Radial Geometry Research Articles

Guar gum solutions for improved delivery of iron particles in porous media (Part 1): Porous medium rheology and guar gum-induced clogging

The present work is the first part of a comprehensive study on the use of guar gum to improve delivery of microscale zero-valent iron particles in contaminated aquifers. Guar gum solutions exhibit peculiar shear thinning properties, with high viscosity in static conditions and lower viscosity in dynamic conditions: this is beneficial both for the storage of MZVI dispersions, and also for the injection in porous media. In the present paper, the processes associated with guar gum injection in porous media are studied performing single-step and multi-step filtration tests in sand-packed columns. The experimental results of single-step tests performed by injecting guar gum solutions prepared at several concentrations and applying different dissolution procedures evidenced that the presence of residual undissolved polymeric particles in the guar gum solution may have a relevant negative impact on the permeability of the porous medium, resulting in evident clogging. The most effective preparation procedure which minimizes the presence of residual particles is dissolution in warm water (60°C) followed by centrifugation (procedure T60C). The multi-step tests (i.e. injection of guar gum at constant concentration with a step increase of flow velocity), performed at three polymer concentrations (1.5, 3 and 4g/l) provided information on the rheological properties of guar gum solutions when flowing through a porous medium at variable discharge rates, which mimic the injection in radial geometry. An experimental protocol was defined for the rheological characterization of the fluids in porous media, and empirical relationships were derived for the quantification of rheological properties and clogging with variable injection rate. These relationships will be implemented in the second companion paper (Part II) in a radial transport model for the simulation of large-scale injection of MZVI-guar gum slurries.

Role of chemical potential in relaxation of faceted crystal structure.

Below the roughening transition, crystal surfaces have macroscopic plateaus, facets, whose evolution is driven by the microscale dynamics of steps. A long-standing puzzle was how to reconcile discrete effects in facet motion with fully continuum approaches. We propose a resolution of this issue via connecting, through a jump condition, the continuum-scale surface chemical potential away from the facet, characterized by variations of the continuum surface free energy, with a chemical potential originating from the decay of atomic steps on top of the facet. The proposed condition accounts for step flow inside a discrete boundary layer near the facet. To validate this approach, we implement in a radial geometry a hybrid discrete-continuum scheme in which the continuum theory is coupled with only a few, minimally three, steps in diffusion-limited kinetics with conical initial data.

Development and validation of a radial variable geometry turbine model for transient pulsating flow applications

This paper presents the development and validation of a one-dimensional radial turbine model able to be used in automotive turbocharger simulations. The model has been validated using results from a numerical 3D CFD simulation of stationary and pulsating flow in a variable geometry radial turbine. As the CFD analysis showed, the main non-quasi-steady behavior of the turbine is due to the volute geometry, so special care was taken in order to properly model it while maintaining low computational costs. The flow in the volute has been decomposed in its radial and azimuthal direction. The azimuthal flow corresponds to the flow moving along the volute, while the radial flow is computed by coupling its flow with a stator model. Although the stator caused fewer accumulation effects than the volute, a small accumulation model has been used for it, which also allows to compute the evolution of the flow inside the turbine with lower costs. The flow in the moving rotor can be considered quasi-steady, so a zero-dimensional model for the rotor has been developed. Several losses models where implemented for both the stator and the rotor. The results show good agreement with the CFD computations.

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality.

