Solid Fraction Profiles Research Articles

Nutrient regeneration processes in bottom sediments in a Po delta lagoon (Italy) and the role of bioturbation in determining the fluxes at the sediment-water interface

A study on nutrient regeneration processes and a measure of their fluxes at the sediment-water interface was carried out in two different stations of a shallow lagoon of the Po delta river (Italy). A few parameters on the solid fraction (grain-size, porosity, C, N) and pore water profiles of o-P, NH3, NO inf3 sup− , SiO2, Tot-CO2, SO inf4 sup2− , Fe, Mn, Ca, Mg, pH, Eh were determined. At both stations the results were typical for fine sediments rich in organic matter. The ratio of variations of sulphate (ΔSO inf4 sup2− ) to total carbonate demonstrates the main role sulphate reduction plays on the organic matter decay. The use of the ratios of variations of sulphate (ΔSO inf4 sup2− ) to ammonia (ΔNH3) and of sulphate (ΔSO inf4 sup2− ) to phosphate (Δo-P) in pore waters enabled us to calculate the C/N/P of the decomposing organic matter. Obtained C/N/P indicated an enrichment of N and P with regard to C/N/P ratios of the solid fraction, due to the selective stripping of N and P during organic matter mineralization. This phenomenon decreases with depth, where organic matter becomes more refractory. Calculations on saturation degrees have shown the possibility of authigenic calcite, apatite and rhodochrosite precipitation in sediments. Nutrient fluxes were estimated for SiO2, NH3 and o-P by means of benthic chambers and modelling the pore water profiles. The model used for the calculation of fluxes allowed us to account for the bioturbation-irrigation influence near the interface, by means of a cumulative diffusion coefficient. Directly measured fluxes proved to be always significantly greater than the theoretical ones. These differences seem to be due to surface processes which do not affect pore water concentrations (degradation of fresh materials at the interface; micro-bioturbation by small gasteropoda such as Hydrobia ventrosa) and/or to the different concept of the two methods in time and space. Number, size and biomass of macrobenthic species living in the sediment underneath the benthic chambers were determined. The comparison between data on macrobenthic populations and flux values showed a good relationship between the number of organisms and benthic fluxes within each station. However, flux variations between stations are to be attributed mainly to the different arrangement of the tubes of the polychaetes Polydora ciliata in the sediment.

Gravity-Driven Granular Flows of Smooth, Inelastic Spheres Down Bumpy Inclines

We employ a kinetic constitutive theory that includes the effects of particle transport and collisions to analyze steady, fully developed, gravity-driven flows of smooth, inelastic spheres down bumpy inclines. By replacing the solid fraction by its depth-averaged value wherever it occurs in the balance equations, we obtain a closed-form solution for the granular temperature profile, which when employed in the constitutive relations for the normal and shear stresses determines the solid fraction and mean velocity profiles. The solutions ensure that the stresses and energy flux vanish at the free surface and that the balance of momentum and energy are satisfied at the base. We also determine for fixed flow rates the ranges of inclinations within which steady flows are possible, and for fixed inclinations the depths of the resulting flows. Most striking are the inclinations and flow rates at which both a dilute, fast flow and a dense, slow flow are possible.

Measurements of Solid Spheres Bouncing Off Flat Plates

Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction). The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985).

Mathematical representation of the velocity, temperature and solid fraction in an electromagnetically stirred solidifying melt.

A mathematical model has been developed to describe the velocity, temperature and solid fraction in an electromagnetically stirred Al-5%Cu alloy in which 15% B4C particles were initially suspended. In the model, we allowed for the rheology of the melt-solid slurry and the release of latent heat either at the melt-solid interface, in the bulk or at an intermediate stage between those extremes. The calculations have shown that the evolution of the temperature and solid fraction profiles were not significantly affected, either by the stirring rate or by the choice of the location of release of latent heat.

A theory for granular materials exhibiting normal stress effects based on Enskog's dense gas theory

Granular materials exhibit phenomena such as normal stress differences, which are typical of materials whose response is non-linear. For example, when a non-linearly elastic slab is sheared, its motion is not determined by the shear force but by the normal forces that manifest themselves due to the shearing (Poynting effect). Another example is a non-linear fluid which exhibits normal stress differences that lead to phenomena like “die-swell” or “rod-climbing,” which is again a manifestation of the stresses that develop orthogonal to planes of shear. In this paper, an expression for the stress tensor of a granular material that can exhibit normal-stress effects due to a solids fraction gradient is derived from both continuum and kinetic models. The continuum model motivates and develops the form of the stress tensor, but introduces undetermined coefficients. The kinetic model evaluates those coefficients using Enskog's dense gas theory. The dependence of the granular stress tensor on the solids fraction gradient arises by requiring that the correlating factor that links the two-particle distribution function to the two single-particle distribution functions be the contact value for the radial distribution function of a non-homogeneous, hard-sphere fluid. A representation for that contact value is found by developing the generalized van der Waals theory expression for a stress tensor element of a nonhomogeneous fluid (a fluid that exhibits a density gradient) in equilibrium, and comparing it to the exact expression. That representation of the contact value is introduced into the two-particle distribution function, and its contribution to the stress tensor is found. The resulting stress tensor expression is applied to a simple shear flow problem in which a linear, solids-fraction profile is transverse to the flow. The resulting normal-stress effects increase with the solids-fraction and its gradient.

Development of a mathematical model for multihearth roasters

A simultaneous heat and mass transfer model has been developed for the multiheart roasters, considering dead roasting of chalcopyrite as a typical roasting reaction. Various mass and energy balances have been worked out during the development of this model yielding coupled nonlinear partial differential equations with highly complex boundary conditions. These equations have been solved numerically using a line-by-line finite difference approach to obtain profiles of gas temperature, solid temperature, oxygen concentration, and solid fraction reacted in the roaster. The trend of the computed results appears to be realistic and can be easily explained from simple physical considerations. The effects of gas preheating and the heat transfer coefficient between the solid and the gas upon the roasting process are examined. The results show that gas preheating is beneficial for the roasting process, and the process parameters, such as particle size, gas flow rate,etc., must be adjusted so as to give the desirable value of the heat transfer coefficient needed for proper roasting.

Boundary effects on granular shear flows of smooth disks

We obtain boundary conditions for two-dimensional flows of identical, nearly elastic, circular disks that interact with a flat wall to which identical, evenly spaced half-disks have been attached. Expressions for the transfer of momentum and energy from the boundary to the flow are obtained by statistical averaging over all possible wall-flow disk collisions. We improve upon the expressions derived by Jenkins and Richman [1986] by employing in the averaging process a more elaborate velocity distribution function obtained through the method of moments. In addition we expand the distribution function about a point near the flat wall that guarantees positive slip velocities. With these boundary conditions, we analyze a two-dimensional shear flow driven by parallel bumpy boundaries. The constitutive theory employed includes both the effects of particle collisions and particle transport on the transfer of momentum and energy throughout the flow. We demonstrate how the resulting profiles of velocity, granular temperature, and solid fraction are affected by changes in the geometry of the boundary. We also predict how the induced stresses vary with the geometry of the boundary and the average solid fraction within the flow.

Chute Flows of Granular Material: Some Computer Simulations

A computer simulation has been developed to describe unidirectional flows of granular materials. Results are presented for a simulation of the two-dimensional flow of disks or cylinders down an inclined plane or chute. Velocity and solid fraction profiles were measured from the simulated systems and compared with theoretical analyses and are compared with the limited experimental results now available. The behavior is shown to be critically dependent on a third field quantity—the “granular temperature”—a measure of the kinetic energy contained in the random motions of the particles.