Initial Solid Volume Fraction Research Articles

Structural Analysis of Articular Cartilage Using Multiphoton Microscopy: Input for Biomechanical Modeling

The 3-D morphology of chicken articular cartilage was quantified using multiphoton microscopy (MPM) for use in continuum-mechanical modeling. To motivate this morphological study we propose aspects of a new, 3-D finite strain constitutive model for articular cartilage focusing on the essential load-bearing morphology: an inhomogeneous, poro-(visco)elastic solid matrix reinforced by an anisotropic, (visco)elastic dispersed fiber fabric which is saturated by an incompressible fluid residing in strain-dependent pores. Samples of fresh chicken cartilage were sectioned in three orthogonal planes and imaged using MPM, specifically imaging the collagen fibers using second harmonic generation. Employing image analysis techniques based on Fourier analysis, we derived the principal directionality and dispersion of the collagen fiber fabric in the superficial layer. In the middle layer, objective thresholding techniques were used to extract the volume fraction occupied by extracellular collagen matrix. In conjunction with information available in the literature, or additional experimental testing, we show how this data can be used to derive a 3-D map of the initial solid volume fraction and Darcy permeability.

Meso-scale analysis of deformation wave heating in metalized solid explosive

Deformation induced heating of reactive solids is a physically complex process. As such, the effects of meso-structure, component thermomechanical properties, component mass fractions, and porosity on their impact response is not well-understood. In this study, an explicit, 2-D, Lagrangian finite and discrete element technique is used to examine thermomechanical fields in metal-explosive (aluminum-HMX) particle mix- tures due to piston supported uniaxial deformation waves. The meso-scale description uses a plane strain, thermoelastic-viscoplastic and friction constitutive theory to describe the motion and deformation of individual particles, and an energy consistent, penalty based method to describe inter-particle contact. The deformation response of material having an initial solid volume fraction of φ 0 s = 0.835 is characterized for different metal mass fractions and wave strengths. Predictions indicate that the response can be classified into strength dominated and pressure dominated regions depending on wave strength. Average thermomechanical fields that define the macro-scale wave structure are found to differ both qualitatively and quantitatively between the two regions.

A centrifugation method for the assessment of low pressure compressibility of particulate suspensions

This work describes an easy methodology for assessing the compressibility of particulate suspensions at relatively low pressures. The material used in this study was an anaerobically digested waste water sludge. Using a centrifuge, the equilibrium sediment bed height was recorded as a function of rotational speed during the centrifugation. This approach avoids errors due to expansion of the sediment bed after the centrifugation is stopped, a phenomenon typically seen with waste water sludges. A straightforward numerical method was used to solve a one-dimensional centrifugation model describing the equilibrium sediment bed height as a function of rotational speed. It has been shown that this approach yields realistic results. The one-dimensional model is able to describe the compressibility of the anaerobically digested sludge. Besides yielding a close fit for the measured sediment bed heights, extrapolating these results to a different initial solids volume fraction resulted in a good prediction of the bed height as well. Different constitutive equations for the relation between solids pressure and solids volume fraction were assessed. The typical power law functions [F. Tiller, W. Leu, Basic data fitting in filtration, Journal of the Chinese Institute of Chemical Engineers 11 (1980) 61–70], often used in filtration modelling, were the most adequate for describing the compressional behaviour of the sludge. A functional relation based on the osmotic pressure within the solids network, suggested for describing the phenomenology of filtration dewatering [K. Keiding, M. Rasmussen, Osmotic effects in sludge dewatering, Advances in Environmental Research 7 (2003) 641–645], could not be used to adequately describe the behaviour of the sludge at the low pressures generated during centrifugation.

A numerical model of iceberg scour

A numerical model of iceberg seabed scour is presented. Deformation of the seabed soil follows a Mohr–Coulomb yield criterion, and a pressure–solids volume fraction relationship. The model employs a Particle-In-Cell (PIC) advection scheme, which is suited to dealing with large displacements and discontinuities. Simulations addressed cases of two-dimensional deformation caused by a moving rigid indentor, representing an iceberg. The resulting deformation patterns display expected failure zones and the development of shear layers. The simulations examined the dependence of stresses on scour depth, soil properties, compaction and scour velocity. Comparisons with experimental measurements are also carried out. The results show that the mean normal stress on the iceberg increased with deeper scours and the angle of internal friction of the sand. A decay of stresses was observed in the seabed under the scouring iceberg with higher stress values observed for higher initial solids volume fraction of the sand.