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10(-4) so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ(c) and τ(g). The constant τ(c) describes the approach to the stationary state of the total charge and the potential. τ(c) is several orders of magnitude smaller than the geometry-dependent constant τ(g), which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

Polycrystalline solids under nonhydrostatic compression: Determination of strength from x-ray diffraction data

A polycrystalline sample compressed in a diamond anvil cell (DAC) without any pressure transmitting medium develops a stress state at the centre of the sample that is axially symmetric about the load axis. The axial stress component is larger than the radial component and the difference t between the two is taken as a measure of the compressive strength of the sample material at a confining pressure that equals the mean normal stress. A proper analysis of the diffraction data yields t. The data taken with the radial diffraction geometry, wherein the incident x-ray beam is perpendicular to the load axis of the DAC, give reliable estimates of strength. The diffraction data obtained with the conventional geometry, wherein the incident x-ray beam passes parallel to the DAC axis, provide reasonable estimates of strength. However, even in this case, reliable strength data can be obtained by combining the measured pressure-volume data under nonhydrostatic compression and the hydrostat derived from an independent source. The determination of strength from high pressure diffraction data is discussed.

The strength of ruby from X-ray diffraction under non-hydrostatic compression to 68 GPa

Polycrystalline ruby (α-Al2O3:Cr3+), a widely used pressure calibrant in high-pressure experiments, was compressed to 68.1 GPa at room temperature under non-hydrostatic conditions in a diamond anvil cell. Angle-dispersive X-ray diffraction experiments in a radial geometry were conducted at beamline X17C of the National Synchrotron Light Source. The stress state of ruby at high pressure and room temperature was analyzed based on the measured lattice strain. The differential stress of ruby increases with pressure from ~3.4 % of the shear modulus at 18.5 GPa to ~6.5 % at 68.1 GPa. The polycrystalline ruby sample can support a maximum differential stress of ~16 GPa at 68.1 GPa under non-hydrostatic compression. The results of this study provide a better understanding of the mechanical properties of this important material for high-pressure science. From a synthesis of existing data for strong ceramic materials, we find that the high-pressure yield strength correlates well with the ambient pressure Vickers hardness.

Constant pressure gas-driven displacement of a shear-thinning liquid in a partially filled radial Hele-Shaw cell: Thin films, bursting and instability

In this manuscript we present experimental data and quantitative analysis for the fingering instability along the interface of finite volume of Newtonian (mineral oil) and dilute shear-thinning non-Newtonian (high molecular weight polyisobutylene in mineral oil) fluids. The instability is generated by air penetrating the liquid in a radial Hele-Shaw cell geometry. The novel feature of the experiment is that the gas is driven at constant pressure generating an exponential gas area expansion independent of the presence of the instability. Furthermore, we show that the instability growth along the interface is proportional to teωξt, or in other terms the instability growth rate is constant when the gas area expansion is considered. There are clear differences and similarities in the fingering growth rate, bursting time and film thickness properties when comparing Newtonian and shear-thinning non-Newtonian fluids. It is surprising that similarities occur despite side branching for the shear-thinning liquids at higher pressures.

Modular discretization of the AdS2/CFT1 holography

We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.

ENDF/B-VII.0, JEFF-3.1 and JENDL-4 Iron and Water Cross Sections Analysis Using the PCA-REPLICA Shielding

An accurate calculation of neutrons penetration through the side-shield of a Pressurized Water Reactor (PWR) is important for the estimation of nuclear heating in the thermal shields and in the Reactor Pressure Vessel (RPV), also for estimate the leakage of the particles in the reactor cavity. The cross section data and the calculation method have an important role in this kind of problems. For this object the PCA-REPLICA benchmark where the neutron transports through typical PWR were performed at AEA technology Winfrith, UK (United Kingdom). This work aims to contribute validation of the method of calculation and analyse the cross sections, for Iron ( Fe 56 ) and water ( H 1 and O 16 ), presented by: ENDF/B-VII.0, JEFF-3.1 and JENDL-4 libraries, for the PCA-REPICA benchmark, using the Monte Carlo approach by the mean of MCNPX code. The benchmark analysis was made based on the calculated-to-measured (C/M) dosimetry reaction rates of In 103 monitors, at different depth in a water/iron shield reproducing the ex-core radial geometry of a PWR. The calculations of PCA-REPLICA experiment showed us that calculation method is effective for the protection study of the REP. And generally, the average C/M ratios obtained for the three detectors are reasonably good when the uncertainties of the measurements are taken into account.

