167 research outputs found
Microfluidics: Fluid physics at the nanoliter scale
Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world
Chaotic advection and mixing in a western boundary current-recirculation system : laboratory experiments
Thesis (S.M.)--Joint Program in Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), February 2001.Includes bibliographical references (p. 116-118).I study the exchange between a boundary current and flanking horizontal recirculations in a 'sliced-cylinder' rotating tank laboratory experiment. Two flow configurations are investigated: a single recirculation and a double, figure-8, recirculation. The latter case involves a hyperbolic point, while the former does not. I investigate the stirring and mixing under both steady and unsteady forcing. I quantify the mixing in each case using effective diffusivity, Keff, and a corollary effective length, Leff, as derived by Nakamura (1995, 1996). This approach involves diagnosing the geometric complexity of a tracer field. Geometric complexity is indicative of advective stirring. Because stirring creates high gradients, flows with high advective stirring also have high diffusion, and stronger overall mixing. I calculate effective length from images of dye in the tank and find much higher values of Leff in the unsteady hyperbolic cases than in the other cases. Slight unsteadiness in flows involving hyperbolic points gives rise to a chaotic advection mechanism known as 'lobe dynamics'. These lobes carry fluid in and out of the recirculations, acting as extremely effective stirring mechanisms. I demonstrate the existence of these exchange lobes in the unsteady hyperbolic (figure-8) flow. The velocity field in the tank is calculated utilizing particle image velocimetry (PIV) techniques and a time series U(t) demonstrates the (forced) unsteadiness in the flow. Images of dye in the tank show exchange lobes forming at this same forcing period, and carrying fluid in and out of the recirculation. Based on the results of these experiments, I am able to confirm that, at least in this controlled environment, basic geometry has a profound effect on the mixing effectiveness of a recirculation. I demonstrate radically increased stirring and mixing in the unsteady hyperbolic flow as compared to steady flows and flows without hyperbolic points. Recirculations are ubiquitous in the world ocean; they occur on a variety of scales, in many different configurations, and at all depths. Some of these configurations involve hyperbolic points, while others do not. Chaotic advection via lobe exchange may be an important component of the mixing at multiple locations in the ocean where hyperbolic recirculation geometries exist.by Heather E. Deese.S.M
Chaotic advection and mixing in a western boundary current-recirculation system : laboratory experiments
Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2001I study the exchange between a boundary current and flanking horizontal
recirculations in a 'sliced-cylinder' rotating tank laboratory experiment. Two flow
configurations are investigated: a single recirculation and a double, figure-8, recirculation.
The latter case involves a hyperbolic point, while the former does not. I investigate the
stirring and mixing under both steady and unsteady forcing.
I quantify the mixing in each case using effective diffusivity, Keff, and a corollary
effective length, Leff, as derived by Nakamura (1995, 1996). This approach involves
diagnosing the geometric complexity of a tracer field. Geometric complexity is indicative
of advective stirring. Because stirring creates high gradients, flows with high advective
stirring also have high diffusion, and stronger overall mixing. I calculate effective length
from images of dye in the tank and find much higher values of Leff in the unsteady
hyperbolic cases than in the other cases.
Slight unsteadiness in flows involving hyperbolic points gives rise to a chaotic
advection mechanism known as 'lobe dynamics'. These lobes carry fluid in and out of the
recirculations, acting as extremely effective stirring mechanisms. I demonstrate the
existence of these exchange lobes in the unsteady hyperbolic (figure-8) flow. The velocity
field in the tank is calculated utilizing particle image velocimetry (PIV) techniques and a
time series U(t) demonstrates the (forced) unsteadiness in the flow. Images of dye in the
tank show exchange lobes forming at this same forcing period, and caring fluid in and
out of the recirculation.
Based on the results of these experiments, I am able to confirm that, at least in this
controlled environment, basic geometry has a profound effect on the mixing effectiveness
of a recirculation. I demonstrate radically increased stirring and mixing in the unsteady
hyperbolic flow as compared to steady flows and flows without hyperbolic points.