Effect of particle distribution on the compaction behavior of granular beds

This research determines how particle size and particle distribution affects the compaction of granular beds. A modelling and experimental effort was recently designed to compare the compaction behavior of two types of granular HMX: prepressed conventional (coarse) HMX material (mean diameter of 40μm) and microfine HMX (mean diameter <5μm) [M. Greenaway, Journal of Applied Physics 97, 093521 (2005)]. The microfine material demonstrated higher levels of granular bed strength. Mesoscale modelling of granular beds that are of fixed initial solid volume fraction but vary in particle size and distribution have been undertaken that include a simple elastic-plastic strength model. These suggest that it is not inherently the “size” of a particle that controls the bed strength but the morphology and distribution of particle grains. These solutions are compared with the behavior predicted from continuum scale models of material compaction.

Predictions for the Impact of a Granular Solid Having Spatially Non-uniform Bulk Porosity

Continuum equations are numerically integrated using a high-resolution method to characterize the thermomechanical response due to planar impact of initially stress-free granular solid having spatially varying bulk porosity. This response depends on strain history because the crush-up stress necessary for inelastic compaction increases with initial solid volume fraction (ϕ0). Emphasis is placed on characterizing the influence of initial porosity and piston speed on both the grain surface heat flux variation and peak temperature rise within compaction wave profiles for the granular explosive HMX (C4H8N8O8). Heat fluxes near 586 MW/m2, resulting in temperature rises in excess of 400 K, are predicted for weak compaction of granular HMX having an initially dense region adjacent to a highly porous region (ϕ0=0.99, 0.655). Phenomena associated with reflected and transmitted waves from material interfaces are highlighted. Predicted compaction zone end states and heat flux profiles are shown to agree well with those given by a steady-state theory.

Numerical simulation of a dissolution process in a stirred tank reactor

A dissolution process of solid particles suspended in a turbulent flow of a Rushton turbine stirred tank is studied numerically by large eddy simulations including passive scalar transport and particle tracking. The lattice-Boltzmann flow solver and the Smagorinsky subgrid-scale model are adopted for solving the stirred tank flow. To the LES a finite volume scheme is coupled that solves the convection–diffusion equation for the solute. The solid particles are tracked in the Eulerian flow field through solving the dynamic equations of linear and rotational motion of the particles. Particle–particle and particle–wall collisions are included, and the particle transport code is two-way coupled. The simulation has been restricted to a lab-scale tank with a volume equal to 10 - 2 m 3 . A set of 7 × 10 6 spherical particles 0.3 mm in diameter are released in the top part of the tank ( 10 % of the tank volume), resulting in a local initial solids volume fraction of 10 % . The particle properties are such that they resemble those of calcium chloride beads. The focus is on solids and scalar concentration distributions, particle size distributions, and the dissolution time. For the particular process considered, the dissolution time is found to be at most one order of magnitude larger than the time needed to fully disperse the solids throughout the tank.

A stochastic constitutive model for disordered cellular materials: Finite-strain uni-axial compression

A stochastic constitutive model is developed for describing the continuum-scale mechanical response of disordered cellular materials. In the present work, attention is restricted to finite-strain uni-axial compression under quasi-static loading conditions. The development begins with an established cellular-scale mechanical model, but departs from traditional modeling approaches by generalizing the cellular-scale model to accommodate finite strain. The continuum-scale model is obtained by averaging the cellular-scale mechanical response over an ensemble of foam cells. Various stochastic material representations are considered through the use of probability density functions for the relevant material parameters, and the effects of the various representations on the continuum-scale response are investigated. Combining cellular-scale mechanics with a stochastic material representation to derive a continuum-scale constitutive model offers a promising new approach for simulating the finite-strain response of cellular materials. Results demonstrate that increasing a material’s degree of polydispersity can produce the same stiffening effects as increasing the initial solid-volume fraction. Additionally, particular stochastic material representations are shown to provide upper and lower bounds on the mechanical response of the cellular materials under investigation, while suitable choices for the stochastic representation are shown to accurately reproduce experimental stress–strain data through the large deformations associated with densification.