Radial propagation in population dynamics with density-dependent diffusion

Population dynamics that evolve in a radial symmetric geometry are investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate analytical solution to this equation is found. It shows that the population density evolves from the initial state and propagates in a traveling-wave-like manner for a long-time scale. If the distance is insufficiently long, the curvature has an ineluctable influence on the density profile and front speed. In comparison, the analytical solution is in agreement with the numerical solution.

Halogen bonding in the gas phase: a comparison of the iodine bond in B⋯ICl and B⋯ICF3 for simple Lewis Bases B.

Methods for observing the rotational spectra of the halogen-bonded complexes B⋯ICl and B⋯ICF3 (B = N2, CO, HC≡CH, H2C=CH2, H2O, H2S, PH3 or NH3) and deriving from them properties such as angular geometry, radial geometry, the strength of the intermolecular bond, and the extent of electron redistribution on complex formation are described. Comparison of various properties reveals several similarities between the two series. Thus, the B⋯ICF3 obey a set of rules which were originally proposed to rationalise the angular geometries of hydrogen-bonded complexes of the type B⋯HX, but which were subsequently found to apply to their halogen-bonded analogues B⋯XY, where XY is a dihalogen molecule, including ICl. Important for establishing the validity of these rules in both series B⋯ICl and B⋯ICF3 were the complexes with B = H2O or H2S. The configuration at O in H2O⋯ICF3 and H2O⋯ICl is effectively planar. On the other hand, the configuration at S in H2S⋯ICF3 and H2S⋯ICl is permanently pyramidal. Ab initio calculations of potential energy functions for inversion at O or S performed at the CCSD(T)(F12*)/cc-pVDZ-F12 level of theory confirmed these conclusions. Comparison of the intermolecular stretching force constants k σ show that the series B⋯ICF3 is systematically more weakly bound than B⋯ICl. Interpretation of k σ in terms of nucleophilicities N B of B and electrophilicities E IR of ICl and ICF3 reveals that [Formula: see text]. Experimental and ab initio values of distances r(Z⋯I), where Z is the acceptor atom/region of B, show that, for a given B, the intermolecular bond of B⋯ICF3 is longer than that of B⋯ICl. The electronic charge redistributed from B to ICF3 on formation of B⋯ICF3 is probably negligibly small.

Radiographic outcomes of percutaneous pinning for displaced extra-articular fractures of the distal radius: a time course study.

Introduction. Although not all malunited distal radius fractures are symptomatic, the goal of treatment for displaced extra-articular fractures of the distal radius should be to restore and to maintain the radial geometry until bone healing. However, the time course change after surgery for these fractures is unclear. Methods. We, therefore, performed a retrospective cohort study on patients who sustained such fractures treated with percutaneous pinning. The main outcome measures in this study included four radiographic measurements: radial height, radial inclination, radial tilt, and ulnar variance. Results. Assessment of the monthly changes in these measurements revealed that early fracture collapse with loss of the reduced radial tilt occurred. Besides, among the 4 measurements, the normal radial tilt was the most difficult to be achieved when repositioning and pinning the fractured fragments. Conclusions. Even though the modified Kapandji technique provided a superior ability to maintain the reduced position until bone healing over the Willenegger method, we recommended that refinement of surgical techniques and postoperative hand care program may be necessary to fulfill the treatment objectives of stable surgical fixation and early joint motion.

Application of Simplex Search Method for Predicting Unknown Parameters in an Annular Fin Subjected to Thermal Stresses

This article presents an inverse approach aimed at estimating the unknown parameters such as the coefficient of thermal expansion and the Biot number for satisfying a prescribed thermal stresses field in radial fin geometry. The variation of temperature with the radius of fin is obtained by solving the heat conduction-convection equation using regular perturbation method and applying proper boundary conditions. A closed form solution for the temperature dependent stress field has been derived by employing the classical elasticity theory coupled with semi-analytical solution for the temperature field. Using the data obtained from a forward method based on the analytical solution, two unknown parameters such as the coefficient of thermal expansion and the Biot number of the fin are simultaneously estimated by an inverse technique using the Nelder-Mead simplex search method. Effects of measurement errors and number of measurement points have been analyzed in detail. It is found that even with 10 measurement points a fairly good reconstruction of the stress field can be achieved.

