Angular velocimetry for fluid flows: an optical sensor using structured light and machine learning.

Most velocimetry approaches for fluid flows measure linear components of the velocity vector; yet, the angular velocity components, particularly at small scales in turbulent flows, also need to be resolved to study energy transfer and other important flow characteristics. Here, we detail an optical sensor approach to determine a component of the angular velocity vector. This approach uses beams of structured light and a machine learning-based analysis. We discuss the methodology to train the machine learning model and test it in experimentally validated simulations. This approach represents an interesting new direction for fluid flow velocimetry which may be extended to sense other flow parameters by selecting different light structures.

Robust scalable high throughput production of monodisperse drops.

Monodisperse drops with diameters between 20 µm and 200 µm can be used to produce particles or capsules for many applications such as for cosmetics, food, and biotechnology. Drops composed of low viscosity fluids can be conveniently made using microfluidic devices. However, the throughput of microfluidic devices is limited and scale-up, achieved by increasing the number of devices run in parallel, can compromise the narrow drop-size distribution. In this paper, we present a microfluidic device, the millipede device, which forms drops through a static instability such that the fluid volume that is pinched off is the same every time a drop forms. As a result, the drops are highly monodisperse because their size is solely determined by the device geometry. This makes the operation of the device very robust. Therefore, the device can be scaled to a large number of nozzles operating simultaneously on the same chip; we demonstrate the operation of more than 500 nozzles on a single chip that produces up to 150 mL h-1 of highly monodisperse drops.

Scaling and shear transformations capture beak shape variation in Darwin's finches.

Evolution by natural selection has resulted in a remarkable diversity of organism morphologies that has long fascinated scientists and served to establish the first relations among species. Despite the essential role of morphology as a phenotype of species, there is not yet a formal, mathematical scheme to quantify morphological phenotype and relate it to both the genotype and the underlying developmental genetics. Herein we demonstrate that the morphological diversity in the beaks of Darwin's Finches is quantitatively accounted for by the mathematical group of affine transformations. Specifically, we show that all beak shapes of Ground Finches (genus Geospiza) are related by scaling transformations (a subgroup of the affine group), and the same relationship holds true for all the beak shapes of Tree, Cocos, and Warbler Finches (three distinct genera). This analysis shows that the beak shapes within each of these groups differ only by their scales, such as length and depth, which are genetically controlled by Bmp4 and Calmodulin. By measuring Bmp4 expression in the beak primordia of the species in the genus Geospiza, we provide a quantitative map between beak morphology and the expression levels of Bmp4. The complete morphological variation within the beaks of Darwin's finches can be explained by extending the scaling transformations to the entire affine group, by including shear transformations. Altogether our results suggest that the mathematical theory of groups can help decode morphological variation, and points to a potentially hierarchical structure of morphological diversity and the underlying developmental processes.

Spatial reduction algorithm for atmospheric chemical transport models.

Numerical modeling of global atmospheric chemical dynamics presents an enormous challenge, associated with simulating hundreds of chemical species with time scales varying from milliseconds to years. Here we present an algorithm that provides a significant reduction in computational cost. Because most of the fast reactants and their quickly decomposing reaction products are localized near emission sources, we use a series of reduced chemical models of decreasing complexity with increasing distance from the source. The algorithm diagnoses the chemical dynamics on-the-run, locally and separately for every species according to its characteristic reaction time. Unlike conventional time-scale separation methods, the spatial reduction algorithm speeds up not only the chemical solver but also advection-diffusion integration. Through several examples we demonstrate that the algorithm can reduce computational cost by at least an order of magnitude for typical atmospheric chemical kinetic mechanisms.

Electric-field-induced capillary attraction between like-charged particles at liquid interfaces.

