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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