arXiv subjects

Karen E. Daniels

Publications and source records attributed to Karen E. Daniels.

At least 55 records · Page 3Linked to original sources

arXiv2017

Focus on Imaging Methods in Granular Physics

Granular materials are complex multi-particle ensembles in which macroscopic properties are largely determined by inter-particle interactions between their numerous constituents. In order to understand and to predict their macroscopic physical behavior, it is necessary to analyze the composition and interactions at the level of individual contacts and grains. To do so requires the ability to image individual particles and their local configurations to high precision. A variety of competing and complementary imaging techniques have been developed for that task. In this introductory paper accompanying the Focus Issue, we provide an overview of these imaging methods and discuss their advantages and drawbacks, as well as their limits of application.

physics.ins-det↗

arXiv2017

An experimental investigation of the force network ensemble

We present an experiment in which a horizontal quasi-2D granular system with a fixed neighbor network is cyclically compressed and decompressed over 1000 cycles. We remove basal friction by floating the particles on a thin air cushion, so that particles only interact in-plane. As expected for a granular system, the applied load is not distributed uniformly, but is instead concentrated in force chains which form a network throughout the system. To visualize the structure of these networks, we use particles made from photoelastic material. The experimental setup and a new data-processing pipeline allow us to map out the evolution subject to the cyclic compressions. We characterize several statistical properties of the packing, including the probability density function of the contact force, and compare them with theoretical and numerical predictions from the force network ensemble theory.

cond-mat.soft↗

arXiv2017

Oxidation-Mediated Fingering in Liquid Metals

We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a gallium-based liquid metal alloy to values approaching zero, thereby inducing drastic shape changes, including the formation of fractals. The measured fractal dimension ($D = 1.3 \pm 0.05$) places the instability in a different universality class than other fingering instabilities. By characterizing changes in morphology and dynamics as a function of droplet volume and applied electric potential, we identify the three main forces involved in this process: interfacial tension, gravity, and oxidative stress. Importantly, we find that electrochemical oxidation can generate compressive interfacial forces that oppose the tensile forces at a liquid interface. Thus, the surface oxide layer not only induces instabilities, but ultimately provides a physical barrier that halts the instabilities at larger positive potentials. Controlling the competition between surface tension and oxidative (compressive) stresses at the interface is important for the development of reconfigurable electronic, electromagnetic, and optical devices that take advantage of the metallic properties of liquid metals.

cond-mat.soft↗

arXiv2016

Photoelastic force measurements in granular materials

Photoelastic techniques are used to make both qualitative and quantitative measurements of the forces within idealized granular materials. The method is based on placing a birefringent granular material between a pair of polarizing filters, so that each region of the material rotates the polarization of light according to the amount of local of stress. In this review paper, we summarize past work using the technique, describe the optics underlying the technique, and illustrate how it can be used to quantitatively determine the vector contact forces between particles in a 2D granular system. We provide a description of software resources available to perform this task, as well as key techniques and resources for building an experimental apparatus.

cond-mat.soft↗

arXiv2016

Capillary fracture of ultrasoft gels: heterogeneity and delayed nucleation

A droplet of surfactant spreading on an ultrasoft ($E \lesssim 100$ Pa) gel substrate will produce capillary fractures at the gel surface; these fractures originate at the contact-line and propagate outwards in a starburst pattern. There is an inherent variability in both the number of fractures formed and the time delay before fractures form. In the regime where single fractures form, we observe a Weibull-like distribution of delay times, consistent with a thermally-activated process. The shape parameter is close to 1 for softer gels (a Poisson process), and larger for stiffer gels (indicative of aging). For single fractures, the characteristic delay time is primarily set by the elastocapillary length of the system, calculated from the differential in surface tension between the droplet and the substrate, rather than the elastic modulus as for stiffer systems. For multiple fractures, all fractures appear simultaneously and long delay times are suppressed. The delay time distribution provides a new technique for probing the energy landscape and fracture toughness of ultrasoft materials.

cond-mat.soft↗

arXiv2016

Deformation of an Elastic Substrate Due to a Resting Sessile Droplet

On a sufficiently-soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates which deform under loading. It remains an open question whether the contact line transmits a non-zero radial force to the substrate surface in addition to the conventional vertical force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a nonzero radial contact line force, it is necessary to include a previously-neglected radial traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally-accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero radial contact line forces.

