LEADER 00000nam  2200349   4500 
001    AAI3252809 
005    20071009090547.5 
008    071009s2007                        eng d 
035    (UMI)AAI3252809 
040    UMI|cUMI 
100 1  John, Thomas 
245 10 Transport, reaction and mixing in fluid flows 
300    200 p 
500    Source: Dissertation Abstracts International, Volume: 68-
       02, Section: B, page: 1253 
500    Adviser: Igor Mezic 
502    Thesis (Ph.D.)--University of California, Santa Barbara, 
       2007 
520    An important area of interest in microfluidics research is
       the transport of suspended particles in micro-devices. 
       Particle transport in low Reynolds number flows is also 
       important in sedimentation, blood flow, polymer processing
       and other chemical and biological processes. In this 
       dissertation, we present a study of transport, mixing and 
       reaction of orientable rods and present backwards 
       probabilistic techniques for solving transport equations 
520    The problem of enhancing reaction between orientable 
       particles in a microdevice is considered. Achieving this 
       objective is more complex than in the case of particulate 
       matter because of the apparently conflicting requirements 
       of alignment in orientation space while at the same time 
       enhancing the mixing in physical space. A model framework 
       is developed within which one may study reaction dynamics 
       under various velocity fields 
520    We study the evolution of individual particle densities in
       position-orientation space. Trends in the amount and 
       distribution of reaction product are obtained with 
       variations in Peclet, rotational Peclet and Damkohler 
       numbers in laminar microchannel. We demonstrate that a 
       shear superposition micromixer can be used to achieve the 
       dual objective of mixing and alignment. Simulations show 
       that it is possible to achieve a significant enhancement 
       of the reaction rate by using a shear superposition 
       micromixer 
520    Traditional methods of solving transport PDEs become very 
       expensive with high Peclet numbers and when the problem is
       high dimensional. For these reasons, we consider Monte 
       Carlo methods that do not suffer from these difficulties. 
       The commonly used forward Monte Carlo methods, however, 
       suffer from sampling difficulties and can be very 
       expensive when we wish to obtain statistically meaningful 
       results. We develop backwards methods to study the 
       evolution of particle densities which have several 
       advantages when compared with the more traditional 
       methods. These methods are based on the link between PDEs 
       and Brownian motion, known as the Feynman-Kac relation 
520    These backward Monte Carlo methods to compute the effect 
       of diffusion are ideally suited for application to 
       microfluidic devices where velocity profiles are 
       obtainable relatively easily and Peclet numbers are often 
       very high. We demonstrate the efficiency and flexibility 
       of this approach via applications to studying density 
       evolution in a laminar microchannel flow as well as in a 
       chaotic flow in the shear superposition micromixer. We 
       present an extension of this method that takes into 
       account anisotropic diffusion and lack of volume 
       preservation by the velocity field, which are present in 
       the case of orientable particles. Numerical experiments 
       demonstrate the further advantages of this technique when 
       the density distribution in the domain is highly non-
       uniform and when we only wish to solve the density in a 
       small sub-domain 
520    Mixing is also studied in the context of macroscopic flows
       as well. One important mixing mechanism is through the 
       free shear layer, which is found in atmospheric flow, 
       oceans and in industrial applications such as combustion 
       chambers and diffusers. A vortex sheet is an idealization 
       of a free shear layer. Vortex sheet evolution is, however,
       an ill-posed problem. We employ the recently discovered 
       Euler-alpha equations to regularize vortex sheet 
       evolution. We perform a linear stability analysis and 
       determine the dispersion relation for the problem. We find
       that the smoothed transport velocity from the Euler-alpha 
       model helps stabilize the core of the sheet during roll-up
       and prevents self-intersection of the curve. In the non-
       linear regime, we discover a scaling of size of the rolled
       -up sheet with alpha, the regularization parameter 
590    School code: 0035 
590    DDC 
650  4 Engineering, Mechanical 
690    0548 
710 20 University of California, Santa Barbara 
773 0  |tDissertation Abstracts International|g68-02B 
856 40 |uhttp://pqdd.sinica.edu.tw/twdaoapp/servlet/
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