Feedback control of inertial microfluidics using axial control forces

Inertial microfluidics is a promising tool for many lab-on-a-chip applications. Particles in channel flows with Reynolds numbers above one undergo cross-streamline migration to a discrete set of equilibrium positions in square and rectangular channel cross sections. This effect has been used extensively for particle sorting and the analysis of particle properties. Using the lattice Boltzmann method, we determine equilibrium positions in square and rectangular cross sections and classify their types of stability for different Reynolds numbers, particle sizes, and channel aspect ratios. Our findings thereby help to design microfluidic channels for particle sorting. Furthermore, we demonstrate how an axial control force, which slows down the particles, shifts the stable equilibrium position towards the channel center. Ultimately, the particles then stay on the centerline for forces exceeding a threshold value. This effect is sensitive to particle size and channel Reynolds number and therefore suggests an efficient method for particle separation. In combination with a hysteretic feedback scheme, we can even increase particle throughput

Metachronal waves in a chain of rowers with hydrodynamic interactions

Filaments on the surface of a microorganism such as Paramecium or Ophalina beat highly synchronized and form so-called metachronal waves that travel along the surfaces. In order to study under what principal conditions these waves form, we introduce a chain of beads, called rowers, each periodically driven by an external force on a straight line segment. To implement hydrodynamic interactions between the beads, they are considered point-like. Two beads synchronize in antiphase or in phase depending on the positive or negative curvature of their driving-force potential. Concentrating on in-phase synchronizing rowers, we find that they display only transient synchronization in a bulk fluid. On the other hand, metachronal waves with wavelengths of 7-10 rower distances emerge, when we restrict the range of hydrodynamic interactions either artificially to nearest neighbors or by the presence of a bounding surface as in any relevant biological system.Comment: 9 pages, 10 figure

Collisional Grooming Models of the Kuiper Belt Dust Cloud

We modeled the 3-D structure of the Kuiper Belt dust cloud at four different dust production rates, incorporating both planet-dust interactions and grain-grain collisions using the collisional grooming algorithm. Simulated images of a model with a face-on optical depth of ~10^-4 primarily show an azimuthally-symmetric ring at 40-47 AU in submillimeter and infrared wavelengths; this ring is associated with the cold classical Kuiper Belt. For models with lower optical depths (10^-6 and 10^-7), synthetic infrared images show that the ring widens and a gap opens in the ring at the location of of Neptune; this feature is caused by trapping of dust grains in Neptune's mean motion resonances. At low optical depths, a secondary ring also appears associated with the hole cleared in the center of the disk by Saturn. Our simulations, which incorporate 25 different grain sizes, illustrate that grain-grain collisions are important in sculpting today's Kuiper Belt dust, and probably other aspects of the Solar System dust complex; collisions erase all signs of azimuthal asymmetry from the submillimeter image of the disk at every dust level we considered. The model images switch from being dominated by resonantly-trapped small grains ("transport dominated") to being dominated by the birth ring ("collision dominated") when the optical depth reaches a critical value of tau ~ v/c, where v is the local Keplerian speed.Comment: 31 pages, including 9 figure

Controlling inertial focussing using rotational motion

In inertial microfluidics lift forces cause a particle to migrate across streamlines to specific positions in the cross section of a microchannel. We control the rotational motion of a particle and demonstrate that this allows to manipulate the lift-force profile and thereby the particle's equilibrium positions. We perform two-dimensional simulation studies using the method of multi-particle collision dynamics. Particles with unconstrained rotational motion occupy stable equilibrium positions in both halfs of the channel while the center is unstable. When an external torque is applied to the particle, two equilibrium positions annihilate by passing a saddle-node bifurcation and only one stable fixpoint remains so that all particles move to one side of the channel. In contrast, non-rotating particles accumulate in the center and are pushed into one half of the channel when the angular velocity is fixed to a non-zero value

Decoding Images of Debris Disks

Current observations of debris disks reveal a wealth of radial and azimuthal structures likely created by planet-disk interactions. Future images of exozodiacal disks may reveal similar structures. In this work I summarize my observations and modeling of the structure of exozodiacal dust clouds. I present our observations of the 51 Ophiuchi circumstellar disk made with the Keck Interferometer operating in nulling mode at N-band. I modeled these data simultaneously with VLTI-MIDI visibility data and a Spitzer IRS spectrum and showed that the best-fit disk model is an optically thin disk with size-dependent radial structure. This model has two components, with an inner exozodiacal disk of blackbody grains extending to ~4 AU and an outer disk of small silicate grains extending out to ~1200 AU. This model is consistent with an inner "birth" disk of continually colliding parent bodies producing an extended envelope of ejected small grains and resembles the disks around Vega, AU Microscopii, and β Pictoris. I produced models of resonant ring structures created by planets in debris disks. I used a custom-tailored hybrid symplectic integrator to model 120 resonant ring structures created by terrestrial-mass planets on circular orbits interacting with collisionless steady-state dust clouds around a Sun-like star. I used these models to estimate the mass of the lowest-mass planet that can be detected through observations of a resonant ring, and showed that the resonant ring morphology is degenerate and depends on only two parameters: planet mass and ap1/2/β, where ap is the planet's semi-major axis and β is the ratio of radiation pressure force to gravitational force on a grain. I introduced a new computationally-efficient "collisional grooming" algorithm that enables us to model grain-grain collisions in structured debris disks and used this algorithm to show how collisions can alter the morphology of a resonant ring structure. My collisional models reveal that collisions act to remove azimuthal and radial asymmetries from the disk. I showed that the collision rate for background particles in a resonant ring structure is enhanced by a factor of a few compared to the rest of the disk, and dust grains in or near mean motion resonances have even higher collision rates. I also used this algorithm to model the 3-D structure of the Kuiper Belt's dust cloud at four different dust levels. I found that the Kuiper Belt dust would look like an azimuthally symmetric ring at 40-45 AU when viewed from afar at submillimeter wavelengths. At visible wavelengths, the Kuiper Belt dust cloud would reveal two resonant ring structures: one created by Saturn near 10 AU and one created by Neptune near 30 AU. A denser version of our Kuiper Belt dust cloud, with an optical depth 1000 times greater, would look qualitatively similar at submillimeter wavelengths, but would be void of Neptune's resonant ring structure at visible wavelengths. My simulations suggest that mean motion resonances with planets can play strong roles in the sculpting of debris disks even in the presence of collisions, though their roles are somewhat different than what has been anticipated

FARM BUSINESS GOALS AND COMPETITIVE ADVANTAGE

This paper investigates empirically the relationship between both farm business goals and sources of competitive advantage, and various farm and producer characteristics using new primary data collected from a survey of Ohio farmers. Results show that most farmers do not recognize sources of competitive advantage and practice strategy implementation beyond reliance on longstanding paradigms for success within the context of government farm program support and the use of traditional risk management tools. However, several key insights emerge. Farmers who engage in cost leadership strategies are more profitable. Farmers who suggest that the goal of their farming operation is to enhance profitability/efficiency use more management tools, while lifestyle farmers use fewer. Larger farmers are more apt to engage in a cost leadership strategy, while those with higher debt-to-asset ratios and those that are more livestock oriented are more likely to engage in differentiation or focus strategies. Smaller farmers and those that produce specialty or value-added crops are more likely to focus on a particular niche market. Lastly, the use of the Internet as part of the farming operation does not influence the probability of engaging in any particular business strategy. It is apparent that the government farm program has contributed to a strategic where few producers have an explicit or implicit farm business strategy beyond "working the program" and acting as price takers. Or if a strategic choice is apparent, it rests primarily with cost leadership.Farm Management,