cond-mat.soft↗

arXiv2016

Topological and geometric measurements of force chain structure

Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts to a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force chain structure, with the goal of identifying shape differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here, we discuss a trio of related but fundamentally distinct measurements of mesoscale structure of force chains in arbitrary 2D packings, including a novel statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.

cond-mat.soft↗

arXiv2016

High refractive index immersion liquid for super-resolution 3D imaging using sapphire-based aNAIL optics

Optically-transparent immersion liquids with refractive index (n ~ 1.77) to match sapphire-based aplanatic numerical aperture increasing lens (aNAIL) are necessary for achieving deep 3D imaging with high spatial resolution. We report that antimony tribromide (SbBr$_{3}$) salt dissolved in liquid diiodomethane (CH$_{2}$I$_{2}$) provides a new high refractive index immersion liquid for optics applications. The refractive index is tunable from n = 1.74 (pure) to n = 1.873 (saturated), by adjusting either salt concentration or temperature; this allows it to match (or even exceed) the refractive index of sapphire. Importantly, the solution gives excellent light transmittance in the ultraviolet to near-infrared range, an improvement over commercially-available immersion liquids. This refractive index matched immersion liquid formulation has enabled us to develop a sapphire-based aNAIL objective that has both high numerical aperture (NA = 1.17) and long working distance (WD = 12 mm). This opens up new possibilities for deep 3D imaging with high spatial resolution.

physics.optics↗

arXiv2016

Nonaffine deformation under compression and decompression of a flow-stabilized solid

Understanding the particle-scale transition from elastic deformation to plastic flow is central to making predictions about the bulk material properties and response of disordered materials. To address this issue, we perform experiments on flow-stabilized solids composed of micron-scale spheres within a microfluidic channel, in a regime where particle inertia is negligible. Each solid heap exists within a stress gradient imposed by the flow, and we track the positions of particles in response to single impulses of fluid-driven compression or decompression. We find that the resulting deformation field is well-decomposed into an affine field, with a constant strain profile throughout the solid, and a non-affine field. The magnitude of this non-affine response decays with the distance from the free surface in the long-time limit, suggesting that the distance from jamming plays a significant role in controlling the length scale of plastic flow. Finally, we observe that compressive pulses create more rearrangements than decompressive pulses, an effect that we quantify using the $D^2_\mathrm{min}$ statistic for non-affine motion. Unexpectedly, the time scale for the compression response is shorter than for decompression at the same strain (but unequal pressure), providing insight into the coupling between deformation and cage-breaking.

cond-mat.soft↗

arXiv2016

Evolution of network architecture in a granular material under compression

As a granular material is compressed, the particles and forces within the system arrange to form complex heterogeneous structures. Force chains are a prime example and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, characterizing the dynamic nature of mesoscale architectures in granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend current approaches by utilizing multilayer networks as a framework for directly quantifying the evolution of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compression through a series of small, quasistatic steps. Treating particles as network nodes and inter-particle forces as network edges, we construct a multilayer network by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods, and we define quantitative measures to characterize the reconfiguration and evolution of this structure throughout compression. By separately considering the network of normal and tangential forces, we find that they display different structural evolution. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be done by considering the network of tangential forces. The results discussed throughout this study suggest that these novel network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup.

cond-mat.soft↗

arXiv2016

Simulating Surfactant Spreading: Impact of a Physically Motivated Equation of State

For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension. Previous choices of the model EoS have been an ad-hoc decreasing function. Here, we instead propose an empirically-motivated equation of state; this provides a route to resolving some discrepancies and raises new issues to be pursued in future experiments. In addition, we test the influence of the choice of initial conditions and values for the non-dimensional groups. We demonstrate that the choice of EoS improves the agreement in surfactant distribution morphology between simulations and experiments, and impacts the dynamics of the simulations. The relevant feature of the EoS, the gradient, has distinct regions for empirically motivated choices, which suggests that future work will need to consider more than one timescale. We observe that the non-dimensional number controlling the relative importance of gravitational vs. capillary forces has a larger impact on the dynamics than the other non-dimensional groups. Finally, we observe that the experimental approach of using a ring to contain the surfactant could affect the surfactant and fluid dynamics if it disrupts the intended initial surfactant distribution. However, the meniscus itself does not significantly affect the dynamics.

physics.flu-dyn↗

arXiv2016

Spatio-temporal Patterns in Inclined Layer Convection

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $γ$ and the Rayleigh number $R$. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck-Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy-driven and shear-flow driven pattern forming mechanisms. The former are expressed as \rm{longitudinal} convection rolls with their axes oriented parallel to the incline, the latter as perpendicular \rm{transverse} rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3D convection patterns above onset of convection in the $γ-R$ plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies.

physics.flu-dyn↗

arXiv2015

Solid Capillarity: When and How does Surface Tension Deform Soft Solids?