Influence of finite radial geometry on the growth rate of ion-channel free electron laser

The influence of finite radial geometry on the instability of a tenuous relativistic electron beam propagating in an ion-channel in a waveguide is investigated. The instability analysis is based on the linearized Vlasov-Maxwell equations for the perturbation about a self-consistent beam equilibrium. With the help of characteristic method the dispersion relation for the TE-mode is derived and analyzed through the numerical solutions. It is found that the positioning of the beam radius Rb relative to the waveguide radius Rc, and the ion-channel frequency can have a large influence on the maximum growth rate and corresponding wave number.

Analysis and Design of Direct Steam Injection for Tomato Concentrate Sterilization

Abstract Direct steam injection is a sterilization technique which is often used for high-viscosity fluid food, when the preservation of the quality characteristics and energy efficiency are the priority. In this work, an apparatus for the sterilization of tomato concentrate has been analyzed by means of a 3D computational fluid dynamics (CFD) model, in order to optimize the exchanger performance in terms of temperature distribution inside the product. A multidimensional two-phase model of steam injection inside a non-Newtonian pseudoplastic fluid was adopted to evaluate the thermal history of the product and the condensation rate of the steam injected in the heat exchanger during the thermal process. Subsequently, the CFD analysis has been extended to examine the effects of the different process parameters (sterilization temperature, steam flow rate, radial and axial temperature profiles and nozzle geometry) on the resulting product. Results obtained allowed to understand the effects of process parameters on the behavior of the condensing steam and obtain better performance of the exchanger in terms of temperature distribution of the treated product.

Determination of Dosimetric Characteristics of IrSeed 125I Brachytherapy Source

Introduction: Low dose rate brachytherapy sources have been widely used for interstitial implants in tumor sites, particularly in prostate. Dosimetric characteristics of a new IrSeed 125I brachytherapy source have been determined using the LiF thermoluminescent dosimeter (TLD) chips. Materials and Methods: Dose rate constant, radial dose function, and anisotropy function around the IrSeed 125I source were measured in a plexiglass phantom using TLD-100 chips. A plexiglass slab phantom with dimensions of 30×30×7.3 cm3 was used to measure dose distribution around the source. Results: Dose rate constant was measured to be equal to 0.965±0.006 cGyh-1U-1. Radial dose function, anisotropy function, and geometry function have been presented as tabulated data for the IrSeed source. Conclusion: Basically, the dosimetric parameters presented here for this new IrSeed source have clinical and treatment planning applications.

Fluidic Automation of Nitrate and Nitrite Bioassays in Whole Blood by Dissolvable-Film Based Centrifugo-Pneumatic Actuation

This paper demonstrates the full centrifugal microfluidic integration and automation of all liquid handling steps of a 7-step fluorescence-linked immunosorbent assay (FLISA) for quantifying nitrate and nitrite levels in whole blood within about 15 min. The assay protocol encompasses the extraction of metered plasma, the controlled release of sample and reagents (enzymes, co-factors and fluorescent labels), and incubation and detection steps. Flow control is implemented by a rotationally actuated dissolvable film (DF) valving scheme. In the valves, the burst pressure is primarily determined by the radial position, geometry and volume of the valve chamber and its inlet channel and can thus be individually tuned over an extraordinarily wide range of equivalent spin rates between 1,000 RPM and 5,500 RPM. Furthermore, the vapour barrier properties of the DF valves are investigated in this paper in order to further show the potential for commercially relevant on-board storage of liquid reagents during shelf-life of bioanalytical, ready-to-use discs.