Liquid–solid relative motion during slow squeeze flow of pastes

Slow squeeze flow of a paste between two parallel circular discs of radius R is considered. A previous analysis [J.D. Sherwood, Liquid–solid relative motion during squeeze flow of pastes, J. Non-Newtonian Fluid Mech. 104 (2002) 1–32] predicts that the solids volume fraction within the paste becomes very non-uniform, with a high solids volume fraction near the axis of the two discs. If squeezing is so slow that the liquid within the paste has ample time to move relative to the particles, the liquid pressure within the paste remains close to uniform. This limit is considered in detail. The matrix of particles within a central region r < r 1 ( h ) near the axis compacts uniaxially. The wall shear stress in this central region is insufficient for the matrix of particles to slip at the wall, and only liquid is squeezed outwards. In the outer region r > r 1 particles and liquid move radially outwards, though at different velocities. Initially r 1 = R , but the central region of unixial compaction shrinks and eventually vanishes. If the initial solids volume fraction of the paste is low, the matrix of solid particles in the paste is very compressible and uniaxial compaction plays a major role in the early stages of compression. Numerical analysis is then required in order to follow the compaction history of the paste.

Estimation of the hindered settling function R(ϕ) from batch‐settling tests

AbstractThe hindered settling function R(ϕ) is a material function that quantifies the interphase drag of colloidal suspensions for all solids volume fractions ϕ. A method is presented to estimate R(ϕ) from batch‐settling tests for solids volume fractions between the initial solids volume fraction, ϕ0, and the solids volume fraction at which the suspension forms a continuously networked structure, ϕg, known as the gel point. The method is based on an analytic solution of the associated inverse problem. Techniques are presented to address initialization mechanics observed in such tests as well as experimental noise and discrete data. Analysis of synthetic and experimental data suggests that accurate estimates of R(ϕ) are possible in most cases. These results provide scope for characterization of suspension dewaterability from batch‐settling tests alone. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Predictions for weak mechanical ignition of strain hardened granular explosive

Predictions are given for the coupled bulk and grain scale response of initially unstressed, strain hardened granular HMX (C4H8N8O8) due to mild piston impact (impact speeds &amp;lt;100 m/s). Importantly, this response depends on the material’s strain history as the stress necessary for bulk inelastic compaction (crush up) increases with the solid volume fraction. Although the quasistatic compaction behavior of HMX is well characterized, the influence of strain history on the bulk and grain scale dynamic loading response has largely been unexplored. In this study, the initial solid volume fraction of the unstressed material is varied over the range of φf⩽φ0⩽1, where φf=0.655 is its free pour value. A Hugoniot analysis for the bulk material identifies three dispersed compaction wave structures that depend on the impact speed and initial solid volume fraction, and are analogous to elastic-plastic waves in dynamically loaded solids. For increasing impact speed, these structures consist of (1) a single viscoelastic wave; (2) a leading viscoelastic wave and a trailing viscoplastic wave; and (3) a single viscoplastic wave. It is shown that the resulting localized heating near intergranular contact surfaces can trigger sustained combustion of the material. Predictions for the grain scale thermochemical response indicate that significant bulk viscoplastic heating is required for ignition of materials with φf⩽φ0⩽0.88, whereas bulk viscoelastic heating leads to the ignition of denser materials (φ0&amp;gt;0.91). Both viscoelastic and viscoplastic heating are predicted to be important for ignition of materials having 0.88⩽φ0⩽0.91. Within this transition range there is predicted a sharp increase in impact sensitivity as the power input needed for ignition rapidly decreases to a value close to that for the free pour density (0.40 MW/cm2) before increasing again. This result is important for assessing the impact sensitivity and deflagration-to-detonation transition of damaged explosives.

Predicting filtration time and maximizing throughput in a pressure filter

AbstractThe modeling of pressure filtration of flocculated suspensions using compressional rheology and a knowledge of compressional yield stress Py(ϕ) and a hydraulic resistance factor r(ϕ)(ϕ is the local volume fraction of solids) is shown to yield an initial solids loading that maximizes the throughput of the filter. The optimal initial height h0 is such that the filtration time to reach a specified average volume fraction as output equals the handling time for the filter press. The maximum throughput of the press is then examined as a function of the remaining control parameters, the initial solids volume fraction ϕ0, and the applied piston pressure δP. The dependence of filtration time on ϕ0/∞00 (where ϕ∞is the volume fraction of solids at infinite time under applied pressure δP) enables the construction of a simple numerical model for the pressure filtration process, which accurately approximates predictions of the full compressional rheology model.