Search

We model bidisperse size segregation of granular material in quasi-two-dimensional circular tumbler flow using the advection–diffusion transport equation with an additional term to account for segregation due to percolation. Segregation depends on three dimensionless parameters: the ratio of segregation to advection, ${\it\Lambda}$; the ratio of advection to diffusion, $\mathit{Pe}$; and the dimensionless flowing layer depth, ${\it\epsilon}$. The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, ${\it\Lambda}\,\mathit{Pe}$, and the degree of segregation increases as ${\it\Lambda}\mathit{Pe}$ increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ${\it\epsilon}$ and $\mathit{Pe}$ when ${\it\Lambda}\mathit{Pe}$ is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.

International audience; To better understand the velocity field and flowing layer structure, we have performed a detailed discrete element method study of the flow of monodisperse particles in a partially filled three-dimensional cylindrical rotating tumblers. Similar to what occurs near the poles in spherical and conical tumblers, recirculation cells (secondary flows) develop near the flat endwalls of a cylindrical tumbler in which particles near the surface drift axially toward the endwall, while particles deeper in the flowing layer drift axially toward the midlength of the tumbler. Another recirculation cell with the opposite sense develops next to each endwall recirculation cell, extending to the midlength of the tumbler. For a long enough tumbler, each endwall cell is about one quarter of the tumbler diameter in length. Endwall cells are insensitive to tumbler length and relatively insensitive to rotation speed (so long as the flowing layer remains flat and continuously flowing) or fill level (from 25% to 50% full). However, for shorter tumblers (0.5 to 1.0 length/diameter aspect ratio) the endwall cell size does not change much, while center cells reduce their size and eventually disappear for the shortest tumblers. For longer tumblers (length/diameter aspect ratio larger than 2), a stagnation zone appears in between the central cells. These results provide insight into the mixing of monodisperse particles in rotating cylindrical tumblers as well as the frictional effects of the tumbler endwalls.

We study the transition between steady flows of noncohesive granular materials in quasi-two-dimensional bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing particles that propagates downstream over the rising free surface with a wedge front velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The entire transition is well modeled as a moving boundary problem with a diffusionlike equation derived from local mass balance and a local relation between the flux and the surface slope.

We present an analytic method to find the areas of nonmixing regions in orientation-preserving spherical piecewise isometries (PWIs), and apply it to determine the mixing efficacy of a class of spherical PWIs derived from granular flow in a biaxial tumbler. We show that mixing efficacy has a complex distribution across the protocol space, with local minima in mixing efficacy, termed resonances, that can be determined analytically. These resonances are caused by the interaction of two mode-locking-like phenomena.

While structures and bifurcations controlling tracer particle transport and mixing have been studied extensively for systems with only stretching-and-folding, and to a lesser extent for systems with only cutting-and-shuffling, few studies have considered systems with a combination of both. We demonstrate two bifurcations for non-mixing islands associated with elliptic periodic points that only occur in systems with combined cutting-and-shuffling and stretching-and-folding, using as an example a map approximating biaxial rotation of a less-than-half-full spherical granular tumbler. First, we characterize a bifurcation of elliptic island containment, from containment by manifolds associated with hyperbolic periodic points to containment by cutting line tangency. As a result, the maximum size of the non-mixing region occurs when the island is at the bifurcation point. We also demonstrate a bifurcation where periodic points are annihilated by the cutting-and-shuffling action. Chains of elliptic and hyperbolic periodic points that arise when invariant tori surrounding an elliptic point break up [according to Kolmogorov-Arnold-Moser (KAM) theory] can annihilate when they meet a cutting line. Consequently, the Poincar\'{e} index (a topological invariant of smooth systems) is not preserved.

International audience; Monodisperse and bidisperse granular flows are studied in rotating tumblers using DEM. In spherical tumblers, flowing particles’ trajectories do not follow straight lines but are curved. At the same time particles near the surface drift toward the pole, inducing two global recirculation cells. Combined with radial segregation, drift and curvature compete to impose the axial segregation pattern: Small-Large-Small (SLS) or Large-Small-Large (LSL). Fill level, rotation speed and wall roughness influence drift and curvature, and modify the resulting segregation pattern. In cylindrical tumblers, equivalent recirculation cells occur next to the end walls. A second pair of recirculation cells with a weak drift in the opposite direction appears at the center for long enough tumblers. Unlike the sphere case, curvature and drift in the primary cells combine to push large particles toward the end walls, explaining why large particle bands appear at the end walls for axial segregation in cylinder.

We consider unsteady segregating granular flows, focusing on stratification in bidisperse bounded heap flow. Experiments indicate that periodically changing the feed rate of particles falling onto the upstream portion of the heap results in a stratified segregation much like that which occurs at low feed rates, but with more regular stratified layers of large and small particles and a higher overall feed flow rate. Experiments clarify how a front of large particle at a high feed rate deposits a layer of large particles that is subsequently covered over by a layer of small particles during a low feed rate, thus generating layers of large and small particles. The stratification can be modelled using a version of an advection-segregation-diffusion equation with a segregation velocity. Simply repeatedly switching the model from a low volume flow rate to a high volume flow rate instantaneously along the entire length of the flowing layer results in stratification patterns that are similar to those observed in experiments. Using a modulated feed rate offers the potential to intentionally create extended layers of bidisperse granular materials to enhance the effective degree of mixing of the deposited materials at heap length scales.

