Parallelepiped Cell Research Articles

Analysis of microbial diversity of inocula used in a five-face parallelepiped and standard microbial fuel cells

This work had a double purpose: (i) to study the effect of sulphate-reducing (SR-In) and enriched (E-In) inocula on the characteristics of one-chamber standard microbial fuel cell (MFC-S) and parallelepiped cell and (ii) to analyze the bacterial communities in cells operated with either SR-In or E-In. The MFC-S of 150 mL consisted of one-chamber plexiglass cell with electrodes separated 7.8 cm. The MFC-P consisted of a parallelepiped built in plexiglass with a liquid volume of 270 mL. Five faces of this cell were fitted with ‘sandwich’ cathode–membrane–anode assemblages (CMA). The values of internal resistance (Rint) were 4602 and 687 Ω, for the MFC-S loaded with SR-In and E-In, respectively. The values of Rint were 400 and 84, and 292 and 80 Ω for the faces connected in series and parallel and the MFC-P loaded with SR-In and E-In, respectively. Parallel connection of cell faces also significantly improved the electrochemical characteristics of the P cell (higher powers). In general, use of E-In in both types of MFC lead to improved power densities compared to SR-In. Molecular biology analysis of microbial communities showed that the E-In was less diverse than SR-In (in terms of phyla). An electrochemically active bacterium Geovibrio ferrireducens belonging to phylum Deferribacteres was found in the E-In. Predominance of Deferribacteres was observed in the E-In. Members of this phylum were not found in the SR-In.

Effect of the solute–solvent interface on small-angle neutron scattering from organic solutions of short alkyl chain molecules as revealed by molecular dynamics simulation

The problem of describing the experimental small-angle neutron scattering (SANS) from diluted solutions of saturated monocarboxylic acids with short chain lengths (myristic and stearic acids) in deuterated decalin is considered. The method of classical molecular dynamics simulation (MDS) is used to obtain the atomic number density distributions, and, as a consequence, the scattering length density (SLD) distribution in the solute–solvent interface area (about 1 nm around the acid molecules), assuming the acid molecules to be rigid and non-associated in the solutions. MDS is performed for solutions in a parallelepiped cell of 5.5 × 5.3 × 5.3 nm (one acid molecule per cell) under normal conditions. The time averaging of the obtained distributions is done over 2 ns (after the system thermalization). It is shown that a specific short-range ordering organization of the solvent molecules in the vicinity of the acid molecules has a significant effect on the scattering, which is mainly determined by a relatively large ratio between the effective size of the solvent molecule and the cross-section diameter of the acid molecule. Various approximations to the simulated SLD distributions, based on the cylinder-type symmetry of the acid molecules, are probed to achieve the best consistency with the experimental SANS curves by varying the residual incoherent background.

A numerical study of turbulent mixed convection in an enclosure with heated rectangular elements

By means of direct numerical simulations (DNS), we investigate instantaneous and statistical characteristics of turbulent mixed convection in parallelepiped convective cells with heated parallelepiped obstacles inside. Cold air enters the cell through thin ducts located at the side walls close to the top, and warmer air leaves the cell through the outlet ducts located also at the side walls but close to the bottom. The considered Reynolds numbers, based on the velocity of the inlet flow and the width of the inlet ducts, are and 79 (or 2.37×104 and 1.18×104 if based on the height of the cell) and the Grashof number equals . The results obtained for mixed and forced convection reveal different large-scale circulations of air inside the domain, although the geometry and the Reynolds numbers are the same. The different sense of rotation of the large-scale circulation is attributed to the dominance of buoyancy over inertia in the considered mixed convection cases. The heat flux at the surfaces of the obstacles is determined by the fluid currents around them; therefore, its distribution depends on the orientations of the obstacle surfaces (vertical or horizontal) and their locations within the domain.

Analytical models for the mechanical behavior of closed and open-cell Al foams

Two 3D analytical models are proposed for the determination of mechanical properties of Al closed and open-cell foams under compression load. The first model, referring to closed cell foams, is symmetrical, considering ellipsoid cells equally arranged in a rectangular plate, whereas the second one, related to open-cell foams, consists of a simple unit parallelepiped cell. The closed cell model produces much higher values of the plateau stress than comparable experimental results, mainly due to the associated conditions of symmetry, contrary to the open-cell model which yields values close to experimental and theoretical results of other investigators. Additionally, in the latter case, a unit cubic cell is also considered for comparison reasons. Both models are solved by the finite element method using a commercial program. The open-cell model is simple, time sparing and easy to use. Finally, a fracture analysis of the model is conducted based on the energy density concept and results are given for distortion and dilatational effects.

