Investigation of f/2 and f/4 Waves in Granular Beds Subject to Vertical, Sinusoidal Oscillations

When a deep bed of granular material is subject to vertical, sinusoidal oscillations, a number of phenomena appear including two regimes of standing surface waves that form at one-half and one-quarter of the oscillation forcing frequency. These waves are referred to as f/2 and f/4 waves where f is the oscillation frequency. This paper presents the results from experiments and computer simulations designed to study the wavelength and wave amplitude dependence of the surface waves on the vibration parameters, collision coefficient of restriction, and the particle bed depth

Effects of vertical vibration on hopper flows of granular material

This paper examines the flow of granular material through a wedge-shaped hopper subject to vertical, sinusoidal oscillations. Experiments and discrete element computer simulations were conducted to investigate particle trajectories within and mass discharge rates from the hopper. With the hopper exit closed, side wall convection cells are observed in both the experiments and simulations. The convection cells are oriented such that particles move up along the inclined walls of the hopper and down along the centerline. Results from the computer simulation indicate that the convection cells are a result of the dilation of the granular bed during free fall and interaction with hopper walls. Measurements of the mean mass discharge rate for various vibration parameters were also made in both the experiments and simulations. The ratio of the mass discharge rate for a vibrating hopper to the mass discharge rate for a non-vibrating hopper scales with the oscillation velocity amplitude and exhibits a maximum value just greater than one for oscillation velocity amplitudes less than 0.5. The ratio is less than one for larger velocity amplitudes. A simple model taking into account the change in the effective gravity acting on the granular material over an oscillation cycle is examined. A significant deficiency in the model is that is assumes no material discharges from the hopper during part of each oscillation cycle for acceleration amplitudes greater than gravitational acceleration. Data from the simulations indicate that although the discharge rate from the hopper varies throughout an oscillation cycle, it never equals zero. The simulation was also used to examine particle horizontal position and velocity profiles at the hopper exit. Lastly, preliminary observations of the effects of localized vibration on a granular material in a closed hopper are presented

Granular Flow in a Vertically Vibrating Hopper

The behavior of the flow of glass spheres in a vertically vibrating hopper is examined. A two-dimensional hopper is mounted on a shaker that provides sinusoidal, vertical vibrations. Both the frequency and amplitude of the vibrations are adjustable. Hopper discharge rates and flow patterns are measured as the acceleration amplitude of the vibrations is increased from 0 to 4g's. Comparisons are made with unvibrated hopper flows and with a two-dimensional discrete element simulation model

Harnessing Nanocellulose for Sustainable Carbon Capture: Synthesis, Processing, and Performance Evaluation

Scientists and governments have recognized the need for environmental remediation, most notably with the adoption of the Paris Agreement in 2016. One of the major concerns is the production of greenhouse gases (GHGs). The major GHG is carbon dioxide (CO2) in which humans emit over 36 gigatons yearly. Atmospheric CO2 is responsible for 60% of the heat retained by the earth – resulting in rising temperatures, melting ice caps, and increasing ocean acidification. Therefore, a major goal of the Paris Agreement was to reduce GHG emissions as well as the capture of CO2 from the atmosphere. Here within, a sustainable nanocellulose aerogel is synthesized and characterized for the intended application of CO2 capture. First, arginine, a sustainable amino acid with high amine content, is grafted onto the surface of cellulose nanofibers. Through the water-soluble coupling reactions known as EDC/NHS coupling, it was possible to achieve an arginine loading of 0.78 mmol/g; or near 100% maximum possible grafting of arginine. Following this grafting, aerogels of both the grafted and ungrafted cellulose nanofibers are then processed into aergoels using a sustainable process pioneered by the Carter group. This process results in mechanically robust aerogels, with a modulus of 15.4 MPa, one the highest moduli for highly porous nanocellulose aerogels. These aerogels are then subjected to CO2 adsorption studies using a custom laboratory built instrument. When grafted, we find that the arginine significantly improves the CO2 adsorption compared to the unmodified fibers. Furthermore, this adsorption is relatively fast (\u3c 5 minutes), significantly faster than current nanocellulose CO2 adsorbents

A study on the sensitivity of Drucker–Prager cap model parameters during die compaction of pharmaceutical powders

In powder die compaction, the characteristics of the end product are dictated by the mechanical properties of the powder being processed. A commonly used constitutive model describing the behavior of pharmaceutical powders during compaction is the modified-Drucker Prager Cap (DPC) model. The experiments used to measure DPC parameters are time consuming and, hence, limit the model’s wide-spread use in industry. In the interest of potentially simplifying the DPC parameter measurement procedures, it is of interest to understand the influence each of the model parameters has on the prediction of a tablet’s density field. In this study, a 2 k–p statistical analysis is performed on intratablet density gradients obtained from finite element simulation of powder compaction using a range of DPC parameters. The high and low values for the material parameters are selected based on literature reported values for pharmaceutical powders

Mechanism for Surface Waves in Vibrated Granular Material

We use molecular dynamics simulations to study the formation of surface waves in vertically vibrated granular material. We find that horizontal movements of particles, which are essential for the formation of the waves, consist of two distinct processes. First, the movements sharply increase while the particles are colliding with a bottom plate, where the duration of the collisions is very short compared to the period of the vibration. Next, the movements gradually decrease between the collisions, during which the particles move through the material. We also find that the horizontal velocity field after the collisions is strongly correlated to the surface profile before the collisions.Comment: 6 pages, 3 figures (included

Effects of vertical vibration on hopper flows of granular material

The discharge of granular material from a hopper subject to vertical sinusoidal oscillations was investigated using experiments and discrete element computer simulations. With the hopper exit closed, side-wall convection cells are observed, oriented such that particles move up along the inclined walls of the hopper and down at the center line. The convection cells are a result of the granular bed dilation during free fall and the subsequent interaction with the hopper walls. The mass discharge rate for a vibrating hopper scaled by the discharge rate without vibration reaches a maximum value at a dimensionless velocity amplitude just greater than 1. Further increases in the velocity decrease the discharge rate. The decrease occurs due to a decrease in the bulk density of the discharging material when vibration is applied

Yielding and hardening of flexible fiber packings during triaxial compression

This paper examines the mechanical response of flexible fiber packings subject to triaxial compression. Short fibers yield in a manner similar to typical granular materials in which the deviatoric stress remains nearly constant with increasing strain after reaching a peak value. Interestingly, long fibers exhibit a hardening behavior, where the stress increases rapidly with increasing strain at large strains and the packing density continuously increases. Phase diagrams for classifying the bulk mechanical response as yielding, hardening, or a transition regime are generated as a function of the fiber aspect ratio, fiber-fiber friction coefficient, and confining pressure. Large fiber aspect ratio, large fiber-fiber friction coefficient, and large confining pressure promote hardening behavior. The hardening packings can support much larger loads than the yielding packings contributing to the stability and consolidation of the granular structure, but larger internal axial forces occur within fibers.Comment: 14 pages, 4 figure