arXiv subjects

Karen E. Daniels

Publications and source records attributed to Karen E. Daniels.

At least 73 records · Page 4Linked to original sources

arXiv2014

The Statistical Physics of Athermal Materials

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

cond-mat.stat-mech↗

arXiv2014

Self-healing Dynamics of Surfactant Coatings on Thin Viscous Films

We investigate the dynamics of an insoluble surfactant on the surface of a thin viscous fluid spreading inward to fill a surfactant-free region. During the initial stages of surfactant self-healing, Marangoni forces drive an axisymmetric ridge inward to coalesce into a growing central distension; this is unlike outward-spreading, in which the ridge decays. In later dynamics, the distension slowly decays and the surfactant concentration equilibrates. We present results from experiments in which we simultaneously measure the surfactant concentration (using fluorescently-tagged lipids) and the fluid height profile (via laser profilometry). We compare the results to simulations of a mathematical model using parameters from our experiments. For surfactant concentrations close to but below the critical monolayer concentration, we observe agreement between the height profiles in the numerical simulations and the experiment, but disagreement in the surfactant distribution. In experiments at lower concentrations, the surfactant spreading and formation of a Marangoni ridge are no longer present, and a persistent lipid-free region remains. This observation, which is not captured by the simulations, has undesirable implications for applications where uniform coverage is advantageous. Finally, we probe the generality of the effect, and find that distensions of similar size are produced independent of initial fluid thickness, size of initial clean region, and surfactant type.

physics.flu-dyn↗

arXiv2013

Capillary fracture of soft gels

A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact-line in a starburst pattern. In this paper, we characterize i) the initiation process in which the number of arms in the starburst is controlled by the ratio of surface tension contrast to the gel's elastic modulus and ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law $L\propto t^{3/4}$. We develop a model for crack initiation by treating the gel as a linear elastic solid and computing the deformations within the substrate from the liquid/solid wetting forces. The elastic solution shows that both the location and magnitude of the wetting forces are critical in providing a quantitative prediction for the number of fractures and, hence, an interpretation of the initiation of capillary fractures. This solution also reveals that the depth of the gel is an important factor in the fracture process, as it can help mitigate large surface tractions; this finding is confirmed with experiments. We then develop a model for crack propagation by considering the transport of an inviscid fluid into the fracture tip of an incompressible material, and find that a simple energy-conservation argument can explain the observed material-independent power law. We compare predictions for both linear elastic and neo-Hookean solids finding that the latter better explains the observed exponent.

cond-mat.soft↗

arXiv2013

Correlations between electrical and mechanical signals during granular stick-slip events

Powders and grains exhibit unpredictable jamming-to-flow transitions that manifest themselves on geophysical scales in catastrophic slip events such as landslides and earthquakes, and on laboratory/industrial scales in profound processing difficulties. Over the past few years, insight into these transitions has been provided by new evidence that slip events may accompanied, or even preceded, by electrical effects. In the present work, we quantify the correlation between slip and the separation of electrical charges, using an archetypal granular material: photoelastic polymers. We measure a strong correlation between material displacement, acoustic emissions, and voltage. We find that the generation of voltage is associated with surface, rather than bulk properties of the granular materials. While voltage precursors are only occasionally observed in this system, there is some asymmetry in the cross-correlation between the slip and voltage signals that indicates differences between the pre-slip and post-slip dynamics.

cond-mat.mtrl-sci↗

arXiv2013

Surfactant Spreading on a Thin Liquid Film: Reconciling Models and Experiments

The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg 1990 describing the spreading of a single layer of insoluble surfactant has become widely accepted, and several experiments on axisymmetric spreading have confirmed its predictions for both the height profile of the free surface and the spreading exponent (the radius of the circular area covered by surfactant grows as t^{1/4}). However, these prior experiments have primarily utilized surfactant quantities exceeding (sometimes far exceeding) a monolayer. In this paper, we report that this regime is characterized by a mismatch between the timescales of the experiment and model, and additionally find that the spatial distribution of surfactant molecules differs substantially from the model prediction. For experiments performed in the monolayer regime for which the model was developed, the surfactant layer is observed to have a spreading exponent of less than 1/10, far below the predicted value, and the surfactant distribution is also in disagreement. These findings suggest that the model is inadequate for describing the spreading of insoluble surfactants on thin fluid layers.

