Self-diffusion in inhomogeneous granular shearing flows.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

How vertical oscillatory motion above a saturated sand bed leads to heap formation.

We show how oscillations in fluid flow over a fluid-saturated and porous sediment bed leads to the development of a bedform. To understand the role of pressure fluctuations on the bed associated with flow oscillations, we analyze how the flow penetrates into and through the bed. We then calculate the corresponding vertical pressure gradients within the bed that tend to expand the bed along the vertical direction. When these pressure gradients are large enough, they facilitate small irreversible rearrangements of the grains within the bed, and so cause granular creep. We conjecture that this granular creep alternates with jamming to produce a granular ratchet that slowly lifts the surface of the bed locally where pressure gradients dominate, and depresses the surface where shear stresses dominate. We observe that the shape of the resulting heap exhibits a constant characteristic width. The height of this heap evolves approximately as the square root of time, in agreement with dimensional arguments predicated on a coarse-grained viscous deformation of the bed. The surface of the heap contracts initially with the square root of time, consistent with an incompressible analysis of the flow of grains within the heap. Near its peak the heap grows due to a dilatation of the bed, to inward radial flux, or to a combination of the two.

Self-diffusion scalings in dense granular flows.

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid volume fractions that are important in those terrestrial gravitational shearing flows that are dominated by collisional interactions. Diffusion over this range of solid fraction has not been well characterized in previous studies. We first compare the measured values with an empirical scaling based on shear rate previously proposed in the literature, and highlight the presence of anisotropy and the solid fraction dependence. We then compare the numerical measurements with those predicted by the kinetic theory for shearing flows of inelastic spheres and offer an explanation for why the measured and predicted values differ.

Erodible, granular beds are fragile.

Geophysical flows that involve the transport of grains and the shearing of colloids and non-Brownian suspensions often take place above a substrate composed of the same particles that can be incorporated into the flow. Despite the importance of understanding such erodible beds to the phrasing of appropriate boundary conditions for the solution of continuum models, a rigorous definition of the erodible bed and the constitutive relations for the stresses within it are still lacking. Here, we use discrete-element simulations to show that the intense, intermittent forming and breaking of contact chains marks the transition to the erodible bed at a critical solid volume fraction, as in shear jamming of steady, homogeneous flows. However, the compressible, collisional flow that confines the bed is not strong enough to insure the stability of the contact network, resulting in a bulk stiffness that is three orders of magnitude less than in shear jamming.

Bedforms Produced on a Particle Bed by Vertical Oscillations of a Plate.

We describe a new mechanism that produces bedforms and characterize the conditions under which it operates. The mechanism is associated with pressure gradients generated in a fluid saturated particle bed by a plate oscillating in the water above it. These vertical pressure gradients cause oscillatory bed failure. This facilitates particle displacement in its interior and transport at and near its surface that contribute to the formation of a heap under the plate. Flows over erodible beds generally cause shear stresses on the bed and these induce bed failure. Failure driven by pressure gradients is different from this. We report on bedforms in a bed of glass beads associated with such fluctuating pressure gradients. We measure the development of the profiles of heaps as a function of time and determine the tangential and normal motion of areas on the beds surface and estimate the depth of penetration of the tangential transport. The measurements compare favorably with a simple model that describes the onset of failure due to oscillations in pressure.

Erosion and deposition in depth-averaged models of dense, dry, inclined, granular flows.

We derive expressions for the rates of erosion and deposition at the interface between a dense, dry, inclined granular flow and an erodible bed. In obtaining these, we assume that the interface between the flowing grains and the bed moves with the speed of a pressure wave in the flow, for deposition, or with the speed of a disturbance through the contacting particles in the bed, for erosion. We employ the expressions for the rates of erosion and deposition to show that after an abrupt change in the angle of inclination of the bed the characteristic time for the motion of the interface is much shorter than the characteristic time of the flow. This eliminates the need for introducing models of erosion and deposition rate in the mass balance; and the instantaneous value of the particle flux is the same function of the instantaneous value of the flow depth as in a steady, uniform flow.

Steady shearing flows of deformable, inelastic spheres.

We extend models for granular flows based on the kinetic theory beyond the critical volume fraction at which a rate-independent contribution to the stresses develops. This involves the incorporation of a measure of the duration of the particle interaction before and after this volume fraction. At volume fractions less than the critical, the stress components contain contributions from momentum exchanged in collisions that are influenced by the particle elasticity. At volume fractions greater than the critical, the stress components contain both static contributions from particle elasticity and dynamic contributions from the momentum transfer associated with the release of elastic energy by the breaking of force chains. A simple expression for the duration of a collision before and after the critical volume fraction permits a smooth transition between the two regimes and predictions for the components of the stress in steady, homogeneous shearing that are in good agreement with the results of numerical simulations. Application of the theory to steady, inhomogeneous flows reproduces the features of such flows seen in numerical simulations and physical experiments.

A continuum model of docking of synaptic vesicle to plasma membrane.