International audience; The present work proposes a Chebyshev-collocation Fourier-Galerkin pseudospectral method for simulating unsteady, three-dimensional, fluid flows in cylindrical geometries with pressure-driven flow through permeable boundaries. Such systems occur in diverse applications and are challenging to simulate due to an additional velocity-pressure coupling on the permeable walls through Darcy's law. The present work extends the projection method of Raspo et al. (2002) to assure Darcy's law is satisfied exactly. A multidomain solver allows the efficient treatment of open boundary conditions that necessitate permeability buffers and a sponge layer. The method is spectrally convergent, and we demonstrate that pressure-prediction is necessary to obtain second-order temporal accuracy. The ability of the method to simulate complicated physical systems is demonstrated by simulating subcritical and supercritical flows in rotating filtration in Taylor-Couette cells. For subcritical cases, numerical results show excellent agreement with analytical solutions. For supercritical cases, the numerical method accurately resolves convectively and absolutely unstable flows with traveling toroidal and helical vortical structures that are in good agreement with a local linear stability analysis and experimental observations.

Mathematical concepts often have applicability in areas that may have surprised their original developers. This is the case with piecewise isometries (PWIs), which transform an object by cutting it into pieces that are then rearranged to reconstruct the original object, and which also provide a paradigm to study mixing via cutting and shuffling in physical sciences and engineering. Every PWI is characterized by a geometric structure called the exceptional set, $E$, whose complement comprises nonmixing regions in the domain. Varying the parameters that define the PWI changes both the structure of $E$ as well as the degree of mixing the PWI produces, which begs the question of how to determine which parameters produce the best mixing. Motivated by mixing of yield stress materials, for example granular media, in physical systems, we use numerical simulations of PWIs on a hemispherical shell and examine how the fat fractal properties of $E$ relate to the degree of mixing for any particular PWI. We present numerical evidence that the fractional coverage of $E$ negatively correlates with the intensity of segregation, a standard measure for the degree of mixing, which suggests that fundamental properties of $E$ such as fractional coverage can be used to predict the effectiveness of a particular PWI as a mixing mechanism.

Neal Amundson's seminal contributions in chemical engineering stem from the mathematically framed elegance of his research and the consequences of rigorous analysis. However, many significant problems in chemical engineering have resisted couching in elegant formalisms, the flow of granular materials being a particularly important example. There are valuable lessons that come sharply into focus by examining the nature of the difficulties. Here, we focus on questions of framing and analysis—determining a theoretical approach, choosing an appropriate level of description, and selecting from multiple quantitative tools—using examples spanning vibration, mixing, surface flow, and segregation and pattern formation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3237–3246, 2013

The concept of face, or mianzi, is quite important in Chinese culture. We examine how public face and private thrift together affect Chinese consumer shopping behaviour based on the results of a survey of nearly 400 Chinese consumers under the age of 40. When a product is used in public or the behaviour occurs in a public place, Chinese consumers are typically willing to spend more money than if a product or service is used in a private place or at home. In addition, non-Chinese or Western brands do not mean more ‘face’ to Chinese consumers. Instead, it is the expense of the item that matters most with the ultimate goal of being praised by others.

We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.

The Angstrom-scale transport characteristics of water and six different solutes, methanol, ethanol, 2-propanol, urea, Na+, and Cl-, were studied for a polyamide reverse osmosis (RO) membrane, FT-30, using non-equilibrium molecular dynamics (NEMD) simulations. Results indicate that water transport increases with an increasing fraction of connected percolated free volume, or water-accessible open space, in the membrane polymer structure. This free volume is enhanced by the dynamic structure of the membrane at the molecular level as it swells when hydrated and vibrates due to molecular collisions allowing a continuous path connecting the opposite membrane surfaces. The tortuous paths available for transport of solutes result in Brownian motion of solute molecules and hopping from pore to pore as they pass through the polymer network structure of the membrane. The transport of alcohol solutes decreases for solutes with larger Van der Waals volume, which corresponds to less available percolated free volume, or solute-accessible space, within the membrane polymer structure. However, the Van der Waals size of the dehydrated solutes is generally not a good measure to predict solute transport or rejection. Urea has reduced transport compared to ethanol, most likely due to more complex chemistry, even though urea has a smaller Van der Waals volume than ethanol. Na+ and Cl- experience the lowest transport, likely due to strong ion-water and ion-ion electrostatic interactions.

