Biomedical subjects

J P Gollub

Publications and source records attributed to J P Gollub.

16 recordsLinked to original sources

PubMed2006

Elastic instabilities of polymer solutions in cross-channel flow.

When polymer molecules pass near the hyperbolic point of a microchannel cross flow, they are strongly stretched. As the strain rate is varied at low Reynolds number (< 10(-2)), tracer and particle-tracking experiments show that molecular stretching produces two flow instabilities: one in which the velocity field becomes strongly asymmetric, and a second in which it fluctuates nonperiodically in time. The flow is strongly perturbed even far from the region of instability, and this phenomenon can be used to produce mixing.

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PubMed2006

Predicting the progress of diffusively limited chemical reactions in the presence of chaotic advection.

The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry, Reynolds number, and mean path length affect the spatial distribution and time dependence of the reaction product. A single parameter lambdaN , where lambda is the mean Lyapunov exponent N and is the number of mixing cycles, can be used to predict the time-dependent total product for flows having different dynamical features.

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PubMed2005

Chaos and threshold for irreversibility in sheared suspensions.

Systems governed by time reversible equations of motion often give rise to irreversible behaviour. The transition from reversible to irreversible behaviour is fundamental to statistical physics, but has not been observed experimentally in many-body systems. The flow of a newtonian fluid at low Reynolds number can be reversible: for example, if the fluid between concentric cylinders is sheared by boundary motion that is subsequently reversed, then all fluid elements return to their starting positions. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science, are governed by time reversible equations of motion. Here we report an experiment showing precisely how time reversibility fails for slowly sheared suspensions. We find that there is a concentration dependent threshold for the deformation or strain beyond which particles do not return to their starting configurations after one or more cycles. Instead, their displacements follow the statistics of an anisotropic random walk. By comparing the experimental results with numerical simulations, we demonstrate that the threshold strain is associated with a pronounced growth in the Lyapunov exponent (a measure of the strength of chaotic particle interactions). The comparison illuminates the connections between chaos, reversibility and predictability.

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PubMed2005

Granular packings sheared in an annular channel: flow localization and grain size dependence.

We investigate experimentally a quasistatic flow of glass beads in an annular channel, in which particles are packed and sheared from above under a constant normal load. The experiments utilize techniques of refractive-index-matched fluorescent imaging to determine the motion of individual particles and the velocity fields inside the sheared packing. We demonstrated in a previous paper [Phys. Rev. E 70, 031303 (2004)] that an ordering transition has a significant impact on the velocity profile. Here, we report the effects of layer thickness, channel width, and particle size on the internal velocity field. For very thin layers, the grain velocity exhibits a linear vertical profile. As the layer thickness increases, a strongly nonlinear velocity profile emerges, with particle motion that is largely localized to a narrow region (shear band) near the driving surface. Once the packing has reached its steady state, the velocity field is insensitive to the size of grains being used--the velocity profile does not scale with grain size. However, the vertical decay of grain velocity becomes significantly steeper as the horizontal width of the channel decreases. In addition, we demonstrate that changing the direction of shearing generates an anomalous mobility of grains in the deep interior that is sensitive to particle size. The transient grain motion is accompanied by an abrupt volume compaction and a gradual recovery as the shearing proceeds. Reviewing results from this and other works reveals that the velocity profiles of granular shear flows are often geometry specific. We present a heuristic continuum model that qualitatively captures the shear banding observed in this geometry.

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PubMed2005

A chiral granular gas.

Inspired by rattleback toys, we created small chiral wires that rotate in a preferred direction on a vertically oscillating platform and quantified their motion with experiment and simulation. We demonstrate experimentally that angular momentum of rotation about particle centers of mass is converted to collective angular momentum of center-of-mass motion in a granular gas of these wires, and we introduce a continuum model that explains our observations.

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PubMed2004

Structures and chaotic fluctuations of granular clusters in a vibrated fluid layer.

Particles that oscillate with respect to a background fluid experience a long-range attraction and a short-range repulsion that give rise to clustering at a preferred separation. We have studied the structure and dynamics of these clusters for both small (2<N<7) and large (N=25 or 48) clusters. For small clusters, the particles often form well-defined structures with chaotic fluctuations about the mean particle positions. However, for a given N , there are generally several different structures, e.g., both isosceles and equilateral triangles. The nearest neighbor spacings grow systematically with the dimensionless driving acceleration Gamma. Large clusters are less rigid, and show much larger velocity fluctuations than do small clusters, for sufficiently large Gamma. The fluctuation amplitude grows systematically with Gamma for large clusters, but not for small ones. The instantaneous particle velocity is typically largest when a particle moves through a region where its probability density is low. Some of the observed phenomena suggest a variational model in which particles seek minima in an effective potential, and are perturbed by dynamically generated noise arising from the nonlinear interactions between particles. However, pairwise forces cannot account for all of the results. We discuss the nature of the fluctuations, including the low apparent dimension of the occupied set in configuration space for clusters of modest size.

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PubMed2004

Slowly sheared dense granular flows: crystallization and nonunique final states.

Simultaneous time-resolved measurements of internal structure, granular volume, and boundary shear force are reported for dense granular packing steadily sheared under a fixed normal load. We identify features of the crystallization transition for a deep shear flow, whose height-dependent local mean velocity spans more than five orders of magnitude. This structural change is accompanied by a significant decrease of granular volume and shear force, with a more rapid falloff of particle velocity with depth than occurs in the disordered state. Boundary conditions can have a profound influence on the crystallization of the entire packing. We find that continuously sheared flow can exhibit nonunique final states even under identical boundary conditions; a few cycles of oscillatory pretreatment can initiate states that evolve into either a crystallized or a disordered final state after long-term unidirectional shearing. On the other hand, the disordered state can be stabilized after being sufficiently compacted by unidirectional shear. These experiments raise interesting questions about how prior history is recorded in the internal structure of granular packings, affecting their instantaneous rheology and long-term evolution in response to shear.