physics.flu-dyn↗

arXiv2012

Acoustic measurement of a granular density of modes

In glasses and other disordered materials, measurements of the vibrational density of states reveal that an excess number of long-wavelength (low-frequency) modes, as compared to the Debye scaling seen in crystalline materials, is associated with a loss of mechanical rigidity. In this paper, we present a novel technique for measuring the density of modes (DOM) in a real granular material, in which we mimic thermal excitations using white noise acoustic waves. The resulting vibrations are detected with piezoelectric sensors embedded inside a subset of the particles, from which we are able to compute the DOM via the spectrum of the velocity autocorrelation function, a technique previously applied in thermal systems. The velocity distribution for individual particles is observed to be Gaussian, but the ensemble distribution is non-Gaussian due to varying widths of the individual distributions. In spite of this deviation from a true thermal system, we find that the DOM exhibits several thermal-like features, including Debye scaling in a compressed hexagonally ordered packing, and an increase in low-frequency modes as the confining pressure is decreased. In disordered packings, we find that a characteristic frequency $f_c$ increases with pressure, but more weakly than has been observed in simulations of frictionless packings.

cond-mat.soft↗

arXiv2012

Flow-Driven Formation of Solid-like Microsphere Heaps

We observe the formation of heaps of repulsive microspheres, created by flowing a colloidal microsphere suspension towards a flat-topped ridge placed within a quasi two-dimensional microfluidic channel. This configuration allows for both shear and normal forces on the microspheres in contact with the ridge. The heaps, which form against the ridge, are characterized by two distinct phases: a solid-like bulk phase in the interior, and a highly-fluctuating, liquid-like state which exists along its leading edge. We observe that heaps only form above a critical flow velocity, (v_c), and that they are destroyed by thermal rearrangements when the flow ceases. We monitor the dynamics of heap formation using fluorescence video microscopy, measuring the heap volume and the angle of repose in response to microsphere deposition and erosion processes. We find that the steady-state angle of repose, (θ_f), increases as a function of inflow velocity, (v_\infty), with a functional form (θ_f \propto \sqrt{v_\infty - v_c}).

cond-mat.soft↗

arXiv2012

Equilibrating temperature-like variables in jammed granular subsystems

Although jammed granular systems are athermal, several thermodynamic-like descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding temperature-like variable. We perform experiments with an apparatus designed to generate a large number of independent, jammed, two-dimensional configurations. Each configuration consists of a single layer of photoelastic disks supported by a gentle layer of air. New configurations are generated by alternately dilating and re-compacting the system through a series of boundary displacements. Within each configuration, a bath of particles surrounds a smaller subsystem of particles with a different inter-particle friction coefficient than the bath. The use of photoelastic particles permits us to find all particle positions as well as the vector forces at each inter-particle contact. By comparing the temperature-like quantities in both systems, we find compactivity (conjugate to the volume) does not equilibrate between the systems, while the angoricity (conjugate to the stress) does. Both independent components of the angoricity are linearly dependent on the hydrostatic pressure, in agreement with predictions of the stress ensemble.

cond-mat.soft↗

arXiv2012

The Influence of Network Topology on Sound Propagation in Granular Materials

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.

cond-mat.soft↗

arXiv2012

Granular segregation in dense systems: the role of statistical mechanics and entropy

Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating drums -- which suggest that the dynamics of systems at intermediate and high density might be amenable to a statistical mechanics approach.

cond-mat.soft↗

arXiv2012

Trajectory entanglement in dense granular materials

The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient $D$. However, this measure discards the collective and topological information known to be an important characteristic of particle trajectories in dense systems. Direct measurement of the entanglement of particle space-time trajectories can be obtained via the topological braid entropy $\Sbraid$, which has previously been used to quantify mixing efficiency in fluid systems. Here, we investigate the utility of $\Sbraid$ in characterizing the dynamics of a dense, driven granular material at packing densities near the static jamming point $ϕ_J$. From particle trajectories measured within a two-dimensional granular material, we typically observe that $\Sbraid$ is well-defined and extensive. However, for systems where $ϕ\gtrsim 0.79$, we find that $\Sbraid$ (like $D$) is not well-defined, signifying that these systems are not ergodic on the experimental timescale. Both $\Sbraid$ and $D$ decrease with either increasing packing density or confining pressure, independent of the applied boundary condition. The related braiding factor provides a means to identify multi-particle phenomena such as collective rearrangements. We discuss possible uses for this measure in characterizing granular systems.