Size bidisperse granular materials in a spherical tumbler segregate into two different patterns of three bands with either small particles at the equator and large particles at the poles or vice versa, depending upon the fill level in the tumbler. Here we use discrete element method (DEM) simulations with supporting qualitative experiments to explore the effect of the tumbler wall roughness on the segregation pattern, modeling the tumbler walls as either a closely packed monolayer of fixed particles resulting in a rough wall, or as a geometrically smooth wall. Even though the tumbler wall is in contact with the flowing layer only at its periphery, the impact of wall roughness is profound. Smooth walls tend toward a small-large-small (SLS) band pattern at the pole-equator-pole at all but the highest fill fractions; rough walls tend toward a large-small-large (LSL) band pattern at all but the lowest fill fractions. This comes about because smooth walls induce poleward axial drift of small particles and an equator-directed drift for large particles, resulting in an SLS band pattern. On the other hand, rough walls result in both sizes of particles moving poleward at the surface of the flow, but due to radial segregation, small particles percolate lower in the flowing layer where there is a return drift toward the equator while large particles remain at the surface near the pole, resulting in an LSL band pattern. The tendency toward either of the two band patterns depends on the fill level in the tumbler and the roughness of the tumbler's bounding wall., Comment: submitted to Phys. Rev. E

We report on a computational parameter space study of mixing protocols for a half-full biaxial spherical granular tumbler. The quality of mixing is quantified via the intensity of segregation (concentration variance) and computed as a function of three system parameters: angles of rotation about each tumbler axis and the flowing layer depth. Only the symmetric case is considered in which the flowing layer depth is the same for each rotation. We also consider the dependence on \(\bar{R}\), which parametrizes the concentric spheroids (“shells”) that comprise the volume of the tumbler. The intensity of segregation is computed over 100 periods of the mixing protocol for each choice of parameters. Each curve is classified via a time constant, \(\tau \), and an asymptotic mixing value, bias. We find that most choices of angles and most shells throughout the tumbler volume mix well, with mixing near the center of the tumbler being consistently faster (small \(\tau \)) and more complete (small bias). We conclude with examples and discussion of the pathological mixing behaviors of the outliers in the so-called \(\tau \)-bias scatterplots.

Despite the success of reverse osmosis (RO) for water purification, the molecular-level physico-chemical processes of contaminant rejection are not well understood. Here we carry out non-equilibrium molecular dynamics (NEMD) simulations on a model polyamide RO membrane to understand the mechanisms of transport and rejection of both ionic and inorganic contaminants in water. While it is commonly presumed that the contaminant rejection rate is correlated with the dehydrated solute size, this approximation does not hold for the organic solutes and ions studied. In particular, the rejection of urea (2.4 A radius) is higher than ethanol (2.6 A radius), and the rejections for organic solutes (2.2–2.8 A radius) are lower than Na+ (1.4 A radius) or Cl− (2.3 A radius). We show that this can be explained in terms of the solute accessible intermolecular volume in the membrane and the solute-water pair interaction energy. If the smallest open spaces in the membrane's molecular structure are all larger than the solute size including its hydration shell, then the solute-water pair interaction energy does not matter. However, when the open spaces in the polymeric structure are such that solutes have to shed at least one water molecule to pass through a portion of the membrane molecular structure, as occurs in RO membranes, the pair interaction energy governs solute rejection. The high pair interaction energy for water molecules in the solvation shell for ions makes the water molecules difficult to shed, thus enhancing the rejection of ions. On the other hand, the organic solute-water interaction energies are governed by the water molecules that are hydrogen bonded to the solute. While these hydrogen bonds have pair interaction energies that are much larger than that of the non-hydrogen bonded water molecules in the solute solvation shell, they are significantly less than the ion-water pair interaction energy. Thus, organic solutes more easily shed water molecules than ions to pass through the RO membrane. Since urea molecules have more hydrogen-bonding sites than alcohol molecules, urea forms more hydrogen bonds with the membrane polymer chains leading to a higher rejection of urea than occurs for ethanol, a molecule of similar size but with fewer hydrogen bonding sites. These findings underline the importance of the solute's solvation shell and solute-water-membrane chemistry in the context of reverse osmosis, thus providing new insights into solute transport and rejection in RO membranes.

Although there are several methods for high sensitivity gas composition detection, typically off-line and laboratory-based, approaches for real-time, moderate-sensitivity detection are few. An approach based on Quantitative Acoustic Relaxation Spectroscopy (QARS) is proposed here. The methodology is based on the frequency-dependent acoustic propagation in a gas mixture, which depends on the concentration of contaminant gases in a known base gas. After describing the molecular acoustics model and QARS algorithm, we provide examples related to the identification of “mine gas” contamination in air, a mining safety application, and detecting impurities in low quality natural gas, an important issue in the natural gas processing industry. In both of these cases where moderate-sensitivity, continuous gas composition sensing would be useful, the QARS approach shows significant promise, at least theoretically, for realistic contaminant levels. Of course, further work is needed to refine several aspects of the molecular relaxation model that is necessary for the approach to be successful, not to mention challenges related to the development of a sensor based on the technique. Nevertheless, QARS holds potential to be a simple, robust, and inexpensive approach for moderate-sensitivity, continuous, real-time gas composition sensing.

