Entrainment, motion and deposition of coarse particles transported by water over a sloping mobile bed

In gravel-bed rivers, bedload transport exhibits considerable variability in time and space. Recently, stochastic bedload transport theories have been developed to address the mechanisms and effects of bedload transport fluctuations. Stochastic models involve parameters such as particle diffusivity, entrainment and deposition rates. The lack of hard information on how these parameters vary with flow conditions is a clear impediment to their application to real-world scenarios. In this paper, we determined the closure equations for the above parameters from laboratory experiments. We focused on shallow supercritical flow on a sloping mobile bed in straight channels, a setting that was representative of flow conditions in mountain rivers. Experiments were run at low sediment transport rates under steady nonuniform flow conditions (i.e., the water discharge was kept constant, but bedforms developed and migrated upstream, making flow nonuniform). Using image processing, we reconstructed particle paths to deduce the particle velocity and its probability distribution, particle diffusivity, and rates of deposition and entrainment. We found that on average, particle acceleration, velocity and deposition rate were responsive to local flow conditions, whereas entrainment rate depended strongly on local bed activity. Particle diffusivity varied linearly with the depth-averaged flow velocity. The empirical probability distribution of particle velocity was well approximated by a Gaussian distribution when all particle positions were considered together. In contrast, the particles located in close vicinity to the bed had exponentially distributed velocities. Our experimental results provide closure equations for stochastic or deterministic bedload transport models.Comment: Submitted to Journal of Geophysical Researc

Stationary shear flows of dense granular materials : a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent agreement with the experimental or numerical results concerning free-surface shear flows as well as confined shear flow

0-level Vacuum Packaging RT Process for MEMS Resonators

A new Room Temperature (RT) 0-level vacuum package is demonstrated in this work, using amorphous silicon (aSi) as sacrificial layer and SiO2 as structural layer. The process is compatible with most of MEMS resonators and Resonant Suspended-Gate MOSFET [1] fabrication processes. This paper presents a study on the influence of releasing hole dimensions on the releasing time and hole clogging. It discusses mass production compatibility in terms of packaging stress during back-end plastic injection process. The packaging is done at room temperature making it fully compatible with IC-processed wafers and avoiding any subsequent degradation of the active devices.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

Segregation of large particles in dense granular flows: A granular Saffman effect?

We report on the scaling between the lift force and the velocity lag experienced by a single particle of different size in a monodisperse dense granular chute flow. The similarity of this scaling to the Saffman lift force in (micro) fluids, suggests an inertial origin for the lift force responsible for segregation of (isolated, large) intruders in dense granular flows. We also observe an anisotropic pressure/stress field surrounding the particle, which potentially lies at the origin of the velocity lag. These findings are relevant for modelling and theoretical predictions of particle-size segregation. At the same time, the suggested interplay between polydispersity and inertial effects in dense granular flows with stress- and strain-gradients, implies striking new parallels between fluids, suspensions and granular flows with wide application perspectives

Entrainment and motion of coarse particles in a shallow water stream down a steep slope

We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth-death immigration-emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the pape

MEMS tunable capacitors with fragmented electrodes and rotational electro-thermal drive

This paper reports on the design, simulation and fabrication of tunable MEMS capacitors with fragmented metal (AlSi 4%) electrodes. We examine a rotational electro-thermal actuation. An analytic model of the rotational effect thermal actuator was established in order to show the periodicity of the capacitance when the angle increases. Evaluation of the impact of fringing fields on the capacitance has been carried out using finite element analysis (FEA). The MEMS capacitors were fabricated using metal surface micromachining with polyimide sacrificial layer. The maximum rotation, corresponding to a maximum angle of 7°, was obtained near 1.2V and 299mA. The proposed capacitor has a practical tuning range of 30%. FEA has shown that this figure can be improved with design optimization. The MEMS architecture based on rotational effect and fragmented electrodes does not suffer from the pull in effect and offers a practical solution for future above-IC capacitor

Plug flow and the breakdown of Bagnold scaling in cohesive granular flows

Cohesive granular media flowing down an inclined plane are studied by discrete element simulations. Previous work on cohesionless granular media demonstrated that within the steady flow regime where gravitational energy is balanced by dissipation arising from intergrain forces, the velocity profile in the flow direction scales with depth in a manner consistent with the predictions of Bagnold. Here we demonstrate that this Bagnold scaling does not hold for the analogous steady-flows in cohesive granular media. We develop a generalization of the Bagnold constitutive relation to account for our observation and speculate as to the underlying physical mechanisms responsible for the different constitutive laws for cohesive and noncohesive granular media.Comment: 8 pages, 10 figure

Statistical description of sediment transport experiments

A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep twodimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion (rest, rolling, or saltating motion), and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein’s theory on sediment and derived the statistical properties (probability distribution and autocorrelation function) of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models

Granular flow down a rough inclined plane: transition between thin and thick piles

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $\theta$. Three angles determine the phase diagram: $\theta_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $\theta_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $\theta_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $\theta_{r}<\theta<\theta_{max}$, three flow regimes can be distinguished that depend on how close $\theta$ is to $\theta_{r}$: i) $\theta>>\theta_{r}$: Bagnold rheology, characterized by a mean particle velocity $v_{x}$ in the direction of flow that scales as $v_{x}\propto h^{3/2}$, for a pile of height $h$, ii) $\theta\gtrsim\theta_{r}$: the slow flow regime, characterized by a linear velocity profile with depth, and iii) $\theta\approx\theta_{r}$: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming.Comment: 19 pages, 14 figs, submitted to Physics of Fluid

Lattice-Boltzmann Method for Geophysical Plastic Flows

We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.Comment: in W. Wu, R.I. Borja (Edts.) Recent advances in modelling landslides and debris flow, Springer Series in Geomechanics and Geoengineering (2014), ISBN 978-3-319-11052-3, pp. 131-14