Project paper - The Department of Physics and Astronomy

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25Seperation (Δx) (mm)201510y = 0.4509e 1.0354xR² = 0.9527502 2.25 2.5 2.75 3 3.25 3.5 3.75 4Time (s)Figure 13: Exponential separation of two particles with similar initial conditions in a blinkingvortex flow with vortices spinning at 1000 rpm807060Seperation (Δx) (mm)504030201000 6 12 18Time (s)Figure 14: The seperation between the same two particles over a longer period of time.Notice that the exponential trend only continues for a short period at the fluid is contained.12
7 Results and ConclusionWe successfully constructed an experimental blinking vortex flow. We have measured positionof test tracer particles in a variety of fluids at various velocities over time. Theparameters of the blinking vortex system, such as period, size etc can easily be modified.The system has been shown to be advective in nature, as it can be reversed. We have alsoverified the equations that we assumed to be true, both using our numerical simulation, aswell as with experimental data.We have shown that the position of the particles deviates exponentially (figure 13) andhave characterized the Lyapunov exponent. For glycerin at ∼1000rpm this dimensionlessparameter is 1.0354. The separation over longer period is not exponential (as shown byfigure 14), and this is because the system is contained, and thus while the particles mightdiverge exponential over a small period, over longer timespan the separation between anytwo particles is limited and thus will oscillate over time.The blinking vortex system is thus a successful system with which to accomplish chaoticmixing. This is an advective system, where particles with small initial separation will divergeexponentially. It has a slew of applications, mainly in industry, for the mixing of materialsboth large and small.13
Page 1 and 2: PHY492: Final ReportChaotic Advecti
Page 3 and 4: 3 TheoryThe blinking vortex system
Page 5 and 6: These glass rods were fully immerse
Page 7 and 8: Figure 4: A periodic function passe
Page 9 and 10: Figure 8: Data or particle traced o
Page 11: 80ForwardReverse60x-Position (mm)40
Page 15 and 16: 8 Appendix: Code/∗B l i n k i n g
Page 17 and 18: sendPlotData ( ” f r e q ” , f

Project paper - The Department of Physics and Astronomy

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