arXiv subjects

Martin van Hecke

Publications and source records attributed to Martin van Hecke.

At least 73 records · Page 4Linked to original sources

arXiv2012

Onset of Irreversibility in Cyclic Shear of Granular Packings

We investigate the onset of irreversibility in a dense granular medium subjected to cyclic shear in a split-bottom geometry. To probe the micro and mesoscale we image bead trajectories in 3D throughout a series of shear strain oscillations. Though beads lose and regain contact with neighbors during a cycle, the topology of the contact network exhibits reversible properties for small oscillation amplitudes. With increasing reversal amplitude a transition to an irreversible diffusive regime occurs.

cond-mat.soft↗

arXiv2011

Shocks near Jamming

Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly non-linear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.

cond-mat.soft↗

arXiv2011

The Jamming Perspective on Wet Foams

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can {\em jam} into a rigid, disordered state where they withstand finite shear stresses before yielding. The jamming transition has been studied extensively, in particular in computer simulations of frictionless, soft, purely repulsive spheres. Foams and emulsions are the closest realizations of this model, and in foams, the (un)jamming point corresponds to the wet limit, where the bubbles become spherical and just form contacts. Here we sketch the relevance of the jamming perspective for the geometry and flow of foams --- and also discuss the impact that foams studies may have on theoretical studies on jamming. We first briefly review insights into the crucial role of disorder in these systems, culminating in the breakdown of the affine assumption that underlies the rich mechanics near jamming. Second, we discuss how crucial theoretical predictions, such as the square root scaling of contact number with packing fraction, and the nontrivial role of disorder and fluctuations for flow have been observed in experiments on 2D foams. Third, we discuss a scaling model for the rheology of disordered media that appears to capture the key features of the flow of foams, emulsions and soft colloidal suspensions. Finally, we discuss how best to confront predictions of this model with experimental data.

cond-mat.soft↗

arXiv2010

From Frictional to Viscous Behavior: Three Dimensional Imaging and Rheology of Gravitational Suspensions

We probe the three dimensional flow structure and rheology of gravitational (non-density matched) suspensions for a range of driving rates in a split-bottom geometry. We establish that for sufficiently slow flows, the suspension flows as if it were a dry granular medium, and confirm recent theoretical modeling on the rheology of split-bottom flows. For faster driving, the flow behavior is shown to be consistent with the rheological behavior predicted by the recently developed "inertial number approaches for suspension flows.

cond-mat.soft↗

arXiv2010

Dynamical Heterogeneities in Grains and Foams

Dynamical heterogeneities have been introduced in the context of the glass transition of molecular liquids and the lengthscale associated with them has been argued to be at the origin of the observed quasi-universal behaviour of glassy systems. Dense amorphous packings of granular media and foams also exhibit slow dynamics, intermittency and heterogeneities. We review a number of recent experimental studies of these systems, where one has direct access to the relevant space-time dynamics, allowing for direct visualisations of the dynamical heterogeneities. On one hand these visualisations provide a unique opportunity to access the microscopic mechanisms responsible for the growth of dynamical correlations. On the other hand focussing on the differences in these heterogeneities in microscopically different systems allows to discuss the range of the analogies between molecular thermal glasses and athermal glasses such as granular media and foams. Finally this review is the opportunity to discuss various approaches to actually extract quantitatively the dynamical lengthscale from experimental data.

cond-mat.soft↗

arXiv2010

Jaming and Geometry of Two-Dimensional Foams

We experimentally probe the vicinity of the jamming point J, located at a density $ϕ$ corresponding to random close packing ($ϕ_{rcp} = 0.842$), in two dimensional, bidisperse packings of foam bubbles. We vary the density of the foam layer and extract geometrical measures by image analysis. We confirm the predicted scaling of the average contact number Z with $ϕ$ and compare the distribution of local contact numbers to a simple model. We further establish that the distribution of areas $p(A)$ strongly depends on $ϕ$. Finally, we find that the distribution of contact forces $p(f)$ systematically varies with density.

cond-mat.soft↗

arXiv2010

Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.

cond-mat.soft↗

arXiv2010

The force network ensemble for granular packings

For packings of hard but not perfectly rigid particles, the length scales that govern the packing geometry and the contact forces are well separated. This separation of length scales is explored in the force network ensemble, where one studies the space of allowed force configurations for a given, frozen contact geometry. Here we review results of this approach, which yields nontrivial predictions for the effect of packing dimension and anisotropy on the contact force distribution $P(f)$, the response to overall shear and point forcing, all of which can be studied in great numerical detail. Moreover, there are emerging analytical approaches that very effectively capture, for example, the form of force distributions.

cond-mat.soft↗

arXiv2010

Granular Flows in Split-Bottom Geometries

There is a simple and general experimental protocol to generate slow granular flows that exhibit wide shear zones, qualitatively different from the narrow shear bands that are usually observed in granular materials . The essence is to drive the granular medium not from the sidewalls, but to split the bottom of the container that supports the grains in two parts and slide these parts past each other. Here we review the main features of granular flows in such split-bottom geometries.