Recirculations are ubiquitous in the world ocean; they occur on a variety of scales,
in many different configurations, and at all depths. Some of these configurations involve
hyperbolic points, while others do not. Chaotic advection via lobe exchange may be an
important component of the mixing at multiple locations in the ocean where hyperbolic
recirculation geometries exist.I am grateful for funding provided by a National Defense Science and Engineering
Graduate Fellowship and for funding from
ONR #N00014-99-1-0258 and NSF #OCE-961694
Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence
We consider the closure problem for turbulence in the dry convective atmospheric boundary
layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large
plumes in the well mixed middle part up to the inversion that separates the CBL from the
stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF
approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02)
that additionally includes a term for background turbulence. Thus an exact solution is derived
and all higher order moments (HOMs) are explained by second order moments, correlation
coefficients and the skewness. The solution provides a proof of the extended universality
hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi-
normality of FOM). This refined hypothesis states that CBL turbulence can be considered as
result of a linear interpolation between the Gaussian and the very skewed turbulence regimes.
Although the extended universality hypothesis was confirmed by results of field
measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained
unexplained. These are now answered by the new model including the reasons of the
universality of the functional form of the HOMs, the significant scatter of the values of the
coefficients and the source of the magic of the linear interpolation. Finally, the closures
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predicted by the model are tested against measurements and LES data. Some of the other
issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area
coverage parameters of plumes (so called filling factors) with HOM will be discussed also
NASA Microgravity Materials Science Conference
The Microgravity Materials Science Conference was held June 10-11, 1996 at the Von Braun Civic Center in Huntsville, AL. It was organized by the Microgravity Materials Science Discipline Working Group, sponsored by the Microgravity Science and Applications Division at NASA Headquarters, and hosted by the NASA Marshall Space Flight Center and the Alliance for Microgravity Materials Science and Applications (AMMSA). It was the second NASA conference of this type in the microgravity materials science discipline. The microgravity science program sponsored approximately 80 investigations and 69 principal investigators in FY96, all of whom made oral or poster presentations at this conference. The conference's purpose was to inform the materials science community of research opportunities in reduced gravity in preparation for a NASA Research Announcement (NRA) scheduled for release in late 1996 by the Microgravity Science and Applications Division at NASA Headquarters. The conference was aimed at materials science researchers from academia, industry, and government. A tour of the MSFC microgravity research facilities was held on June 12, 1996. This volume is comprised of the research reports submitted by the principal investigators after the conference and presentations made by various NASA microgravity science managers
Rates of mixing in models of fluid devices with discontinuities
In the simplest sense, mixing acts on an initially heterogeneous system, transforming it to a homogeneous state through the actions of stirring and diffusion. The theory of dynamical systems has been successful in improving understanding of underlying features in fluid mixing, and how smooth stirring fields, coherent structures and boundaries affect mixing rates. The main stirring mechanism in fluids at low Reynolds number is the stretching and folding of fluid elements, although this is not the only mechanism to achieve complicated dynamics.
Mixing by cutting and shuffling occurs in many situations, for example in micro–fluidic split and recombine flows, through the closing and re-orientation of values in sink–source flows, and within the bulk flow of
granular material. The dynamics of this mixing mechanism are subtle and not well understood. Here, mixing rates arising from fundamental models capturing the essence of discontinuous, chaotic stirring with diffusion are investigated.
In purely cutting and shuffling flows it is found that the number of cuts introduced iteratively is the most important mechanism driving the approach to uniformity. A balance between cutting, shuffling and diffusion achieves a long-time exponential mixing rate, but similar mechanisms dominate the finite time mixing observed through
the interaction of many slowly decaying eigenfunctions. The time to achieve a mixed condition varies polynomially with diffusivity rate
κ, obeying t ∝ κ^{−η} . For the transformations meeting good stirring criteria, η < 1. Considering the time to achieve a mixed condition
to be governed by a balance between cutting, shuffling, and diffusion derives η ∼ 1/2, which shows good agreement with numerical results.
In stirring fields which are predominantly chaotic and exponentially mixing, it is observed that the addition of discontinuous transformations contaminates mixing when the stretching rates are uniform, or close to uniform. The contamination comes from an increase in scales of the concentration field by the reassembly of striations when cut
and shuffled. Mixing stemming from this process is unpredictable, and the discontinuities destroy the possibility to approximate early mixing rates from stretching histories. A speed up in mixing rate can
be achieved if the discontinuity aids particle transport into islands of the original transformation, or chops and rearranges large striations generated from highly non-uniform stretching. The long-time mixing rates and time to achieve a mixed condition are shown to behave counter-intuitively when varying the diffusivity rate. A deceleration of mixing with increasing diffusion coefficient is observed, sometimes
overshooting analytically derived bounds
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