arXiv subjects

D. J. Durian

Publications and source records attributed to D. J. Durian.

At least 19 recordsLinked to original sources

arXiv2020

Resolving Tensions Surrounding Massive Pulleys

The distribution of string tension on the contact line between an ideal string and a massive pulley is a frequently-discussed but incompletely-posed problem that confronts students in introductory mechanics. We highlight ambiguities in the usual presentation of this problem by the massive Atwood's machine and discuss two compact resolutions that treat situations where the pulley or the string elastically deform. We propose experiments that can be developed in an intermediate laboratory to determine the tension profile.

physics.ed-ph↗

arXiv2018

The Hindered Settling Function at Low Re Has Two Branches

We analyze hindered settling speed versus volume fraction $ϕ$ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well-described by a hindered settling function of the Richardson-Zaki form $H(ϕ)=(1-ϕ)^n$ but with different exponents: $n=5.6\pm0.1$ for Brownian systems with Péclet number ${\rm Pe}<{\rm Pe}_c$, and $n=4.48\pm0.04$ for non-Brownian systems with ${\rm Pe}>{\rm Pe}_c$. The crossover Péclet number is ${\rm Pe}_c\approx10^8$, which is surprisingly large.

cond-mat.soft↗

arXiv2018

The Spectrum of Structure for Jammed and Unjammed Soft Disks

We investigate the short, medium, and long-range structure of soft disk configurations for a wide range of area fractions and simulation protocols by converting the real-space spectrum of volume fraction fluctuations for windows of width $L$ to the distance $h(L)$ from the window boundary over which fluctuations occur. Rapidly quenched unjammed configurations exhibit size-dependent super-Poissonian long-range features that, surprisingly, approach the totally-random limit even close to jamming. Above and just below jamming, the spectra exhibit a plateau, $h(L)=h_e$, for $L$ larger than particle size and smaller than a cutoff $L_c$ beyond which there are long-range fluctuations. The value of $h_e$ is independent of protocol and characterizes the putative hyperuniform limit. This behavior is compared with that for Einstein solids, with and without hyperuniformity-destroying defects. We find that key structural features of the particle configurations are more evident, as well as easier and more intuitive to quantify, using the real-space spectrum of hyperuniformity lengths rather than the spectral density.

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arXiv2017

Characterizing Pixel and Point Patterns with a Hyperuniformity Disorder Length

We introduce the concept of a hyperuniformity disorder length that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance $h$ from the boundary of the window. We first compute special expectations and bounds in $d$ dimensions, and then illustrate the range of behavior of $h$ versus window size $L$ by analyzing three different types of simulated two-dimensional pixel pattern - where particle positions are stored as a binary digital image in which pixels have value zero/one if empty/contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result $h=L/2$. Next we consider vacancy patterns, where a fraction $f$ of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with $h=(L/2)(f/d)$ for small $f$. For a hyperuniform system with no long-range density fluctuations, we consider Einstein patterns where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large $L$, $h$ approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to grayscale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of $h(L)$ versus $L$. We call this approach Hyperuniformity Disorder Length Spectroscopy.

cond-mat.soft↗

arXiv2017

Hyperuniformity Disorder Length Spectroscopy for Extended Particles

The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial configuration of the particles, and provides a way to diagnose the degree of hyperuniformity in terms of the scaling of $h$ and its value in comparison with established bounds. Here, this approach is generalized for extended particles, which are larger than the image resolution and can lie partially inside and partially outside the measuring windows. The starting point is an expression for the volume fraction variance in terms of four distinct volumes: that of the particle, the measuring window, the mean-squared overlap between particle and region, and the region over which particles have non-zero overlap with the measuring window. After establishing limiting behaviors, computational methods are developed for both continuum and pixelated particles. Exact results are presented for particles of special shape, and for measuring windows of special shape. Comparison is made for other particle shapes, using simulated Poisson patterns. And the effects of polydisersity and image errors are discussed. For small measuring windows, both particle shape and spatial arrangement affect the form of the variance. For large regions, the variance scaling depends only on arrangement but particle shape sets the numerical proportionality. The combined understanding permit the measured variance to be translated to the spectrum of hyperuniformity lengths versus region size, as the quantifier of spatial arrangement. This program is demonstrated for a system of non-overlapping particles at a series of increasing packing fractions as well as for an Einstein pattern of particles with several different extended shapes.

cond-mat.soft↗

arXiv2017

Border-Crossing Model for the Diffusive Coarsening of Two-Dimensional and Quasi-Two-Dimensional Wet Foams

For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called "border-blocking" models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux, however, this approximation dramatically fails in the wet/unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-2d foams. And we show how the $dA/dt=K_0(n-6)$ von~Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von~Neumann law to compute the growth rate of the average bubble area, which is not constant.