Neurotransmitter release from neuronal terminals is governed by synaptic vesicle fusion. Vesicles filled with transmitters are docked at the neuronal membrane by means of the SNARE machinery. After a series of events leading up to the fusion pore formation, neurotransmitters are released into the synaptic cleft. In this paper, we study the mechanics of the docking process. A continuum model is used to determine the deformation of a spherical vesicle and a plasma membrane, under the influence of SNARE-machinery forces and electrostatic repulsion. Our analysis provides information on the variation of in-plane stress in the membranes, which is known to affect fusion. Also, a simple model is proposed to study hemifusion.

Excretion and toxicity of gold-iron nanoparticles.

Though gold nanoparticles have been considered bio-inert, recent studies have questioned their safety. To reduce the potential for toxicity, we developed a nanoclustering of gold and iron oxide as a nanoparticle (nanorose) which biodegrades into subunits to facilitate rapid excretion. In this present study, we demonstrate acid and macrophage lysosomal degradation of nanorose via loss of the near-infrared optical shift, and clearance of the nanorose in vivo following i.v. administration in C57BL/6 mice by showing gold concentration is significantly reduced in 11 murine tissues in as little as 31 days (P < 0.01). Hematology and chemistry show no toxicity of nanorose injected mice up to 14 days after administration. We conclude that the clustering design of nanorose does enhance the excretion of these nanoparticles, and that this could be a viable strategy to limit the potential toxicity of gold nanoparticles for clinical applications. FROM THE CLINICAL EDITOR: The potential toxicity of nanomaterials is a critically important limiting factor in their more widespread clinical application. Gold nanoparticles have been classically considered bio-inert, but recent studies have questioned their safety. The authors of this study have developed a clustering gold and iron oxide nanoparticle (nanorose), which biodegrades into subunits to facilitate rapid excretion, resulting in reduced toxicity.

Computational simulation of hemodynamic-driven growth and remodeling of embryonic atrioventricular valves.

Embryonic heart valves develop under continuous and demanding hemodynamic loading. The particular contributions of fluid pressure and shear tractions in valve morphogenesis are difficult to decouple experimentally. To better understand how fluid loads could direct valve formation, we developed a computational model of avian embryonic atrioventricular (AV) valve (cushion) growth and remodeling using experimentally derived parameters for the blood flow and the cushion stiffness. Through an iterative scheme, we first solved the fluid loads on the axisymmetric AV canal and cushion model geometry. We then applied the fluid loads to the cushion and integrated the evolution equations to determine the growth and remodeling. After a set time of growth, we updated the fluid domain to reflect the change in cushion geometry and resolved for the fluid forces. The rate of growth and remodeling was assumed to be a function of the difference between the current stress and an isotropic homeostatic stress state. The magnitude of the homeostatic stress modulated the rate of volume addition during the evolution. We found that the pressure distribution on the AV cushion was sufficient to generate leaflet-like elongation in the direction of flow, through inducing tissue resorption on the inflow side of cushion and expansion on the outflow side. Conversely, shear tractions minimally altered tissue volume, but regulated the remodeling of tissue near the cushion surface, particular at the leading edge. Significant shear and circumferential residual stresses developed as the cushion evolved. This model offers insight into how natural and perturbed mechanical environments may direct AV valvulogenesis and provides an initial framework on which to incorporate more mechano-biological details.

Left ventricular epicardial admittance measurement for detection of acute LV dilation.

There are two implanted heart failure warning systems incorporated into biventricular pacemakers/automatic implantable cardiac defibrillators and tested in clinical trials: right heart pressures, and lung conductance measurements. However, both warning systems postdate measures of the earliest indicator of impending heart failure: left ventricular (LV) volume. There are currently no proposed implanted technologies that can perform LV blood volume measurements in humans. We propose to solve this problem by incorporating an admittance measurement system onto currently deployed biventricular and automatic implantable cardiac defibrillator leads. This study will demonstrate that an admittance measurement system can detect LV blood conductance from the epicardial position, despite the current generating and sensing electrodes being in constant motion with the heart, and with dynamic removal of the myocardial component of the returning voltage signal. Specifically, in 11 pigs, it will be demonstrated that 1) a physiological LV blood conductance signal can be derived; 2) LV dilation in response to dose-response intravenous neosynephrine can be detected by blood conductance in a similar fashion to the standard of endocardial crystals when admittance is used, but not when only traditional conductance is used; 3) the physiological impact of acute left anterior descending coronary artery occlusion and resultant LV dilation can be detected by blood conductance, before the anticipated secondary rise in right ventricular systolic pressure; and 4) a pleural effusion simulated by placing saline outside the pericardium does not serve as a source of artifact for blood conductance measurements.

Dynamic correction for parallel conductance, GP, and gain factor, alpha, in invasive murine left ventricular volume measurements.