Cutting and shuffling, a novel approach to mixing, can be used to predict the degree of mixing for three-dimensional (3D) granular flows in rotating tumblers. An idealized prototype, a half-full “blinking” spherical tumbler alternating in rotation about each of two horizontal axes in the limit of a vanishingly thin flowing layer, is studied using piecewise isometries (PWIs). Mixing is characterized by the normalized difference between the center of mass of a collection of tracer particles and the centroid of the filled portion of the container. The degree of mixing is highly dependent on the combination of rotation angles about the two axes and the angle between the axes of rotation. Various rotation angle combinations ( θ 1 , θ 2 ) are investigated over 1 ° ≤ θ i ≤ 89 ° (in 1° increments). Combinations of rotation angles that can lead to good mixing after only a few iterations of the blinking flow are identified. Protocols with non-orthogonal axes are also studied by varying the angle ϕ between rotation axes over 15 ° ≤ ϕ ≤ 90 ° (in 15° increments). When ϕ = 60 ° or 75°, we observe the highest number of rotation angle pairs that lead to good mixing.

Fouling due to biofilms composed primarily of microorganisms and extracellular polymeric substances is a significant hindrance to membrane filtration in water treatment. The goal of this work was to use a reactive membrane surface to reduce membrane biofouling by coating a ceramic ultrafiltration membrane with the nanoparticulate photocatalyst, TiO2. 10-Day biofilm growth experiments were conducted to determine the effect of photocatalytic coatings on the formation of a Pseudomonas putida biofilm and subsequent changes in membrane flux. Results indicate that a highly hydrophilic, photoreactive coating of mixed phase TiO2 nanoparticles is effective for the control of biofouling on ceramic ultrafiltration membranes.

The mechanisms underlying chaotic advection and mixing in inertial flow at Reynolds numbers above the Stokes flow regime are incompletely understood. This paper describes numerical investigations of chaotic advection and mixing for time-periodic inertial flow in a two-dimensional rectangular cavity driven by alternating motion of the upper and lower walls. The effects of inertia are analyzed in terms of the flow topology and tracer dynamics. The periodic unsteady high Reynolds number laminar flow results in the evolution of the Poincare map as the Reynolds number increases. Periodic points shift in position from their original locations in Stokes flow, and the Poincare sections transition from those characteristic of Stokes flow to a different characteristic pattern at higher Reynolds numbers. Tracer motion exhibits increasing degrees of disorder with increasing Reynolds number and decreasing forcing frequency resulting in increased chaotic mixing. The forcing frequency has a much greater impact on chaoti...

Bacterial attachment is an initial stage in biofilm formation that leads to flux decline in membrane water filtration. This study compares bacterial attachment among three photocatalytic ceramic ultrafiltration membranes for the prevention of biofilm formation. Zirconia ceramic ultrafiltration membranes were dip-coated with anatase and mixed phase titanium dioxide photocatalysts to prevent biofilm growth. The membrane surface was characterized in terms of roughness, hydrophobicity, bacterial cell adhesion, and attached cell viability, all of which are important factors in biofilm formation. The titanium dioxide coatings had minimal impact on the membrane roughness, reduced the hydrophobicity of membranes, prevented Pseudomonas putida attachment, and reduced P. putida viability. Degussa P25 is a particularly promising reactive coating because of its ease of preparation, diminished cell attachment and viability in solutions with low and high organic carbon concentrations, and reduced flux decline. These reactive membranes offer a promising strategy for fouling resistance in water filtration systems.

We report that SWCNTs substantially improve the uniformity and coverage of TiO2 coatings on porous ZrO2 ceramic membrane filters. The ZrO2 filters were dip coated with 100 nm anatase TiO2, TiO2/SWCNT composites, a TiO2+SWCNT mixture, and a TiO2/MWCNT composite at pH 3, 5, and 8. Whereas the TiO2+SWCNT mixture and the TiO2/MWCNT composite promote better coverage and less clumping than TiO2 alone, the TiO2/SWCNT composite forms a complete uniform coating without cracking at pH 5 ( approximately 100% coverage). A combination of chemical and electrostatic effects between TiO2 and SWCNTs forming the composite as well as between the composite and the ZrO2 surface explains these observations.

Electron-hole recombination limits the efficiency of TiO2 photocatalysis. We have investigated the efficacy with which anatase/carbon nanotube (CNT) composite materials reduce charge recombination and enhance reactivity. We synthesized nanostructured assemblies composed of different proportions of anatase (5 or 100 nm) and either single-or multi-walled CNTs. The composites were prepared using a simple low temperature process in which CNTs and anatase nanoparticles were dispersed in water, dehydrated at 80 degrees C, and dried at 104 degrees C. The structures of the various TiO2/CNT composites were characterized by scanning electron microscopy (SEM) and their function was tested by phenol oxidation. Charge recombination was compared by measuring the photoluminescence spectra of select composites. We found that a nanostructured composite assembled from the 100 nm anatase and single-walled CNTs (SWCNTs) exhibited enhanced and selective photocatalytic oxidation of phenol in comparison to both pure anatase and Degussa P25. A mechanism for the enhanced reactivity is proposed in which electrons are shuttled from TiO2 particles to the SWCNTs as a result of an optimal TiO2/ CNT arrangement that stabilizes charge separation and reduces charge recombination. In addition, the SWCNT assembly provides better catalyst-support (dispersal and connection) than multi-walled CNTs.