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement.

cond-mat.soft↗

arXiv2015

Friction and Pressure-Dependence of Force Chain Communities in Granular Materials

Granular materials transmit stress via a network of force chains. Despite the importance of these chains to characterizing the stress state and dynamics of the system, there is no common framework for quantifying their their properties. Recently, attention has turned to the tools of network science as a promising route to such a description. In this paper, we apply community detection techniques to numerically-generated packings of spheres over a range of interparticle friction coefficients and confining pressures. In order to extract chain-like features, we use a modularity maximization with a recently-developed geographical null model \cite{Bassett2015}, and optimize the technique to detect branched structures by minimizing the normalized convex hull of the detected communities. We characterize the force chain communities by their size (number of particles), network strength (internal forces), and normalized convex hull ratio (sparseness). We find the that the first two exhibit an approximately linear correlation and are therefore largely redundant. For both pressure $P$ and interparticle friction $μ$, we observe crossovers in behavior. For $μ\lesssim 0.1$, the packings exhibit more sensitivity to pressure. In addition, we identify a crossover pressure where the frictional dependence switches from having more large/strong communities at low $μ$ vs. high $μ$. We explain these phenomena by comparison to the spatial distribution of communities along the vertical axis of the system. These results provide new tools for considering the mesoscale structure of a granular system and pave the way for reduced descriptions based on the force chain structure.

cond-mat.soft↗

arXiv2015

Stretching Rubber, Stretching Minds: a polymer physics lab for teaching entropy

Entropy is a difficult concept to teach using real-world examples. Unlike temperature, pressure, volume, or work, it's not a quantity which most students encounter in their day-to-day lives. Even the way entropy is often qualitatively described, as a measure of disorder, is incomplete and can be misleading. In an effort to address these obstacles, we have developed a simple laboratory activity, the stretching of an elastic rubber sheet, intended to give students hands-on experience with the concepts of entropy, temperature and work in both adiabatic and quasistatic processes. We present two versions of the apparatus: a double-lever system, which may be reproduced with relatively little cost, and a commercial materials testing system, which provides students experience with scientific instrumentation that is used in research.

physics.ed-ph↗

arXiv2015

Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection

Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.

cond-mat.soft↗

arXiv2014

Nonlinear Elasticity of Flow-Stabilized Solids

Thermal fluctuations, geometric exclusion, and external driving all govern the mechanical response of dense particulate suspensions. Here, we measure the stress-strain response of quasi-two-dimensional flow-stabilized microsphere heaps in a regime in which all three effects are present using a microfluidic device. We observe that the elastic modulus and the mean interparticle separation of the heaps are tunable via the confining stress provided by the fluid flow. Furthermore, the measured stress-strain curves exhibit a universal nonlinear shape which can be predicted from a thermal van der Waals equation of state with excluded volume. This analysis indicates that many-body interactions contribute a significant fraction of the stress supported by the heap.

cond-mat.soft↗

arXiv2014

Elastocapillary deformations on partially-wetting substrates: rival contact-line models

A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate, particularly those at the contact-line. We construct a general solution using a displacement potential function for the elastic deformations within a finite elastic substrate associated with these wetting forces, and compare the results for several different contact-line models. Our work incorporates internal contributions to the surface stress from both liquid/solid $Σ_{ls}$ and solid/gas $Σ_{sg}$ solid surface tensions (surface stress), which results in a non-standard boundary-value problem that we solve using a dual integral equation. We compare our results to relevant experiments and conclude that the generalization of solid surface tension $Σ_{ls} \neq Σ_{sg}$ is an essential feature in any model of partial-wetting. The comparisons also allow us to systematically eliminate some proposed contact-line models.

cond-mat.soft↗