Radial displacement of a fluid annulus in a rotating Hele¿Shaw cell

The radial displacement of a fluid annulus in a rotating circular Hele-Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy's law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interface motion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface, alpha i, is obtained as a function of Ca.

Interfacial instabilities of a fluid annulus in a rotating Hele-Shaw cell

We have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele-Shaw cell rotating with angular velocity Omega. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Extractants to assess zinc phytoavailability in mineral fertilizer and industrial by-products

Efficient analytical methods for the quantification of plant-available Zn contained in mineral fertilizers and industrial by-products are fundamental for the control and marketing of these inputs. In this sense, there are some doubts on the part of the scientific community as well as of the fertilizer production sector, whether the extractor requested by the government (Normative Instruction No. 28, called 2nd extractor), which is citric acid 2 % (2 % CA) (Brasil, 2007b), is effective in predicting the plant availability of Zn via mineral fertilizers and about the agronomic significance of the required minimal solubility of 60 % compared to the total content (HCl) (Brasil, 2007a). The purpose of this study was to evaluate the alternative extractors DTPA, EDTA, neutral ammonium citrate (NAC), buffer solution pH 6.0, 10 % HCl, 10 % sulfuric acid, 1 % acetic acid, water, and hot water to quantify the contents of Zn available for maize and compare them with indices of agronomic efficiency of fertilizers and industrial by-products when applied to dystrophic Clayey Red Latosol and Dystrophic Alic Red Yellow Latosol with medium texture. The rate of Zn applied to the soil was 5 mg kg-1, using the sources zinc sulfate, commercial granular zinc, ash and galvanic sludge, ash and two brass slags. Most Zn was extracted from the sources by DTPA, 10 % HCl, NAC, 1% acetic acid, and 10 % sulfuric acid. Recovery by the extractors 2 % CA, EDTA, water, and hot water was low. The agronomic efficiency index was found to be high when using galvanic sludge (238 %) and commercial granular zinc (142 %) and lower with brass slag I and II (67 and 27 %, respectively). The sources galvanizing ash and brass ash showed solubility lower than 60 % in 2 % CA, despite agronomic efficiency indices of 78 and 125 %, respectively. The low agronomic efficiency index of industrial by-products such as brass slag I and galvanizing ash can be compensated by higher doses, provided there is no restriction, as well as for all other sources, in terms of contaminant levels of arsenic, cadmium, chromium, lead, and mercury as required by law (Normative Instruction No 27/2006). The implementation of 2nd extractor 2 % CA and the requirement of minimum solubility for industrial by-products could restrict the use of alternative sources as potential Zn sources for plants.

Phosphorus availability in oxidic soils treated with lime and silicate applications

Based on the assumption that silicate application can raise soil P availability for crops, the aim of this research was to compare the effect of silicate application on soil P desorption with that of liming, in evaluations based on two extractors and plant growth. The experiment was carried out in randomized blocks with four replications, in a 3 × 3 × 5 factorial design, in which three soil types, three P rates, and four soil acidity correctives were evaluated in 180 experimental plots. Trials were performed in a greenhouse using corn plants in 20-dm³ pots. Three P rates (0, 50 and 150 mg dm-3) were applied in the form of powder triple superphosphate and the soil was incubated for 90 days. After this period, soil samples were collected for routine chemical analysis and P content determination by the extraction methods resin, Mehlich-1 and remaining P. Based on the results, acidity correctives were applied at rates calculated for base saturation increased to 70 %, with subsequent incubation for 60 more days, when P content was determined again. The acidity correctives consisted of: dolomitic lime, steelmaking slag, ladle furnace slag, and wollastonite. Therefore, our results showed that slags raised the soil P content more than lime, suggesting a positive correlation between P and Si in soil. Silicon did not affect the extractor choice since both Mehlich-1 and resin had the same behavior regarding extracted P when silicon was applied to the soil. For all evaluated plant parameters, there was significant interaction between P rates and correctives; highest values were obtained with silicate.