A fundamental characteristic of granular flows is segregation on the basis of particle size or density. For bidisperse mixtures of particles, revolutions of the order of 10 produce a segregation pattern of several radial streaks in quasi-two-dimensional rotating tumblers with fill fractions between 50% and 70%. By extending the duration of the experiments to the order of 102–103 tumbler revolutions, we have found the first evidence of coarsening of the radial streak pattern to as few as one streak, resulting in an unexpected wedge-shaped segregation pattern. This phenomenon occurs for a wide range of conditions including several fill fractions, particle sizes and mixtures of particles varying in both size and density in circular tumblers as well as for particles varying in size in square tumblers. Coarsening seems to be driven by transport of small (or dense) particles from streak to streak through the semicircular radial core, leading to new questions about the physics of coarsening of granular segregation patterns. Mixing two different types of grains in a revolving tumbler produces several radial streaks as the grains segregate. Unexpectedly though, after hundreds of revolutions, only one streak remains.

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimension...

Planetary atmospheres are complex dynamical systems whose structure, composition, and dynamics intimately affect the propagation of sound. Thus, acoustic waves, being coupled directly to the medium, can effectively probe planetary environments. Here we show how the acoustic absorption and speed of sound in the atmospheres of Venus, Mars, Titan, and Earth (as predicted by a recent molecular acoustics model) mirror the different environments. Starting at the surface, where the sound speed ranges from ∼200 m/s for Titan to ∼410 m/s for Venus, the vertical sound speed profiles reveal differences in the atmospheres’ thermal layering and composition. The absorption profiles are relatively smooth for Mars, Titan, and Earth while Venus stands out with a noticeable attenuation dip occurring between 40 and 100 km. We also simulate a descent module sampling the sound field produced by a low-frequency “event” near the surface noting the occurrence of acoustic quiet zones.

Discrete models are an effective method to study mixing of granular materials in a variety of cases. We study the mixing of monodisperse granular materials in 2D tumblers rotating in the avalanching regime using two different discrete models. First, we develop a cellular automata (CA) model based on comparing the heights of columns of particles in the CA grid that results in irregular avalanching and mixing of particles. Second, we use a model based on mapping of wedge regions that has been shown to reproduce experimental results. We compare mixing of like particles in tumblers of various shapes and fill fractions using both models. Mixing rates for half-full tumblers demonstrate a strong dependence on the symmetries of the tumbler shape. More than half-full tumblers give rise to a core of unmixed particles with a shape that changes with fill fraction. This results in multiple extrema in the mixing rate depending on the fill fraction. Mixing is fastest for low fill fractions, and triangular tumblers provide the quickest mixing. While the wedge and CA models produce quantitatively similar results, the cellular automata model is substantially more flexible and typically runs in an order of magnitude less time. © 2007 American Institute of Chemical Engineers AIChE J, 53: 1151–1158, 2007

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Walls in discrete element method simulations of granular flows are sometimes modeled as a closely packed monolayer of fixed particles, resulting in a rough wall rather than a geometrically smooth wall. An implicit assumption is that the resulting rough wall differs from a smooth wall only locally at the particle scale. Here we test this assumption by considering the impact of the wall roughness at the periphery of the flowing layer on the flow of monodisperse particles in a rotating spherical tumbler. We find that varying the wall roughness significantly alters average particle trajectories even far from the wall. Rough walls induce greater poleward axial drift of particles near the flowing layer surface, but decrease the curvature of the trajectories. Increasing the volume fill level in the tumbler has little effect on the axial drift for rough walls, but increases the drift while reducing curvature of the particle trajectories for smooth walls. The mechanism for these effects is related to the degree of local slip at the bounding wall, which alters the flowing layer thickness near the walls, affecting the particle trajectories even far from the walls near the equator of the tumbler. Thus, the proper choice of wall conditions is important in the accurate simulation of granular flows, even far from the bounding wall., 32 pages, 19 figures, regular article, accepted for publication in Physical Review E 2006

Wastewater produced by the crew members on a long-term space mission needs to be recovered as potable water. Reverse osmosis (RO) has long been in use as a physical membrane separation technology for wastewater treatment. However, membrane fouling and concentration polarization have limited the efficiency for high recovery reverse osmosis systems. An advanced high pressure rotating RO device was designed to minimize these problems by the rotation of the cylindrical RO filter producing shear and Taylor vortices in the annulus of the device. We compare the performance of the rotating RO device to a standard spiral wound RO module using a commercially-available RO membrane under conditions of very high recovery and similar permeate flux. The studies were conducted using 0.01N sodium chloride solution and biological water processor effluent (BWPE) as model wastewaters. The results for 100% recovery of water from 0.01N sodium chloride solution show that the spiral wound RO has poor rejection (

