Biomedical subjects

Sidney R Nagel

Publications and source records attributed to Sidney R Nagel.

At least 19 recordsLinked to original sources

PubMed2006

Breakup of air bubbles in water: memory and breakdown of cylindrical symmetry.

Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until the breakup. However, because the air-water interfacial tension does not drive the breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, nonuniversal singularity retains a memory of the nozzle shape, size, and tilt angle. In the last stages, the air appears to tear instead of pinch.

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PubMed2006

Structural signatures of the unjamming transition at zero temperature.

We study the pair correlation function g(r) for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition is approached from the jammed side (at higher packing fraction) the first peak diverges and narrows on the small-r side to a delta function. On the high-r side of this peak, g(r) decays as a power law. In the split second peak, the two subpeaks are both singular at the transition, with power-law behavior on their low-r sides and step-function drop-offs on their high-r sides. These singularities at the transition are reminiscent of empirical criteria that have previously been used to distinguish glassy structures from liquid ones.

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PubMed2006

Stability and growth of single myelin figures.

Myelin figures are long thin cylindrical structures that typically grow as a dense tangle when water is added to the concentrated lamellar phase of certain surfactants. We show that, starting from a well-ordered initial state, single myelin figures can be produced in isolation thus allowing a detailed study of their growth and stability. These structures grow with their base at the exposed edges of bilayer stacks from which material is transported into the myelin. Myelins only form and grow in the presence of a driving stress; when the stress is removed, the myelins retract.

Dimyristoylphosphatidylcholine↗

PubMed2006

Three-dimensional shear in granular flow.

The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations, we find a transition in the nature of the shear as a characteristic height H* is exceeded. Below H* there is a central stationary core; above H* we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height, while the axial width remains narrow and fixed.

Colloids↗

PubMed2005

Effects of compression on the vibrational modes of marginally jammed solids.

Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze, in particular, two systems whose density D(omega) of vibrational modes of angular frequency omega display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed (a) convergence of D(omega) toward a nonzero constant as omega-->0, (b) appearance of a low-frequency cutoff omega*, and (c) power-law increase of omega* with compression. Differences between these two systems occur at a lower frequency. The density of states of the modified system displays an abrupt plateau that appears at omega*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle deltaz:deltaz> or =p1/2, which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.

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PubMed2005

Vibrations and diverging length scales near the unjamming transition.

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition.

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PubMed2005

Effect of air on granular size separation in a vibrated granular bed.

Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a nonmonotonic density dependence of the rise and sink time of the large sphere. We show that air drag causes relative motion between the intruder and the bed during the shaking cycle and is ultimately responsible for the observed density dependence of the risetime. We investigate in detail how the motion of the intruder sphere is influenced by size of the background particles, initial vertical position in the bed, ambient pressure, and convection. We explain our results in the framework of a simple model and find quantitative agreement in key aspects with numerical simulations to the model equations.

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PubMed2005

Structural signature of jamming in granular media.

Glasses are rigid, but flow when the temperature is increased. Similarly, granular materials are rigid, but become unjammed and flow if sufficient shear stress is applied. The rigid and flowing phases are strikingly different, yet measurements reveal that the structures of glass and liquid are virtually indistinguishable. It is therefore natural to ask whether there is a structural signature of the jammed granular state that distinguishes it from its flowing counterpart. Here we find evidence for such a signature, by measuring the contact-force distribution between particles during shearing. Because the forces are sensitive to minute variations in particle position, the distribution of forces can serve as a microscope with which to observe correlations in the positions of nearest neighbours. We find a qualitative change in the force distribution at the onset of jamming. If, as has been proposed, the jamming and glass transitions are related, our observation of a structural signature associated with jamming hints at the existence of a similar structural difference at the glass transition--presumably too subtle for conventional scattering techniques to uncover. Our measurements also provide a determination of a granular temperature that is the counterpart in granular systems to the glass-transition temperature in liquids.

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PubMed2005

Drop splashing on a dry smooth surface.

The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high-speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.

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PubMed2004

Intruders in the dust: air-driven granular size separation.

Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, nonmonotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition, and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and shows how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.

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PubMed2004

Effective temperatures in driven systems: static versus time-dependent relations.

Using simulations of glassy systems under steady-state shear, we compare effective temperatures obtained from static linear response with those from time-dependent fluctuation-dissipation relations. Although these two definitions are not expected to agree, we show that they yield the same answer over two and a half decades of effective temperature. This suggests that a more complete conceptual framework is necessary for effective temperatures in steady-state driven systems.

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PubMed2003

Persistence of memory in drop breakup: the breakdown of universality.

A low-viscosity drop breaking apart inside a viscous fluid is encountered when air bubbles, entrained in thick syrup or honey, rise and break apart. Experiments, simulations, and theory show that the breakup under conditions in which the interior viscosity can be neglected produces an exceptional form of singularity. In contrast to previous studies of drop breakup, universality is violated so that the final shape at breakup retains an imprint of the initial and boundary conditions. A finite interior viscosity, no matter how small, cuts off this form of singularity and produces an unexpectedly long and slender thread. If exterior viscosity is large enough, however, the cutoff does not occur because the minimum drop radius reaches subatomic dimensions first.

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PubMed2003

Jamming at zero temperature and zero applied stress: the epitome of disorder.

We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

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PubMed2002

Force distributions in three-dimensional compressible granular packs.

We present an experimental investigation of the probability distribution of normal contact forces, P(F), at the bottom boundary of static three-dimensional packings of compressible granular materials. We find that the degree of deformation of individual grains plays a large role in determining the form of this distribution. For small amounts of deformation we find a small peak in P(F) below the mean force with an exponential tail for forces larger than the mean force. As the degree of deformation is increased the peak at the mean force grows in height and the slope of the exponential tail increases.

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PubMed2002

Stress transmission through three-dimensional ordered granular arrays.

We measure the local contact forces at both the top and bottom boundaries of three-dimensional face-centered-cubic and hexagonal-close-packed granular crystals in response to an external force applied to a small area at the top surface. Depending on the crystal structure, we find markedly different results which can be understood in terms of force balance considerations in the specific geometry of the crystal. Small amounts of disorder are found to create additional structure at both the top and bottom surfaces.

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PubMed2002

Effective temperatures of a driven system near jamming.

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

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PubMed2002

Scaling at the selective withdrawal transition through a tube suspended above the fluid surface.

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this discontinuous transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling is used to show that steady-state profiles for humps at different flow rates and tube heights can all be scaled onto a single similarity profile.

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PubMed2002

Random packings of frictionless particles.

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.

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