Hydrodynamic fluctuations in fluids under external gradients

Temperature and velocity correlation functions in a fluid subjected to conditions creating both a temperature and a velocity gradient are computed up to second order in the gradients. Temperature and velocity fluctuations are coupled due to convection and viscous heating. When the viscosity goes to infinity one gets the temperature correlation function for a solid under a temperature gradient, which contains a long-ranged contribution, quadratic in the temperature gradient. The velocity correlation function also exhibits long-range behavior. In a particular case its equilibrium term is diagonal whereas the nonequilibrium correction contains nondiagonal terms.

Relaxation dynamics in suspensions of ferromagnetic particles

We have studied the relaxation dynamics of a dilute assembly of ferromagnetic particles in suspension. A formalism based on the Smoluchowski equation, describing the evolution of the probability density for the directions of the magnetic moment and of the axis of easy magnetization of the particles, has been developed. We compute the rotational viscosity from a Green-Kubo formula and give an expression for the relaxation time of the particles which comes from the dynamic equations of the correlation functions. Concerning the relaxation time for the particles, our results agree quite well with experiments performed on different samples of ferromagnetic particles for which the magnetic energy, associated with the interaction between the magnetic moments and the external field, or the energy of anisotropy plays a dominant role.

PHYTOAVAILABILITY OF COPPER IN INDUSTRIAL BY-PRODUCTS AND MINERAL FERTILIZERS

Alternative copper (Cu) sources could be used in fertilizer production, although the bioavailability of copper in these materials is unknown. The objective of this study was to evaluate the extractants neutral ammonium citrate (NAC), 2 % citric acid, 1 % acetic acid, 10 % HCl, 10 % H2SO4, buffer solution pH 6.0, DTPA, EDTA, water, and hot water in the quantification of available Cu content in several sources, relating them to the relative agronomic efficiency (RAE) of wheat grown in a clayey Latossolo Vermelho eutrófico (Oxisol) and Neossolo Quartzarênico (Typic Quartzipsamment). Copper was applied at the rate of 1.5 mg kg-1 as scrap slag, brass slag, Cu ore, granulated copper, and copper sulfate. The extractants 10 % HCl, 10 % H2SO4, and NAC extracted higher Cu concentrations. The RAE values of brass slag and Cu ore were similar to or higher than those of Cu sulfate and granulated Cu. Solubility in the 2nd NAC extractant, officially required for mineral fertilizers with Cu, was lower than 60 % for the scrap slag, Cu ore, and granulated copper sources. This fact indicates that adoption of the NAC extractant may be ineffective for industrial by-products, although no extractant was more efficient in predicting Cu availability for wheat fertilized with the Cu sources tested.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Magnetic properties and domain-wall motion in single-crystal BaFe10.2Sn0.74Co0.66O19

The magnetic properties of BaFe12O19 and BaFe10.2Sn0.74Co0.66O19 single crystals have been investigated in the temperature range (1.8 to 320 K) with a varying field from -5 to +5 T applied parallel and perpendicular to the c axis. Low-temperature magnetic relaxation, which is ascribed to the domain-wall motion, was performed between 1.8 and 15 K. The relaxation of magnetization exhibits a linear dependence on logarithmic time. The magnetic viscosity extracted from the relaxation data, decreases linearly as temperature goes down, which may correspond to the thermal depinning of domain walls. Below 2.5 K, the viscosity begins to deviate from the linear dependence on temperature, tending to be temperature independent. The near temperature independence of viscosity suggests the existence of quantum tunneling of antiferromagnetic domain wall in this temperature range.

