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    Resonance phenomena and long-term chaotic advection in Stokes flows

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    Genre
    Thesis/Dissertation
    Date
    2011
    Author
    Abudu, Alimu
    Advisor
    Vainchtein, Dmitri
    Committee member
    Cohen, Richard
    Won, Chang-Hee, 1967-
    Department
    Mechanical Engineering
    Subject
    Engineering, Mechanical
    Adiabatic Invariant
    Chaotic Advection
    Diffusion
    Resonance
    Stokes Flows
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/629
    
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    DOI
    http://dx.doi.org/10.34944/dspace/611
    Abstract
    Creating chaotic advection is the most efficient strategy to achieve mixing in a microscale or in a very viscous fluid, and it has many important applications in microfluidic devices, material processing and so on. In this paper, we present a quantitative long-term theory of resonant mixing in 3-D near-integrable flows. We use the flow in the annulus between two coaxial elliptic counter-rotating cylinders as a demonstrative model. We illustrate that such resonance phenomena as resonance and separatrix crossings accelerate mixing by causing the jumps of adiabatic invariants. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resulting mixing can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss what must be done to accommodate the effects of the boundaries of the chaotic domain.
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