Classical and enriched finite element formulations for Bloch‐periodic boundary conditions

AbstractIn this paper, classical and enriched finite element (FE) formulations to impose Bloch‐periodic boundary conditions are proposed. Bloch‐periodic boundary conditions arise in the description of wave‐like phenomena in periodic media. We consider the quantum‐mechanical problem in a crystalline solid and derive the weak formulation and matrix equations for the Schrödinger and Poisson equations in a parallelepiped unit cell under Bloch‐periodic and periodic boundary conditions, respectively. For such second‐order problems, these conditions consist of value‐ and derivative‐periodic parts. The value‐periodic part is enforced as an essential boundary condition by construction of a value‐periodic basis, whereas the derivative‐periodic part is enforced as a natural boundary condition in the weak formulation. We show that the resulting matrix equations can be obtained by suitably specifying the connectivity of element matrices in the assembly of the global matrices or by modifying the Neumann matrices via row and column operations. The implementation and accuracy of the new formulation is demonstrated via numerical examples for the three‐dimensional Poisson and Schrödinger equations using classical and enriched (partition‐of‐unity) higher‐order FEs. Copyright © 2008 John Wiley & Sons, Ltd.

A micromechanical characterization of angular bidirectional fibrous composites

A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidirectional fiber packing is assumed to represent the microstructure of the composite. For angular bidirectional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic microstructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible independent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of loading in terms of stresses and strains. The individual elastic properties of the constituents’ materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechanics algorithm, the results for four composites are presented. The results in this paper are mainly focused on the impact of the fiber cross angles on the stiffness properties of the composites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/compliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis.

Static and dynamic structure and the atomic dynamics of liquid Ge from first-principles molecular-dynamics simulations

The first-principles molecular-dynamics simulation was performed for liquid Ge at $1253\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by using two kinds of simulation cells: The cubic cell of 64 atoms and the rectangular parallelepiped one of 128 atoms. The rectangular parallelepiped cell of 128 atoms was adopted to obtain the dynamic structure factor of liquid Ge in the small wave number region. The long simulation time was adopted, i.e., $66\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the cubic cell and $75\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the rectangular parallelepiped one. The present first-principles molecular-dynamics simulation reproduces well the experimental static structure factor and radial distribution function. A broad peak around $100\ifmmode^\circ\else\textdegree\fi{}$ in the obtained bond angle distribution function implies the existence of the tetrahedral atomic unit in liquid Ge. The self-diffusion coefficient for the rectangular parallelepiped cell is 20% larger than that of the cubic one. The obtained dynamic structure factor agrees well with the experimental one obtained by the inelastic x-ray scattering experiment [Hosokawa et al., Phys. Rev. B 63, 134205 (2001)], which shows the ``de Gennes narrowing'' of the main peak and the existence of the side peaks. These side peaks represent a longitudinal vibrational motion, which was also supported by the subsidiary peak around $30\phantom{\rule{0.3em}{0ex}}{\mathrm{ps}}^{\ensuremath{-}1}$ in the spectral density of the velocity autocorrelation function. The gradient of the dispersion relation in the present simulation agrees well with the experimental sound velocity. This ``no positive dispersion'' accords well with the inelastic x-ray scattering experiment of Hosokawa et al. The reason for this ``no positive dispersion'' for liquid Ge is discussed in particular concern with its low kinematic viscosity. Though the velocity autocorrelation function itself does not show a cage effect, a microscopic cage effect can be found by the detailed analysis for the trace and environment of the single atomic motion. The atomic movement as a group of 3--5 atoms seems to be present in liquid Ge in addition to individual atomic motions. The covalent bond seems to be also present at least instantaneously in liquid Ge.

Effect of softness of the potential on the stress anisotropy in liquids

We have performed molecular dynamics simulations of dense liquids using nonconformal and Gaussian potential models. We investigate the effect of the softness of the potential on the pressure tensor of liquids and dense fluids when the simulations are carried out using parallelepiped cells. The combination of periodic boundary conditions and small cross sectional areas induces an anisotropy in the diagonal components of the pressure tensor. This anisotropy results in an artificial stress in the system that has to be taken into account in simulations of explicit interfaces, where the artificial stress introduces errors in the computation of the surface tension. At high liquid densities the stress anisotropy exhibits an oscillatory dependence with the cross sectional area of the simulation box. We find that the softness of the potential has a dramatic effect on the amplitude of the oscillations, which can be significantly reduced in soft potentials, such as those used in the modeling of hydrocarbon liquids or polymers.

Prospects for use of magnetic separator filters for treatment of ceramic suspensions

Use of magnetic separator filters with a granulated (in particular, polybead) working matrix for treatment of different suspensions, including ceramic suspensions, is proposed for removal of ferrous contaminants. A design of the cartridge type is examined as it allows rapidly performing frequent regeneration of the apparatus. The principal parameter of the charge medium — the equivalent pore diameter — is estimated based on a physical model of “fractional” parallelepiped cells and a formal model of the granulated medium pipes.

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.

Study of Madelung constants of complex ionic crystals

A new formula together with the computing method for calculating Madelung constant α is given, based on the parallelepiped neutral cells which are situated around the reference cell,of which 26 such cells constitute the first shell and 98, 218,…,24 N2+2 cells constitute the second, third,…, and the Nth shell respec tively. The α(N) is a rapidly converging series and can be calculated very easily. In this paper Madelung constants and madelung energy for some complex io nic crystals have been computed by this new method which can be applied to all k inds of complex ionic crystals of trigonal ,orthorhombic system and so on.