cond-mat.soft↗

arXiv2011

Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's Law with a van der Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to non-equilibrium systems.

cond-mat.soft↗

arXiv2010

Sound propagation and force chains in granular materials

Granular materials are inherently heterogeneous, leading to challenges in formulating accurate models of sound propagation. In order to quantify acoustic responses in space and time, we perform experiments in a photoelastic granular material in which the internal stress pattern (in the form of force chains) is visible. We utilize two complementary methods, high-speed imaging and piezoelectric transduction, to provide particle-scale measurements of both the amplitude and speed of an acoustic wave in the near-field regime. We observe that the wave amplitude is on average largest within particles experiencing the largest forces, particularly in those chains radiating away from the source, with the force-dependence of this amplitude in qualitative agreement with a simple Hertzian-like model of particle contact area. In addition, we are able to directly observe rare transient force chains formed by the opening and closing of contacts during propagation. The speed of the leading edge of the pulse is in quantitative agreement with predictions for one-dimensional chains, while the slower speed of the peak response suggests that it contains waves which have travelled over multiple paths even within just this near-field region. These effects highlight the importance of particle-scale behaviors in determining the acoustical properties of granular materials.

cond-mat.mtrl-sci↗

arXiv2010

Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $μ$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Voronoï tessellation, we find the variance of the local volume fraction $ϕ$ monotonically decreases as the system becomes more dense, independent of boundary condition and $μ$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar ϕ$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $ϕ$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(ϕ)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model.

cond-mat.soft↗

arXiv2010

Universal shapes formed by two interacting cracks

We investigate the origins of the widely-observed "en passant" crack pattern which forms through interactions between two approaching cracks. A rectangular elastic plate is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lenticular fragment. We find that for materials with diverse mechanical properties, the shape of this fragment has an aspect ratio of 2:1, with the length scale set by the initial crack offset $s$ and the time scale set by the ratio of $s$ to the pulling velocity. The cracks have a universal square root shape which we understand using a simple geometric model of the crack-crack interaction.

cond-mat.mtrl-sci↗

arXiv2010

Fluorescent visualization of a spreading surfactant

The spreading of surfactants on thin films is an industrially and medically important phenomenon, but the dynamics are highly nonlinear and visualization of the surfactant dynamics has been a long-standing experimental challenge. We perform the first quantitative, spatiotemporally-resolved measurements of the spreading of an insoluble surfactant on a thin fluid layer. During the spreading process, we directly observe both the radial height profile of the spreading droplet and the spatial distribution of the fluorescently-tagged surfactant. We find that the leading edge of spreading circular layer of surfactant forms a Marangoni ridge in the underlying fluid, with a trough trailing the ridge as expected. However, several novel features are observed using the fluorescence technique, including a peak in the surfactant concentration which trails the leading edge, and a flat, monolayer-scale spreading film which differs from concentration profiles predicted by current models. Both the Marangoni ridge and surfactant leading edge can be described to spread as $R \propto t^δ$. We find spreading exponents, $δ_H \approx 0.30$ and $δ_Γ\approx 0.22$ for the ridge peak and surfactant leading edge, respectively, which are in good agreement with theoretical predictions of $δ= 1/4$. In addition, we observe that the surfactant leading edge initially leads the peak of the Marangoni ridge, with the peak later catching up to the leading edge.

cond-mat.soft↗

arXiv2010

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case.

math.AP↗

arXiv2010

Equilibration of granular subsystems

We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We extract the statistics of various static and dynamic quantities, and uncover a materials-independent relationship between the average packing fraction and its fluctuations. This relationship defines an intensive parameter which decouples from the volume statistics, and remarkably takes the same value in both subsystems. We also observe that an effective diffusion coefficient also takes the same value in each subsystem, even as the structural relaxation time increases over several orders of magnitude. These observations provide strong constraints on the eventual establishment of a granular equation of state.

cond-mat.soft↗