Resonant spin tunneling in small antiferromagnetic particles

The paper reports a detailed experimental study on magnetic relaxation of natural horse-spleen ferritin. ac susceptibility measurements performed on three samples of different concentration show that dipole-dipole interactions between uncompensated moments play no significant role. Furthermore, the distribution of relaxation times in these samples has been obtained from a scaling of experimental X" data, obtained at different frequencies. The average uncompensated magnetic moment per protein is compatible with a disordered arrangement of atomic spins throughout the core, rather than with surface disorder. The observed field dependence of the blocking temperature suggests that magnetic relaxation is faster at zero field than at intermediate field values. This is confirmed by the fact that the magnetic viscosity peaks at zero field, too. Using the distribution of relaxation times obtained independently, we show that these results cannot be explained in terms of classical relaxation theory. The most plausible explanation of these results is the existence, near zero field, of resonant magnetic tunneling between magnetic states of opposite orientation, which are thermally populated.

An Investigation of the Interstate 80 Rutting in Adair County, October 1983

This investigation was initiated to determine the causes of a rutting problem that occurred on Interstate 80 in Adair County. 1-80 from Iowa 25 to the Dallas County line was opened to traffic in November, 1960. The original pavement consisted of 4-1/2" of asphalt cement concrete over 12" of rolled stone base and 12" of granular subbase. A 5-1/2" overlay of asphalt cement concrete was placed in 1964. In 1970-1972, the roadway was resurfaced with 3" of asphalt cement concrete. In 1982, an asphalt cement concrete inlay, designed for a 10-year life, was placed in the eastbound lane. The mix designs for all courses met or exceeded all current criteria being used to formulate job mixes. Field construction reports indicate .that asphalt usage, densities, field voids and filler bitumen determinations were well within specification limits on a very consistent basis. Field laboratory reports indicate that laboratory voids for the base courses were within the prescribed limits for the base course and below the prescribed limits for the surface course. Instructional memorandums do indicate that extreme caution should be exercised when the voids are at or near the lower limits and traffic is not minimal. There is also a provision that provides for field voids controlling when there is a conflict between laboratory voids and field voids. It appears that contract documents do not adequately address the directions that must be taken when this conflict arises since it can readily be shown that laboratory voids must be in the very low or dangerous range if field voids are to be kept below the maximum limit under the current density specifications. A rut depth survey of January, 1983, identified little or no rutting on this section of roadway. Cross sections obtained in October, 1983, identified rutting which ranged from 0 to 0.9" with a general trend of the rutting to increase from a value of approximately 0.3" at MP 88 to a rut depth of 0.7" at MP 98. No areas of significant rutting were identified in the inside lane. Structural evaluation with the Road Rater indicated adequate structural capacity and also indicated that the longitudinal subdrains were functioning properly to provide adequate soil support values. Two pavement sections taken from the driving lane indicated very little distortion in the lower 7" base course. Essentially all of the distortion had occurred in the upper 2" base course and the 1..;1/2" surface course. Analysis of cores taken from this section of Interstate 80 indicated very little densification of either the surface or the upper or lower base courses. The asphalt cement content of both the Type B base courses and the Type A surface course were substantially higher than the intended asphalt cement content. The only explanation for this is that the salvaged material contained a greater percent of asphalt cement than initial extractions indicated. The penetration and viscosity of the blend of new asphalt cement and the asphalt cement recovered from the salvaged material were relatively close to that intended for this project. The 1983 ambient temperatures were extremely high from June 20 through September 10. The rutting is a result of a combination of adverse factors including, (1) high asphalt content, (2) the difference between laboratory and field voids, (3) lack of intermediate sized crushed particles, (4) high ambient temperatures. The high asphalt content in the 2" upper base course produced an asphalt concrete mix that did not exhibit satisfactory resistance to deformation from heavy loading. The majority of the rutting resulted from distortion of the 2" upper base lift. Heater planing is recommended as an interim corrective action. Further recommendation is to design for a 20-year alternative by removing 2-1/2" of material from the driving lane by milling and replacing with 2-1/2" of asphalt concrete with improved stability. This would be .followed by placing 1-1/2" of high quality resurfacing on the entire roadway. Other recommendations include improved density and stability requirements for asphalt concrete on high traffic roadways.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.