The conductance catheter technique could be improved by determining instantaneous parallel conductance (G(P)), which is known to be time varying, and by including a time-varying calibration factor in Baan's equation [alpha(t)]. We have recently proposed solutions to the problems of both time-varying G(P) and time-varying alpha, which we term "admittance" and "Wei's equation," respectively. We validate both our solutions in mice, compared with the currently accepted methods of hypertonic saline (HS) to determine G(P) and Baan's equation calibrated with both stroke volume (SV) and cuvette. We performed simultaneous echocardiography in closed-chest mice (n = 8) as a reference for left ventricular (LV) volume and demonstrate that an off-center position for the miniaturized pressure-volume (PV) catheter in the LV generates end-systolic and diastolic volumes calculated by admittance with less error (P < 0.03) (-2.49 +/- 15.33 microl error) compared with those same parameters calculated by SV calibrated conductance (35.89 +/- 73.22 microl error) and by cuvette calibrated conductance (-7.53 +/- 16.23 microl ES and -29.10 +/- 31.53 microl ED error). To utilize the admittance approach, myocardial permittivity (epsilon(m)) and conductivity (sigma(m)) were calculated in additional mice (n = 7), and those results are used in this calculation. In aortic banded mice (n = 6), increased myocardial permittivity was measured (11,844 +/- 2,700 control, 21,267 +/- 8,005 banded, P < 0.05), demonstrating that muscle properties vary with disease state. Volume error calculated with respect to echo did not significantly change in aortic banded mice (6.74 +/- 13.06 microl, P = not significant). Increased inotropy in response to intravenous dobutamine was detected with greater sensitivity with the admittance technique compared with traditional conductance [4.9 +/- 1.4 to 12.5 +/- 6.6 mmHg/microl Wei's equation (P < 0.05), 3.3 +/- 1.2 to 8.8 +/- 5.1 mmHg/microl using Baan's equation (P = not significant)]. New theory and method for instantaneous G(P) removal, as well as application of Wei's equation, are presented and validated in vivo in mice. We conclude that, for closed-chest mice, admittance (dynamic G(P)) and Wei's equation (dynamic alpha) provide more accurate volumes than traditional conductance, are more sensitive to inotropic changes, eliminate the need for hypertonic saline, and can be accurately extended to aortic banded mice.

Small multifunctional nanoclusters (nanoroses) for targeted cellular imaging and therapy.

The ability of 20-50 nm nanoparticles to target and modulate the biology of specific types of cells will enable major advancements in cellular imaging and therapy in cancer and atherosclerosis. A key challenge is to load an extremely high degree of targeting, imaging, and therapeutic functionality into small, yet stable particles. Herein we report approximately 30 nm stable uniformly sized near-infrared (NIR) active, superparamagnetic nanoclusters formed by kinetically controlled self-assembly of gold-coated iron oxide nanoparticles. The controlled assembly of nanocomposite particles into clusters with small primary particle spacings produces collective responses of the electrons that shift the absorbance into the NIR region. The nanoclusters of approximately 70 iron oxide primary particles with thin gold coatings display intense NIR (700-850 nm) absorbance with a cross section of approximately 10(-14) m(2). Because of the thin gold shells with an average thickness of only 2 nm, the r(2) spin-spin magnetic relaxivity is 219 mM(-1) s(-1), an order of magnitude larger than observed for typical iron oxide particles with thicker gold shells. Despite only 12% by weight polymeric stabilizer, the particle size and NIR absorbance change very little in deionized water over 8 months. High uptake of the nanoclusters by macrophages is facilitated by the dextran coating, producing intense NIR contrast in dark field and hyperspectral microscopy, both in cell culture and an in vivo rabbit model of atherosclerosis. Small nanoclusters with optical, magnetic, and therapeutic functionality, designed by assembly of nanoparticle building blocks, offer broad opportunities for targeted cellular imaging, therapy, and combined imaging and therapy.

Approximate analytical solutions in a model for highly concentrated granular-fluid flows.

We extend a simple two-phase model for a steady fully developed flow of particles and water over an erodible inclined bed to situations in which the water and particles do not have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that satisfactorily reproduce those measured in experiments.

Aeolian transport with collisional suspension.

This paper considers the aeolian transport of sand by a wind so strong that the concentration of sand near the bed makes collisions between grains inevitable. It employs an improved model of such a collisional flow which includes turbulent suspension, viscous dissipation and new top boundary conditions that are validated by numerical calculations of collisionless trajectories.

Superstable granular heap in a thin channel.

We observed experimentally a new regime for granular flows in an inclined channel with a flow-rate-controlled system. For high flow rates, the flow occurs atop a static granular heap whose angle is considerably higher than those usually exhibited by granular heaps. The properties of such superstable heaps (SSH) are drastically affected by a change in the channel width W. This indicates that the unusual stability of these heaps can be accounted for by the flowing layer and its friction on the sidewalls. A simple depth-averaged model, assuming Coulomb friction, shows that the SSH angle scales as h/W (W being the channel width), and that grain size plays no part.