The packing of spheres in a cylindrical container: the thickness effect

Modeling CO2 Adsorption in a Thin Discrete Packing

Local dynamics of CO2 adsorption in a discrete packing contained in a thin tube was assessed by 3D modeling. Thin tube packed bed adsorbers are currently used over tube structures in thermochemical energy storage systems and atmospheric revitalization of confined spaces. Driven by the interplay between key factors such as the exothermicity and the fluid flow, the advective transport was found less effective than the diffusive one on the breakthrough trends of CO2 which displayed significant concentration gradients at both inter- and intraparticle scales. The lack of angular symmetry inside the particles by the reduction in resistance to mass transfer in the area of solid particles exposed to high velocities led to greater convective transports from the bulk of the gaseous phase to the pores. The result of the modeling agreed with the experimental data obtained at the exit of the adsorber, helping reduction in reliance on the empirical dispersion models used in the one-dimensional modeling.

Effects of spherical confinement and backbone stiffness on flexible polymer jamming

We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.

Dynamic mathematical modeling of heat and mass transfer incorporating with the local nutrient and biomass limitation of growth in a packed-bed solid-state bioreactor

This research develops on our previous semi-mechanistic model that describes the dynamic physical and biochemical processes taking place in a packed-bed bioreactor to analyze the relationship of nutrient limitation, biomass accumulation, metabolic heat generation, and mathematical description of packed-bed porous media. The experimental and simulation data proved that glucose concentration gradients in the biofilm could be neglected due to small biofilm thickness and high diffusivity of glucose in the biofilm. The prediction results also showed that an increase in the initial substrate concentration leads to a rise in the temperature gradient in the bed. The model proposes that if the diameter of substrate particle is too large (r > 0.1 cm), the growth rate will decrease significantly due to the high biomass accumulation in the biofilm, and temperature gradients decrease in the column. This can be used as a strategy to control the overheating problem in the bed.

General combined model for the hydrodynamic behaviour of fixed and fluidised granular beds

This work describes the derivation of a general mathematical model applicable to both fixed and fluidised granular beds, operating within the full hydrodynamic spectrum from viscous to inertial flows. The fundamental insight for the derivation of the model is that practical fluidised beds and fixed beds have similar hydrodynamic properties. The validity of the general model is demonstrated for fluid fractions up to 0.90. A crucial development in the general model is the replacement of hydraulic diameter, which has served as the size descriptor of flow paths in most fixed-bed models derived since the advent of the classic Blake-Kozeny equation. The new, replacement expression is based on the physical structure of the cross section of random porous beds. In addition, the general model contains a tortuosity factor, derived from the results of previous works involving computational fluid dynamics, to correct flow path length and fluid velocity. The model is constructed using regression analysis of experimental data from six previous major works and tested against previous models.

Radical tessellation of the packing of spheres with a log-normal size distribution

The packing of particles with a log-normal size distribution is studied by means of the discrete element method. The packing structures are analyzed in terms of the topological properties such as the number of faces per radical polyhedron and the number of edges per face, and the metric properties such as the perimeter and area per face and the perimeter, area, and volume per radical polyhedron, obtained from the radical tessellation. The effect of the geometric standard deviation in the log-normal distribution on these properties is quantified. It is shown that when the size distribution gets wider, the packing becomes denser; thus the radical tessellation of a particle has decreased topological and metric properties. The quantitative relationships obtained should be useful in the modeling and analysis of structural properties such as effective thermal conductivity and permeability.

Random close packing of disks and spheres in confined geometries

Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. In confined geometries, the structural properties of random-packed systems will change. To understand these changes, we study random close packing in finite-sized confined systems, in both two and three dimensions. Each packing consists of a 50-50 binary mixture with particle size ratio of 1.4. The presence of confining walls significantly lowers the overall maximum area fraction (or volume fraction in three dimensions). A simple model is presented, which quantifies the reduction in packing due to wall-induced structure. This wall-induced structure decays rapidly away from the wall, with characteristic length scales comparable to the small particle diameter.