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kumar CHAOTIC ADVECTION IN PULSED SOURCE SINK SYSTEMS

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					                   CHAOTIC ADVECTION IN PULSED SOURCE-SINK SYSTEMS

                                      Pankaj Kumar and Mark A. Stremler

                                  Department of Engineering Science and Mechanics
                                  Virginia Polytechnic Institute and State University

In a number of microfluidics applications, the mixing of fluid between two closely spaced flat plates at low Reynolds
number, known as Hele-Shaw flow, plays an important role. Under the Stokes flow approximation, the depth-
averaged velocity in a Hele-Shaw flow can be represented by a velocity potential. Effective mixing for these systems
can thus be designed by considering chaotic advection in a two-dimensional potential flow. Pulsed operation of a
source and a sink, produced by injecting and extracting fluid, respectively, through small holes in one of the plates,
has been shown to generate chaotic advection in an unbounded domain [1]. Our present work examines chaotic
advection generated by sources and sinks in a bounded circular domain. In a bounded system, the sources and
sinks must operate in pairs in order to conserve fluid volume [2]. For a source-sink pair placed on the boundary
of a circular domain, particle motions can be given explicitly by a discrete mathematical mapping. In this talk,
several different configurations of source-sink pairs, primarily the two shown in Fig.1 (a) and (b), are examined to
determine the optimal operating parameters for producing chaos in a bounded Hele-Shaw flow. Chaotic particle
motion in this system is primarily controlled by two operating parameters α and θ, where α is the dimensionless
pulse area of the fluid injected and extracted by sources and sinks, respectively, and θ is the angle that the source-
sink pairs make with the horizontal axis as shown in Fig.1. The chaos diagnostics and measures considered in
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this work include Poincar´ sections, Lyapunov exponents, and Kolmogorov (or KS) entropy. An example Poincar´        e
section is shown in Fig.1(c). It is found that configuration (a) gives better mixing than configuration (b) for small
values of α and all possible values of θ. In contrast, configuration (b) gives better mixing for high values of α;
however, configuration (b) with large values of θ gives inefficient mixing. A few other source-sink configurations
are examined for further improvements of fluid mixing in bounded Hele-Shaw flow.




                                (a)                         (b)                         (c)

Figure 1: Arrangement of two source-sink pairs on the boundary of a circular domain. Source and sink locations are indicated
by ⊕ and , respectively. Sources and sinks connected by bold dashed lines form source-sink pairs that are operated together.
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(a) Crossed source-sink pair configuration. (b) Parallel source-sink pair configuration. (c) Poincar´ section of fluid flow for
configuration (a) with θ = 25 and α = 20%.
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References
[1] S. W. Jones and H. Aref, “Chaotic advection in pulsed source-sink systems,” Phys. Fluids, 31, 469-485, 1988.
[2] M. A. Stremler and B. A. Cola, “A maximum entropy approach to optimal mixing in a pulsed source-sink
flow,” Phys. Fluids, 18, 011701, 2006.

				
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posted:12/5/2011
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