Nanometre- and micrometre-sized charged particles at aqueous interfaces are typically stabilized by a repulsive Coulomb interaction. If one of the phases forming the interface is a nonpolar substance (such as air or oil) that cannot sustain a charge, the particles will exhibit long-ranged dipolar repulsion; if the interface area is confined, mutual repulsion between the particles can induce ordering and even crystallization. However, particle ordering has also been observed in the absence of area confinement, suggesting that like-charged particles at interfaces can also experience attractive interactions. Interface deformations are known to cause capillary forces that attract neighbouring particles to each other, but a satisfying explanation for the origin of such distortions remains outstanding. Here we present quantitative measurements of attractive interactions between colloidal particles at an oil-water interface and show that the attraction can be explained by capillary forces that arise from a distortion of the interface shape that is due to electrostatic stresses caused by the particles' dipolar field. This explanation, which is consistent with all reports on interfacial particle ordering so far, also suggests that the attractive interactions might be controllable: by tuning the polarity of one of the interfacial fluids, it should be possible to adjust the electrostatic stresses of the system and hence the interparticle attractions.

Nonuniversal velocity fluctuations of sedimenting particles.

Velocity fluctuations in sedimentation are studied to investigate the origin of a hypothesized universal scale [P. N. Segre, E. Herbolzheimer, and P. M. Chaikin, Phys. Rev. Lett. 79, 2574 (1997)]. Our experiments show that fluctuations decay continuously in time for sufficiently thick cells, never reaching steady state. Simulations and scaling arguments suggest that the decay arises from increasing vertical stratification of particle concentration due to spreading of the sediment front. The results suggest that the velocity fluctuations in sedimentation depend sensitively on cell geometry.

Ordered clusters and dynamical states of particles in a vibrated fluid.

Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered microcrystallites, time-periodic structures, and chaotic fluctuating patterns with complex dynamics. A model based on streaming flow gives a good quantitative account of the attractive part of the interaction.

Collapsing bacterial cylinders.

Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two distinct stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.

Hydrodynamic coupling of two brownian spheres to a planar surface.

We describe direct imaging measurements of the collective and relative diffusion of two colloidal spheres near a flat plate. The bounding surface modifies the spheres' dynamics, even at separations of tens of radii. This behavior is captured by a stokeslet analysis of fluid flow driven by the spheres' and wall's no-slip boundary conditions. In particular, this analysis reveals surprising asymmetry in the normal modes for pair diffusion near a flat surface.

Physical mechanisms for chemotactic pattern formation by bacteria.

This paper formulates a theory for chemotactic pattern formation by the bacteria Escherichia coli in the presence of excreted attractant. In a chemotactically neutral background, through chemoattractant signaling, the bacteria organize into swarm rings and aggregates. The analysis invokes only those physical processes that are both justifiable by known biochemistry and necessary and sufficient for swarm ring migration and aggregate formation. Swarm rings migrate in the absence of an external chemoattractant gradient. The ring motion is caused by the depletion of a substrate that is necessary to produce attractant. Several scaling laws are proposed and are demonstrated to be consistent with experimental data. Aggregate formation corresponds to finite time singularities in which the bacterial density diverges at a point. Instabilities of swarm rings leading to aggregate formation occur via a mechanism similar to aggregate formation itself: when the mass density of the swarm ring exceeds a threshold, the ring collapses cylindrically and then destabilizes into aggregates. This sequence of events is demonstrated both in the theoretical model and in the experiments.

A cascade of structure in a drop falling from a faucet.

A drop falling from a faucet is a common example of a mass fissioning into two or more pieces. The shape of the liquid in this situation has been investigated by both experiment and computer simulation. As the viscosity of the liquid is varied, the shape of the drop changes dramatically. Near the point of breakup, viscous drops develop long necks that then spawn a series of smaller necks with ever thinner diameters. Simulations indicate that this repeated formation of necks can proceed ad infinitum whenever a small but finite amount of noise is present in the experiment. In this situation, the dynamical singularity occurring when a drop fissions is characterized by a rough interface.