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arXiv2016

Intermittency and Velocity Fluctuations in Hopper Flows Prone to Clogging

We experimentally study the dynamics of granular media in a discharging hopper. In such flows, there often appears to be a critical outlet size $D_c$ such that the flow never clogs for $D > D_c$. We report on the time-averaged velocity distributions, as well as temporal intermittency in the ensemble-averaged velocity of grains in a viewing window, for both $D < D_c$ and $D > D_c$, near and far from the outlet. We characterize the velocity distributions by the standard deviation and the skewness of the distribution of vertical velocities. We propose a measure for intermittency based on the two-sample Kolmogorov-Smirnov $D_{KS}$-statistic for the velocity distributions as a function of time. We find that there is no discontinuity or kink in these various measures as a function of hole size. This result supports the proposition that there is no well-defined $D_c$ and that clogging is always possible. Furthermore, the intermittency time scale of the flow is set by the speed of the grains at the hopper exit. This latter finding is consistent with a model of clogging as the independent sampling for stable configurations at the exit with a rate set by the exiting grain speed [Thomas and Durian, Phys. Rev. Lett. (2015)].

cond-mat.soft↗

arXiv2015

Rheology of sediment transported by a laminar flow

Understanding the dynamics of fluid-driven sediment transport remains challenging, as it is an intermediate region between a granular material and a fluid flow. Boyer \textit{et al.}\citep{Boyer2011} proposed a local rheology unifying dense dry-granular and viscous-suspension flows, but it has been validated only for neutrally-buoyant particles in a confined system. Here we generalize the Boyer \textit{et al.}\citep{Boyer2011} model to account for the weight of a particle by addition of a pressure $P_0$, and test the ability of this model to describe sediment transport in an idealized laboratory river. We subject a bed of settling plastic particles to a laminar-shear flow from above, and use Refractive-Index-Matching to track particles' motion and determine local rheology --- from the fluid-granular interface to deep in the granular bed. Data from all experiments collapse onto a single curve of friction $μ$ as a function of the viscous number $I_v$ over the range $10^{-5} \leq I_v \leq 1$, validating the local rheology model. For $I_v < 10^{-5}$, however, data do not collapse. Instead of undergoing a jamming transition with $μ\rightarrow μ_s$ as expected, particles transition to a creeping regime where we observe a continuous decay of the friction coefficient $μ\leq μ_s$ as $I_v$ decreases. The rheology of this creep regime cannot be described by the local model, and more work is needed to determine whether a non-local rheology model can be modified to account for our findings.

cond-mat.soft↗

arXiv2015

Fraction of clogging configurations sampled by granular hopper flow

We measure the fraction $F$ of flowing grain configurations that precede a clog, based on the average mass discharged between clogging events for various aperture geometries. By tilting the hopper, we demonstrate that $F$ is a function of the hole area projected in the direction of the exiting grain velocity. By varying the length of slits, we demonstrate that grains clog in the same manner as if they were flowing out of a set of smaller independent circular openings. The collapsed data for $F$ can be fit to a decay that is exponential in hole width raised to the power of the system dimensionality. This is consistent with a simple model in which individual grains near the hole have a large but constant probability to precede a clog. Such a picture implies that there is no sharp clogging transition, and that all hoppers have a nonzero probability to clog. See Supplemental Material for models of clogging as a discrete Poisson process, and for resulting alternative measures of l based on the standard deviation of the discharge mass distribution.

cond-mat.soft↗

arXiv2014

Tunable capillary-induced attraction between vertical cylinders

Deformation of a fluid interface caused by the presence of objects at the interface can lead to large lateral forces between the objects. We explore these fluid-mediated attractive force between partially submerged vertical cylinders. Forces are experimentally measured by slowly separating cylinder pairs and cylinder triplets after capillary rise is initially established for cylinders in contact. For cylinder pairs, numerical computations and a theoretical model are found to be in good agreement with measurements. The model provides insight into the relative importance of the contributions to the total force. For small separations, the pressure term dominates, while at large separations, surface tension becomes more important. A cross-over between the two regimes occurs at a separation of around half of a capillary length. The experimentally measured forces between cylinder triplets are also in good agreement with numerical computations, and we show that pair-wise contributions account for nearly all of the attractive force between triplets. For cylinders with equilibrium capillary rise height greater than the height of the cylinder, we find that the attractive force depends on the height of the cylinders above the submersion level, which provides a means to create precisely-controlled tunable cohesive forces between objects deforming a fluid interface.

