Recently, detailed experiments on visco-elastic channel flow have provided convincing evidence for a nonlinear instability scenario which we had argued for based on calculations for visco-elastic... Show moreRecently, detailed experiments on visco-elastic channel flow have provided convincing evidence for a nonlinear instability scenario which we had argued for based on calculations for visco-elastic Couette flow. Motivated by these experiments we extend the previous calculations to the case of visco-elastic Poiseuille flow, using the Oldroyd-B constitutive model. Our results confirm that the subcritical instability scenario is similar for both types of flow, and that the nonlinear transition occurs for Weissenberg numbers somewhat larger than one. We provide detailed results for the convergence of our expansion and for the spatial structure of the mode that drives the instability. This also gives insight into possible similarities with the mechanism of the transition to turbulence in Newtonian pipe flow. Show less
Tighe, B.P.; Woldhuis, E.; Remmers, J.J.C.; Saarloos, W. van; Hecke, M.L. van 2010
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... Show moreWe 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 the values of the exponents depart from prior results. We validate predictions of the model with simulations. Show less
We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By... Show moreWe conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational properties are very similar to those predicted for zero-temperature sphere packings and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition. Show less
By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and... Show moreBy calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine 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 ℓ∗ 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 nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli. Show less
We present simulations of coherent structures in compressible flows near the transition to turbulence using the dissipative particle dynamics method. The structures we find are remarkably... Show moreWe present simulations of coherent structures in compressible flows near the transition to turbulence using the dissipative particle dynamics method. The structures we find are remarkably consistent with experimental observations and direct numerical simulations (DNS) simulations of incompressible flows, despite a difference in Mach number of several orders of magnitude. The bifurcation from the laminar flow is bistable and shifts to higher Reynolds numbers when the fluid becomes more compressible. This work underlines the robustness of coherent structures in the transition to turbulence and illustrates the ability of particle-based methods to reproduce complex nonlinear instabilities. Show less
Zondervan, R.; Xia, T.; Meer, H. van der; Storm, C.; Kulzer, F.M.; Saarloos, W. van; Orrit, M.A.G.J. 2008
We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient μ. The density... Show moreWe probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient μ. The density of vibrational states exhibits a crossover from a plateau at frequencies ω≳ω∗(p,μ) to a linear growth for ω≲ω∗(p,μ). We show that ω∗ is proportional to Δz, the excess number of contacts per grain relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have Δz→0, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity. Show less
Shundyak, K.; Hecke, M.L. van; Saarloos, W. van 2007
We show that in slowly generated two-dimensional packings of frictional spheres, a significant fraction of the friction forces lie at the Coulomb threshold—for small pressure p and friction... Show moreWe show that in slowly generated two-dimensional packings of frictional spheres, a significant fraction of the friction forces lie at the Coulomb threshold—for small pressure p and friction coefficient μ, about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For p→0, our frictional packings approximately satisfy this relation over the full range of μ. This is in agreement with a previous conjecture that gently built packings should be marginal solids at jamming. In addition, the contact numbers and packing densities scale with both p and μ. Show less
Saarloos, W. van; Somfai, E.; Hecke, M. van; Ellenbroek, W.G.; Shundyak, K. 2007
The form of the stress tensor is investigated in smooth, dense granular flows whichare generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatialregion, the... Show moreThe form of the stress tensor is investigated in smooth, dense granular flows whichare generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatialregion, the form of the stress tensor is directly dictated by the flow field: The stress and strain-ratetensors are co-linear. The effective friction, defined as the ratio between shear and normal stressesacting on a shearing plane, is found not to be constant but to vary throughout the flowing zone.This variation cannot be explained by inertial effects, but appears to be set by the local geometryof the flow field. This is in agreement with a recent prediction, but in contrast with most modelsfor slow grain flows, and points to there being a subtle mechanism that selects the flow profiles. Show less
Ellenbroek, W.G.; Somfai, E.; Hecke, M.L. van; Saarloos, W. van 2006
We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and... Show moreWe study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number. Show less