Acoustic attenuation provides the potential to identify and quantify gases in a mixture. We present results for a prototype attenuation gas sensor for binary gas mixtures. Tests are performed in a pressurized test cell between 0.2 and 32atm to accommodate the main molecular relaxation processes. Attenuation measurements using the 215-kHz sensor and a multiseparation, multifrequency research system both generally match theoretical predictions for mixtures of CO2 and CH4 with 2% air. As the pressure in the test cell increases, the standard deviation of sensor measurements typically decreases as a result of the larger gas acoustic impedance.

The reaction of a fire plume to an applied water spray is crucial to fire suppression. While considerable research has been devoted toward fire plumes without suppression, and some computer simulations of fire suppression have provided insight, little experimental data exist detailing how the structure of a fire plume changes during suppression. Experiments were performed in which 5, 15 and 50 kW gas burner fires were exposed to a spray from one of three spray sources. Flow rates from the nozzles or fire sprinkler ranged from 6 to 106 L/min. Contours of infrared (IR) intensity of the fire plume show that the plume decreases in height and increases in width with the increasing strength of the applied spray. Based on the height of the maximum fluctuations of IR intensity, the thermal plume height decreases with increasing spray strength, but the overall projected area of the plume changes very little. The plume height depends on the ratio of the drag of the droplets on the air to the momentum of the plume, allowing the results to be generalized to typical fire suppression applications.

Equations describing the fluid motion in buoyant plumes have been applied to fire plumes by researchers and engineers since Morton et al. developed them in the 1950s. However, in the application of active fire suppression by water droplets, the equations are no longer valid. The equations have been modified to include the effect of a homogeneous, uniform velocity droplet field on the momentum of the fluid. Solving the resulting ordinary differential equations shows that the plume widens and the upward velocity of the plume slows significantly due to the presence of droplets. Results from this simple model appear to match the results of more sophisticated numerical simulations. The model further demonstrates that the interaction between the upward momentum of the plume and the downward momentum of the droplet spray can be critical for fire suppression.

A simple detection method based on fluorescence excitation-emission spectroscopy has been developed to quantify the concentration of Ludox colloidal silica nanoparticles having diameters ranging from 7 to 22 nm. The technique works for suspensions of nominally negatively (SM30, LS, and TM40) and positively (CL) charged colloid silica particles. Without pretreatment, the method detection limits are 1.4 mg/L SiO 2 for CL (12 nm) and TM40 (22 nm) suspensions and 12 mg/L SiO 2 for SM30 (7 nm) and LS (12 nm) suspensions at an excitation wavelength of 308 nm and an emission wavelength of 318 nm. The fluorescence intensities of all the colloidal silica particle suspensions are linear ( R 2 > 0.98) with concentration in the range of 0–300 mg/L SiO 2 . The fluorescence intensity of the negatively charged particle suspensions is constant between pH 3 and 9. The fluorescence intensity of suspensions of particles that are nominally positively charged is constant above pH 5.5, where the particles become negatively charged.

Ion-exchange textiles are used as organic supports for urease immobilization with the aim of developing reactive fibrous materials able to promote urea removal. A non-woven, polypropylene-based cation-exchange textile was prepared using UV-induced graft polymerization. Urease was covalently immobilized onto the cation-exchange textile using three different coupling agents: N-(3-dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDC), N-cyclohexyl-N′-(b-[N-methylmorpholino]ethyl)carbodiimide p-toluenesulfonate (CMC), and glutaraldehyde (GA). The immobilized biocatalyst was characterized by means of FT-IR spectrometry, SEM micrographs, dependence of the enzyme activity on pH and temperature, and according to the kinetic constants of the free and immobilized ureases. The biotextile prepared with EDC in the presence of N-hydroxysuccinimide performs best. The optimum pH was 7.2 for the free urease and 7.6 for the immobilized ureases. The reactivity was maximal at 45 °C for free urease, 50 °C for biotextiles prepared using EDC or CMC, and 55 °C for biotextiles prepared with GA. The activation energy for the immobilized ureases was 4.73–5.67 kcal mol−1, which is somewhat higher than 4.3 kcal mol−1 for free urease. The urea conversion for a continuous-flow immobilized urease reactor is nearly as good as a continuously stirred tank reactor having a much longer residence time, suggesting that the packed bed reactor had sufficient diffusive mixing and residence time to reach nearly optimal results. Urease immobilized on a biotextile using EDC has good storage and operational stability. Copyright © 2006 Society of Chemical Industry