cond-mat.soft↗

arXiv2014

Granular discharge rate for submerged hoppers

The discharge of spherical grains from a hole in the bottom of a right circular cylinder is measured with the entire system underwater. We find that the discharge rate depends on filling height, in contrast to the well-known case of dry non-cohesive grains. It is further surprising that the rate increases up to about twenty five percent, as the hopper empties and the granular pressure head decreases. For deep filling, where the discharge rate is constant, we measure the behavior as a function of both grain and hole diameters. The discharge rate scale is set by the product of hole area and the terminal falling speed of isolated grains. But there is a small-hole cutoff of about two and half grain diameters, which is larger than the analogous cutoff in the Beverloo equation for dry grains.

cond-mat.soft↗

arXiv2014

Rheology of nearly ideal 3d foams

We probe the complex rheology of nearly ideal 3d foam by flowing through a narrow column. The foams we investigate have large bubble size, to minimize the effects of coarsening, and are very dry. Foams of this type cannot be studied via conventional rheometry. The foam flows upward through a vertical rectangular column with a 4:1 cross-sectional aspect ratio, by bubbling gas through a soapy solution at the base of our apparatus. At the column's narrow surfaces are sticky boundaries, which create shear due to the zero velocity boundary condition. As expected, the flow profile between the adjacent slippery broad faces is flat, however the profile between the narrow, sticky faces exhibits a curved velocity profile that is dependent on gas flow rate. We are able to analyze a 2d velocity profile from a 3d bulk system. We employ particle image velocimetry to measure the strain rate, and compute the stress from the pressure drop along the channel, to investigate the local stress-strain relationships in a flowing foam. We find these dry foams to have a Hershel-Bulkley exponent of 0.21, which is significantly lower (more shear thinning) than other results shown in the literature for much wetter foams.

cond-mat.soft↗

arXiv2014

Morphology of rain water channelization in systematically varied model sandy soils

We visualize the formation of fingered flow in dry model sandy soils under different raining conditions using a quasi-2d experimental set-up, and systematically determine the impact of soil grain diameter and surface wetting property on water channelization phenomenon. The model sandy soils we use are random closely-packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates into a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in water infiltration depth, water channel width, and water channel separation. At a fixed raining condition, we combine the effects of grain diameter and surface hydrophobicity into a single parameter and determine its influence on water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to rain water channelization phenomenon, including pre-wetting sandy soils at different level before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers.

cond-mat.soft↗

arXiv2014

Rain water transport and storage in a model sandy soil with hydrogel particle additives

We study rain water infiltration and drainage in a dry model sandy soil with superabsorbent hydrogel particle additives by measuring the mass of retained water for non-ponding rainfall using a self-built 3D laboratory set-up. In the pure model sandy soil, the retained water curve measurements indicate that instead of a stable horizontal wetting front that grows downward uniformly, a narrow fingered flow forms under the top layer of water-saturated soil. This rain water channelization phenomenon not only further reduces the available rain water in the plant root zone, but also affects the efficiency of soil additives, such as superabsorbent hydrogel particles. Our studies show that the shape of the retained water curve for a soil packing with hydrogel particle additives strongly depends on the location and the concentration of the hydrogel particles in the model sandy soil. By carefully choosing the particle size and distribution methods, we may use the swollen hydrogel particles to modify the soil pore structure, to clog or extend the water channels in sandy soils, or to build water reservoirs in the plant root zone.

cond-mat.soft↗

arXiv2013

Structure and coarsening at the surface of a dry three-dimensional aqueous foam

We utilize total-internal reflection to isolate the two-dimensional `surface foam' formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions are independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes, are all very similar to those for two-dimensional foams. However the size number distribution is slightly broader and the shapes are slightly more elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles, due to rearrangement in the bulk. And von Neumann's law is dramatically violated for individual bubbles. But nevertheless, our most striking finding is that von Neumann's law appears to holds on average. Namely the average rate of area change for surface bubbles appears to be proportional to the number of sides minus six, but with individual bubbles showing a distribution of deviations from this average behavior.

cond-mat.soft↗

arXiv2013

Depth-dependent resistance of granular media to vertical penetration

We measure the quasi-static friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasi-static friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.

cond-mat.soft↗

arXiv2013

Drag force scaling for penetration into granular media

Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure and Coulomb friction law. The combined results provide an explanation for the previously-observed penetration depth scaling.

cond-mat.soft↗

arXiv2013

Effect of hydrogel particle additives on water-accessible pore structure of sandy soils: A custom pressure plate apparatus and capillary bundle model

To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution $f(r)$ of the water-accessible pores with radii less than $r$. This is validated by measurements of water expelled from a model sandy soil composed of 2 mm diameter glass beads. In particular, the expelled water is found to depend dramatically on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log-normal, and the total cross-sectional area fraction of the accessible pore space is found to be $f_0=0.34$. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed.

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