviours, the authors proceed to list the dimensionless quantities which compare the magnitude of the various forces at play.
- <math>Re=\rho u L / \mu</math>
- <math>Ca_{flow}=u\mu / \gamma</math>
- <math>We_{flow}=\rho u^2 L/ \gamma</math>