Rejection characteristics of organic and inorganic compounds were examined for six reverse osmosis (RO) membranes and two nanofiltration (NF) membranes that are commercially available. A batch stirred-cell was employed to determine the membrane flux and the solute rejection for solutions at various concentrations and different pH conditions. The results show that for ionic solutes the degree of separation is influenced mainly by electrostatic exclusion, while for organic solutes the removal depends mainly upon the solute radius and molecular structure. In order to provide a better understanding of rejection mechanisms for the RO and NF membranes, the ratio of solute radius (r(i,s)) to effective membrane pore radius (r(p)) was employed to compare rejections. An empirical relation for the dependence of the rejection of organic compounds on the ratio r(i,s)/r(p) is presented. The rejection for organic compounds is over 75% when r(i,s)/r(p) is greater than 0.8. In addition, the rejection of organic compounds is examined using the extended Nernst-Planck equation coupled with a steric hindrance model. The transport of organic solutes is controlled mainly by diffusion for the compounds that have a high r(i,s)/r(p) ratio, while convection is dominant for compounds that have a small r(i,s)/r(p) ratio.

Granular segregation in a rotating tumbler occurs due to differences in either particle size or density, which are often varied individually while the other is held constant. Both cases present theoretical challenges; even more challenging, however, is the case where density and size segregation may compete or reinforce each other. The number of studies addressing this situation is small. Here we present an experimental study of how the combination of size and density of the granular material affects mixing and segregation. Digital images are obtained of experiments performed in a half-filled quasi-2D circular tumbler using a bi-disperse mixture of equal volumes of different sizes of steel and glass beads. For particle size and density combinations where percolation and buoyancy both contribute to segregation, either radial streaks or a “classical” core can occur, depending on the particle size ratio. For particle combinations where percolation and buoyancy oppose one another, there is a transition between a core composed of denser beads to a core composed of smaller beads. Mixing can be achieved instead of segregation if the denser beads are also bigger and if the ratio of particle size is greater than the ratio of particle density. Temporal evolution of these segregated patterns is quantified in terms of a “segregation index” (based on the area of the segregated pattern) and a “shape index” (based on the area and perimeter of the segregated pattern).

Reverse osmosis (RO) is an efficient process for the removal of ionic and organic pollutants from wastewater. However, flux decline and rejection deterioration due to concentration polarization and membrane fouling hinders the application of RO technology. Rotating RO, which takes advantage of high shear and the Taylor–Couette flow instability to reduce the flux decline related to concentration polarization and membrane fouling, was investigated as a novel method for space mission wastewater recovery. Mass transfer in rotating RO was experimentally determined based on film theory. The model developed for rotating RO allows the prediction of flux and pollutant rejection over a wide range of design and operational parameters. The model matches the experimental results from a laboratory‐scale rotating RO system very well. According to the model, rotating RO shows better flux and rejection than a nonrotating system by effectively reducing concentration polarization. Operating parameters, such as rota...

In a previous paper [Y. Dain and R. M. Lueptow, J. Acoust. Soc. Am. 109, 1955 (2001)], a model of acoustic attenuation due to vibration-translation and vibration-vibration relaxation in multiple polyatomic gas mixtures was developed. In this paper, the model is improved by treating binary molecular collisions via fully pairwise vibrational transition probabilities. The sensitivity of the model to small variations in the Lennard-Jones parameters--collision diameter (sigma) and potential depth (epsilon)--is investigated for nitrogen-water-methane mixtures. For a N2(98.97%)-H2O(338 ppm)-CH4(1%) test mixture, the transition probabilities and acoustic absorption curves are much more sensitive to sigma than they are to epsilon. Additionally, when the 1% methane is replaced by nitrogen, the resulting mixture [N2(99.97%)-H2O(338 ppm)] becomes considerably more sensitive to changes of sigma(water). The current model minimizes the underprediction of the acoustic absorption peak magnitudes reported by S. G. Ejakov et al. [J. Acoust. Soc. Am. 113, 1871 (2003)].

Rotating reverse osmosis (RO), which is based on Taylor-Couette flow, offers a means to minimize flux decline due to concentration polarization and membrane fouling. However, the operating conditions play a significant role in determining the effectiveness of the system. In this study, the effect of operating conditions on system performance was explored using a theoretical model. Flux, rejection, recovery, and theoretical power consumption were calculated for a wide variety of operating parameters including transmembrane pressure, rotational speed, and concentrate flow rate. Flux and rejection increase with increasing transmembrane pressure and rotational speed. Operating in the vortical flow regime enhances the filtration performance. Higher concentrate flow increases flux, but decreases recovery. The power consumption for rotating RO is similar to that for conventional RO except at very high rotational speeds.