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PubMed2003

Internal granular dynamics, shear-induced crystallization, and compaction steps.

Internal imaging using index matching, and sensitive volume measurement, are used to investigate the spatial order and dynamics of a deep disordered layer of spheres sheared under a fixed load. Shearing triggers a crystallization transition accompanied by a step compaction event. The delay preceding the transition depends strongly on the layer thickness and can require a translation of about 10(5) particle diameters. The mean velocity varies with depth by more than five decades, and its profile is qualitatively altered by the transition.

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PubMed2002

Experimental measurements of stretching fields in fluid mixing.

Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching field. This quantity, previously available only numerically, attains local maxima along lines that coincide with the stable and unstable manifolds of hyperbolic fixed points of Poincaré maps. Contours of a passive impurity field are found at each instant to be oriented parallel to the lines that have recently experienced large stretching. The local stretching varies by 12 orders of magnitude.

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PubMed2002

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.

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PubMed2001

Granular shear flow dynamics and forces: experiment and continuum theory.

We analyze the main features of granular shear flow through experimental measurements in a Couette geometry and a comparison to a locally Newtonian, continuum model of granular flow. The model is based on earlier hydrodynamic models, adjusted to take into account the experimentally observed coupling between fluctuations in particle motion and mean-flow properties. Experimentally, the local velocity fluctuations are found to decrease more slowly with distance from the shear surface than the velocity. This can be explained by an effective viscosity that diverges more rapidly as the random-close-packing density is approached than is predicted by Enskog theory for dense hard-sphere systems. Experiment and theory are in good agreement, especially for the following key features of granular flow: The flow is confined to a small shear band, fluctuations decay approximately exponentially away from the sheared wall, and the shear stress is approximately independent of the shear velocity. The functional forms of the velocity and fluctuation profiles predicted by the model agree with the experimental results.

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PubMed2001

Two-dimensional granular Poiseuille flow on an incline: multiple dynamical regimes.

We investigate experimentally the flow of a monolayer of spherical beads through a channel on a smooth incline that is bounded by rough sidewalls. Using high-speed video imaging and particle tracking, we measure the positions and velocities of all particles in the field of view. We find that the flows are accelerating and dilute if the channel exit is open. On the other hand, if the exit is constricted, flows can reach a state in which the local time-averaged velocity is invariant along the stream. In the latter case, we find a continuous transition from an oscillatory two-phase flow (2PF) regime with wide density variations to a uniform dense flow regime, depending on the channel width and the mean flow speed. These two regimes exhibit distinct density variation, time regularity, and transverse profiles. The rough sidewalls are found to be necessary for the 2PF regime. In the dense regions of both flows, particles exhibit temporary arches, long-range correlated velocities, inhomogenuous propagation of disturbances, and hexagonal lattice structures. On the other hand, the dilute regions of the two-phase flow are nearly collisionless. Existing models can neither fully describe the dynamics of both the dense and the dilute regions nor explain the spontaneous switching between them.

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PubMed2001

Scarred patterns in surface waves.

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.

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PubMed1999

Propagating front in an excited granular layer.

A partial monolayer of approximately 20 000 uniform spherical steel beads, vibrated vertically on a flat plate, shows remarkable ordering transitions and cooperative behavior just below 1g maximum acceleration. We study the stability of a quiescent disordered or "amorphous" state formed when the acceleration is switched off in the excited "gaseous" state. The transition from the amorphous state back to the gaseous state upon increasing the plate's acceleration is generally subcritical: An external perturbation applied to one bead initiates a propagating front that produces a rapid transition. We measure the front velocity as a function of the applied acceleration. This phenomenon is explained by a model based on a single vibrated particle with multiple attractors that is perturbed by collisions. A simulation shows that a sufficiently high rate of interparticle collisions can prevent trapping in the attractor corresponding to the nonmoving ground state.

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PubMed1999

Frictional mechanics of wet granular material.

The mechanical response of a wet granular layer to imposed shear is studied experimentally at low applied normal stress. The granular material is immersed in water and the shear is applied by sliding a plate resting on the upper surface of the layer. We monitor simultaneously the horizontal and the vertical displacements of the plate to submicron accuracy with millisecond time resolution. The relations between the plate displacement, the dilation of the layer and the measured frictional force are analyzed in detail. When slip begins, the dilation increases exponentially over a slip distance comparable to the particle radius. We find that the total dilation and the steady state frictional force do not depend on the driving velocity, but do depend linearly on the applied normal stress. The frictional force also depends linearly on the dilation rate (rather than the dilation itself), and reaches a maximum value during the transient acceleration. We find that the layer can temporarily sustain a shear stress that is in excess of the critical value that will eventually lead to slip. We describe an empirical model that describes much of what we observe. This model differs in some respects from those used previously at stresses 10(6) times larger.

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PubMed1995

Order and disorder in fluid motion.

The development of complex states of fluid motion is illustrated by reviewing a series of experiments, emphasizing film flows, surface waves, and thermal convection. In one dimension, cellular patterns bifurcate to states of spatiotemporal chaos. In two dimensions, even ordered patterns can be surprisingly intricate when quasiperiodic patterns are included. Spatiotemporal chaos is best characterized statistically, and methods for doing so are evolving. Transport and mixing phenomena can also lead to spatial complexity, but the degree depends on the significance of molecular or thermal diffusion.

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