Toward a microscopic description of flow near the jamming threshold

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that (i) the viscosity {\eta} diverges with the coordination z as {\eta} ~ (z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure

Dynamics of Strongly Deformed Polymers in Solution

Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a powerful method for the determination of the complete relaxation spectrum of fluctuations at {\it steady state}. In general, the spectrum and modes differ significantly from those of the linear Rouse model. For a tethered polymer in uniform flow the differences are mainly caused by an inhomogeneous distribution of tension along the chain and are most pronounced due to the finite chain extensibility. Beyond the dynamics of steady state fluctuations we also investigate the nonlinear response of the polymer to a {\em large sudden change} in the flow. This response exhibits several distinct regimes with characteristic decay laws and shows features which are beyond the scope of single mode theories such as the dumbbell model.Comment: 7 pages, 3 figure

Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses

In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define normal modes. In this Letter we use these tools to analyze the activated transitions between meta-bassins, both in the aging regime deep in the glass phase and near the glass transition. We observe numerically that structural relaxation occurs mostly along a very small number of nearly-unstable extended modes. This number decays for denser packing and is significantly lowered as the system undergoes the glass transition. This observation supports that structural relaxation and marginal modes share common properties. In particular theoretical results [2, 3] show that these modes extend at least on some length scale $l^*\sim (\phi_c-\phi)^{-1/2}$ where $\phi_c$ corresponds to the maximum packing fraction, i.e. the jamming transition. This prediction is consistent with very recent numerical observations of sheared systems near the jamming threshold [4], where a similar exponent is found, and with the commonly observed growth of the rearranging regions with compression near the glass transition.Comment: 6 pages, improved versio

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p

Bulk and Interfacial Shear Thinning of Immiscible Polymers

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear rate dependence of the interfacial viscosity is consistent with a shorter effective chain length $s^*$ that also describes the width of the interface. This $s^*$ is independent of chain length $N$ and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate.Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of $N$ and consistent with the bulk behavior for chains of length $s^*$. The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing $N$, while shear induced changes at the ends of chains are independent of $N$.Comment: 8 pages, 8 figure

Force balance in canonical ensembles of static granular packings

We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA

Long-range Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents

The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir interaction at the isotropic-to-nematic transition can discontinuously induce the collapse of a flexible polymer chain from the swollen state to the globular state, without crossing the Theta-point.Comment: 6 pages, 1 figur

Aspiration of biological viscoelastic drops

Spherical cellular aggregates are in vitro systems to study the physical and biophysical properties of tissues. We present a novel approach to characterize the mechanical properties of cellular aggregates using micropipette aspiration technique. We observe an aspiration in two distinct regimes, a fast elastic deformation followed by a viscous flow. We develop a model based on this viscoelastic behavior to deduce the surface tension, viscosity, and elastic modulus. A major result is the increase of the surface tension with the applied force, interpreted as an effect of cellular mechanosensing.Comment: 4 pages, 4 figures

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(w) of vibrational modes of angular frequency w 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(w) toward a non-zero constant as w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law increase of w* with compression. Differences between these two systems occur at lower frequency. The density of states of the modified system displays an abrupt plateau that appears at w*, 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 dz: dz > p^(1/2), 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.Comment: 13 pages, 8 figure

Angoricity and compactivity describe the jamming transition in soft particulate matter

The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems-- particulate grains or droplets-- a key concept is to replace the energy ensemble describing conservative systems by the volume-stress ensemble. Here, we test the applicability of the volume-stress ensemble to describe the jamming transition by comparing the jammed configurations obtained by dynamics with those averaged over the ensemble as a probe of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. We elucidate the thermodynamic order of the jamming transition by showing the absence of critical fluctuations in static observables like pressure and volume. The approach allows to calculate observables such as the entropy, volume, pressure, coordination number and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint.Comment: 27 pages, 13 figure