A dominant aspect of granular flows is flow in thin surface layers. While an understanding of the dynamics of dry granular surface flow has begun to emerge, the case of flow when air is completely replaced by a liquid is largely unexplored. Experiments were performed using particle tracking velocimetry (PTV) in a quasi-two-dimensional rotating tumbler to measure the velocity field within the flowing layer of monodisperse spherical particles fully submerged in liquids, a granular slurry, for a range of Froude numbers, bead sizes, fluid densities and fluid viscosities. The thickness of the flowing layer and the angle of repose with a liquid interstitial fluid are generally larger than for the dry system under similar conditions, although the shear rate is generally smaller

International audience; The finite length of a Taylor-Couette cell introduces endwall effects that interact with the centrifugal instability and the subsequent wavy vortex flow. We investigate the interaction between the endwall Ekman boundary layers and the wavy vortices in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers, we consider three endwall boundary conditions: fixed endwalls, endwalls rotating with the inner cylinder, and stress-free endwalls. Near the endwalls, the waviness is diminished, primarily due to the effect of the flatness of the endwall rather than as a result of the no-slip boundary condition at the endwall. However, the waviness is present just one or two vortices away from the endwalls, indicating that the effect of the endwall on waviness does not penetrate far from the endwall. The interaction of the waviness with the endwall Ekman layer does not appear to result in disorder in the flow, either in the endwall vortex or farther from the endwall. Likewise, the waviness does not significantly alter Ekman layer thickness from that predicted based on theory

A simple method for the computer-aided calibration of an X-probe is described. This method requires the X-probe to be pitched in the free-stream at several velocities. From the corresponding output voltages, a calibration look-up table can be generated. The technique requires fewer assumptions than traditional methods based on King's law.

Rotating membrane filtration is a means of dynamic filtration that incorporates both high shear and flow instabilities to reduce membrane fouling. The device consists of a cylindrical membrane filter rotating within an outer cylindrical shell. The superior performance of rotating membrane filtration appears to be a consequence of the high shear in the annulus, which is enhanced by the redistribution of azimuthal momentum by the appearance of Taylor vortices in the annulus. The anti-fouling characteristics of rotating filtration can be utilized for reverse osmosis in addition to microfiltration. In this paper, we review the physics underlying rotating filtration, examine the anti-fouling mechanisms in rotating filtration, and describe recent efforts to apply rotating filtration to reverse osmosis.

The influence of intrinsic absorption in a relaxing medium and the resulting three-dimensional diffraction correction of the magnitude of the acoustic pressure averaged over the surface of a receiver is investigated for a tone burst. A rigorous formula for the damped acoustic pressure average at the receiver was obtained for arbitrary pulsed waves in a mono-relaxing medium. Depending on the pulse oscillation frequency, envelope duration, and relaxation frequency of the media, the plane wave burst envelope can be reduced, amplified, or otherwise deformed.

Scale formation of soluble salts is one of the major factors limiting the application of reverse osmosis (RO) membranes. In this study, rotating RO, which takes advantage of Taylor-Couette flow instabilities to reduce concentration polarization and membrane fouling, was investigated as a novel method to control CaSO4 scale formation. The permeate flux for rotating RO at ω = 180 rpm remains constant up to a volume concentration factor (VCF) of 4.2, while the permeate flux declines steadily with increasing VCF for no rotation. This is probably because vortices in rotating RO induce bulk crystallization and prevent scale particle deposition on the membrane surface. The anti-scaling effect in rotating RO increases with increasing rotational speed and depends to some extent on transmembrane pressure.

The stability of wavy supercritical cylindrical Couette flow has been studied extensively, but few measurements of the velocity field in flow have been made. Particle image velocimetry was used to measure the azimuthal and radial velocities in latitudinal planes perpendicular to the axis of rotation for wavy cylindrical Couette flow in the annulus between a rotating inner cylinder and a fixed outer cylinder. These measurements were matched to previous measurements of the axial and radial velocity measured in several meridional planes resulting in an experimentally measured, time-resolved, three-dimensional, three-component velocity field for wavy cylindrical Couette flow. Using this complete velocity field it is possible to evaluate details of the flow field. The vortical motion transports azimuthal momentum radially while the axial exchange of fluid between vortices in wavy flow transports azimuthal momentum axially. As the Reynolds number increases, these effects strengthen. Streams of net axial flow stretch axially along the length of the annulus and wind around the vortices from the inner cylinder to the outer cylinder and back while also winding azimuthally in the annulus. The azimuthal velocity measured at the center of a vortex is similar to the azimuthal wave speed. Measurements of the azimuthal velocity in cylindrical surfaces concentric with the axis of rotation suggest that the origin of the waviness is related to a jet-like azimuthal velocity profile rather than the radial outflow jet. Near both cylinder walls, the shear stress is quite large, decreasing to near zero at the middle of the annular gap.

Sound travelling through a gas propagates at different speeds and its intensity attenuates to different degrees depending upon the composition of the gas. Theoretically, a real-time gaseous composition sensor could be based on measuring the sound speed and the acoustic attenuation. To this end, the speed of sound was modelled using standard relations, and the acoustic attenuation was modelled using the theory for vibrational relaxation of gas molecules. The concept for a gas composition sensor is demonstrated theoretically for nitrogen-methane-water and hydrogen-oxygen-water mixtures. For a three-component gas mixture, the measured sound speed and acoustic attenuation each define separate lines in the composition plane of two of the gases. The intersection of the two lines defines the gas composition. It should also be possible to use the concept for mixtures of more than three components, if the nature of the gas composition is known to some extent.