cond-mat.soft↗

arXiv2009

Local contact numbers in two dimensional packings of frictional disks

We analyze the local structure of two dimensional packings of frictional disks numerically. We focus on the fractions x_i of particles that are in contact with i neighbors, and systematically vary the confining pressure p and friction coefficient μ. We find that for all μ, the fractions x_i exhibit powerlaw scaling with p, which allows us to obtain an accurate estimate for x_i at zero pressure. We uncover how these zero pressure fractions x_i vary with μ, and introduce a simple model that captures most of this variation. We also probe the correlations between the contact numbers of neighboring particles.

cond-mat.soft↗

arXiv2009

Flow-induced Agitations Create a Granular Fluid

We fluidize a granular medium through localized stirring and probe the mechanical response of quiescent regions far away from the main flow. In these regions the material behaves like a liquid: high-density probes sink, low-density probes float at the depth given by Archimedes' law, and drag forces on moving probes scale linearly with the velocity. The fluid-like character of the material is set by agitations generated in the stirred region, suggesting a non-local rheology: the relation between applied stress and observed strain rate in one location depends on the strain rate in another location.

cond-mat.other↗

arXiv2009

Jammed frictionless discs: connecting local and global response

By calculating the linear response of packings of soft frictionless discs to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and non-affine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale $\ell^*$ up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as $1/Δz$, where $Δz$ is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the non-affine displacements of the particles using the \emph{displacement angle distribution}, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli.

cond-mat.soft↗

arXiv2009

Non-affine response: jammed packings versus spring networks

We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.

cond-mat.soft↗

arXiv2009

Flow in linearly sheared two dimensional foams: from bubble to bulk scale

We probe the flow of two dimensional foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous (shear banded) velocity profiles, while monodisperse, ordered foams are also shear banded, but essentially rate independent. Second, we introduce a simple model based on balancing the averaged drag forces between the bubbles and the top plate and the averaged bubble-bubble drag forces. This model captures the observed rate dependent flows, and the rate independent flows. Third, we perform independent rheological measurements, both for ordered and disordered systems, and find these to be fully consistent with the scaling forms of the drag forces assumed in the simple model, and we see that disorder modifies the scaling. Fourth, we vary the packing fraction $ϕ$ of the foam over a substantial range, and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, our model describes flow profiles and rate dependence over the whole range of packing fractions with the same power law exponents -- only a dimensionless number $k$ which measures the ratio of the pre-factors of the viscous drag laws is seen to vary with packing fraction. We find that $k \sim (ϕ-ϕ_c)^{-1}$, where $ϕ_c \approx 0.84$, corresponding to the 2d jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power law) rheology observed in a wide range of disordered materials.

cond-mat.soft↗

arXiv2009

Relaxation and flow in linearly sheared two-dimensional foams

We probe the relation between shear induced structural relaxation and rheology in experiments on sheared two-dimensional foams. The relaxation time, which marks the crossover to diffusive bubble motion, is found to scale non-trivially with the local strain rate. The rheology of the foam is shown to be intimately linked to the scaling of the relaxation time, thus connecting macroscopic flow and microscopic bubble motion.

cond-mat.soft↗

arXiv2008

Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams

The shear flow of two dimensional foams is probed as a function of shear rate and disorder. Disordered foams exhibit strongly rate dependent velocity profiles, whereas ordered foams show rate independence. Both behaviors are captured quantitatively in a simple model based on the balance of the time-averaged drag forces in the foam, which are found to exhibit power-law scaling with the foam velocity and strain rate. Disorder modifies the scaling of the averaged inter-bubble drag forces, which in turn causes the observed rate dependence in disordered foams.

cond-mat.soft↗

arXiv2007

Stresses in Smooth Flows of Dense Granular Media

The form of the stress tensor is investigated in smooth, dense granular flows which are generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatial region, the form of the stress tensor is directly dictated by the flow field: The stress and strain-rate tensors are co-linear. The effective friction, defined as the ratio between shear and normal stresses acting on a shearing plane, is found not to be constant but to vary throughout the flowing zone. This variation can not be explained by inertial effects, but appears to be set by the local geometry of the flow field. This is in agreement with a recent prediction, but in contrast with most models for slow grain flows, and points to there being a subtle mechanism that selects the flow profiles.

cond-mat.soft↗

arXiv2007

MR Imaging of Reynolds Dilatancy in the Bulk of Smooth Granular Flows

Dense granular matter has to expand in order to flow, a phenomenon known as dilatancy. Here we perform, by means of Magnetic Resonance Imaging, direct measurements of the evolution of the local packing density of a slow and smooth granular shear flow generated in a split-bottomed geometry. The dilatancy is found to be surprisingly strong. The dilated zone follow the region of large strain rate and slowly spreads as a function of time. This suggests that the local packing density is governed by the total amount of local strain experienced since the start of the experiment.

cond-mat.soft↗