Shear wave anisotropy in textured phase D and constraints on deep water recycling in subduction zones

Regions of low seismic velocity and high shear anisotropies in cold subducted slabs have often been related to anisotropic fabrics in hydrous phases mainly induced by slab deformation. The interpretation of these seismic anomalies in terms of hydration thus relies on a better knowledge of the elasticity and plastic deformation mechanisms of candidate hydrous phases. Here we investigate the development of lattice preferred orientations (LPO) in phase D [MgSi2H2O6, 10–18 wt% H2O], the ultimate water carrier in hydrous subducted peridotite. The samples were deformed non-hydrostatically up to 48 GPa in a diamond anvil cell and the texture and strength were obtained from analysis of the X-ray diffraction patterns collected in radial diffraction geometry. We find that at low strains the layered structure of phase D displays strong 0001 texture, where the stacking fault axis (c-axis) preferentially align parallel to the compression axis. A subsidiary 101¯0 texture develops at higher strains. Plasticity simulations in polycrystalline aggregates using a viscoplastic self-consistent model suggest that these LPO patterns are consistent with shape preferred orientation mechanism during the first compaction steps and, with dominant easy glide on basal planes and harder first order pyramidal slip, respectively, upon further compression. We find that phase D displays the lowest strength and the highest anisotropy among phases in hydrous peridotite in the uppermost lower mantle and might thus control the shear wave anisotropy generated in subducted slabs below the transition zone. We further evaluate the effect of textured phase D on the seismic velocity structure and shear wave anisotropy of deformed hydrous peridotite and compare the results to seismic observations in Tonga subduction. We show that 16 vol% of phase D in hydrous subducted peridotite is required to explain the negative velocity anomalies of 3%, the extent of shear wave splitting (0.9±0.3%) and the shear wave ray polarization geometry (VSH>VSV) observed in a detached fragment of the Tonga slab laying sub-horizontally below the transition zone. Seismic observations may thus place constraints on the degree of hydration of the Tonga slab beyond the transition zone, leading to the requirement that a minimum of 1.2 wt% H2O is retained in the slab by hydrous peridotite below 670 km depth.

Laplacian growth in a channel and Hurwitz numbers

We study the integrable structure of the 2D Laplacian growth problem with zero surface tension in an infinite channel with periodic boundary conditions in a transverse direction. Similarly to the Laplacian growth in radial geometry, this problem can be embedded into the 2D Toda lattice hierarchy in the zero dispersion limit. However, the relevant solution to the hierarchy is different. We characterize this solution by the string equations and construct the corresponding dispersionless tau-function. This tau-function is shown to coincide with the genus-zero part of the generating function for double Hurwitz numbers.

Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy

The multi-sphere method and JKR model are used in the discrete element method simulation to investigate the effect of the particle size, aspect ratios, and cohesiveness on the packing structure, characterized by porosity, radial distribution function (RDF), coordination number and contact geometry. In the absence of cohesive force, the porosity is nearly invariable with fixed aspect ratio, regardless of the size of the particles. In contrast, as surface energy increases, the porosity increases with decreasing particle size and increasing aspect ratio. The RDF results show that the number of peaks for different aspect ratios changes and show trends similar to the relaxation algorithm, expected for the finer particles. In the case of finer, cohesive particles, the most novel outcome of contact analysis is the existence of single contact, attributed to the formation of a cage structure, which has not been previously reported. The peak position and the width of the contact distributions are affected by higher surface energy because fewer contacts are required to achieve the mechanical equilibrium. Another interesting observation is that higher porosity does not always imply fewer contacts for particles with non-zero aspect ratios and high surface energies. The analysis of the distribution of the contact vector angles is found to better explain increased porosity in spite of higher coordination numbers. The results presented shed light on the packing density and structure, revealing features not easily discerned via experiments, and confirming the important role of the cohesion and aspect ratio in packing.