The estimation of electrolyte temperature in small-scale cells under electric current flow

An approximate method for estimating electrolyte temperature in small parallelepiped and cube cells is presented. The sensitivity of temperature to working electrode potential, and the heat of overall cell reaction is illustrated via a numerical example, involving a single-electron reversible electrode reaction.

VISUALIZATION OF SPATIALLY INHOMOGENEOUS SPIN RELAXATION PHENOMENA IN LIQUID 3HE-4HE MIXTURES

By using the Magnetic Resonance Imaging (MRI) technique, we studied the spatial recovery of the longitudinal magnetization of liquid 3 He- 4 He mixtures in a 2mm × 2mm × 20mm rectangular parallelepiped sample cell below 1 K. We applied saturation pulses to destroy the magnetization and took two-dimensional pictures of the recovery of the magnetization in three orthogonal planes by the MRI as a function of waiting times. We found from the MRI pictures that the bulk relaxation process was so slow that the surface relaxation and the subsequent diffusion process were dominant mechanisms for the 3He spin relaxation. When the mixture was phase-separated, the magnetization in the concentrated side recovered much faster than that in the diluted side. It was also shown that there was no extra magnetization recovery at the phase boundary. As a result, the magnetization diffused from the concentrated side, flowed through the phase boundary into the diluted side and caused a magnetization recovery in the diluted side.

Non-equilibrium molecular dynamics simulation of the shear viscosity of liquid methanol: adaptation of the Ewald sum to Lees-Edwards boundary conditions

The Ewald sum method is commonly used in equilibrium simulations of polar fluids to enhance convergence of long-range Coulombic forces within modest-sized cubic simulation cells. In this work, we derive a form of the standard Ewald sum technique for use with non-equilibrium molecular dynamics (NEMD) simulations of viscosity that make use of the Lees–Edwards boundary conditions. This generalized Ewald sum can be used for any parallelepiped simulation cell. The method was tested by performing NEMD simulations at various temperatures and densities for simulated liquid methanol. The results were in excellent agreement with experimental data for methanol and Green–Kubo simulations of the viscosity using the standard cubic-cell Ewald sum. A simple truncation of the polar interactions at 10 Å was found to produce errors of over 200% in the simulated viscosities. Values obtained with the polar interactions turned off (i.e. using only dispersion forces) were generally 40–60% below the experimental values. These results show that long-range Coulombic interactions may be significant in simulated liquid viscosities and that they can be accurately handled in NEMD simulations with the proposed extension of the Ewald sum.

Non-equilibrium molecular dynamics simulation of the shear viscosity of liquid methanol: adaptation of the Ewald sum to Lees-Edwards boundary conditions

The Ewald sum method is commonly used in equilibrium simulations of polar fluids to enhance convergence of long-range Coulombic forces within modest-sized cubic simulation cells. In this work, we derive a form of the standard Ewald sum technique for use with non-equilibrium molecular dynamics (NEMD) simulations of viscosity that make use of the Lees–Edwards boundary conditions. This generalized Ewald sum can be used for any parallelepiped simulation cell. The method was tested by performing NEMD simulations at various temperatures and densities for simulated liquid methanol. The results were in excellent agreement with experimental data for methanol and Green–Kubo simulations of the viscosity using the standard cubic-cell Ewald sum. A simple truncation of the polar interactions at 10 Å was found to produce errors of over 200% in the simulated viscosities. Values obtained with the polar interactions turned off (i.e. using only dispersion forces) were generally 40–60% below the experimental values. These results show that long-range Coulombic interactions may be significant in simulated liquid viscosities and that they can be accurately handled in NEMD simulations with the proposed extension of the Ewald sum.

Influence of adsorbed polymers on the removal of mineral particles from a planar surface

Experimental results on the role of adsorbed polymers on the particle adhesion are presented. Both Brownian (silica particles) and non-Brownian (glass beads) particles were used. The particles were deposited onto the internal surface of a glass parallelepiped cell, and then submitted to increasing laminar flow rates. The pH and the ionic strength of the electrolytes were fixed. The adhesive force was related to the hydrodynamic force required to dislodge 50% of the initially attached beads. We found that high molecular weight PEO had little effect on the adhesion of small silica beads due to the low affinity of the polymer for silica or glass surfaces. On the contrary, PEO greatly enhanced the adhesion of bigger glass beads forced to deposit on the capillary surface because of gravity. The increase was all the more pronounced as the molecular weight of the polymer was high. The effect of high molecular weight cationic copolymers on the adhesion of silica particles was drastic. The maximal force (1500 pN) applied by the device could not enable any particle detachment even using polymers of low cationicity rate (5%), showing the efficiency of electrostatic attractions. When copolymers were adsorbed on both surfaces (particles and plane), the adhesive force exhibited a maximum at intermediate coverage of particles. This optimum was related to the optimum flocculation concentration classically observed in flocculation of suspensions by polymers.

Onset of traveling waves in isothermal double diffusive convection.

Experiments on double diffusive convection sustained by imposed vertical concentration gradients have been conducted in a novel thin isothermal parallelepiped cell. The measured critical Rayleigh number and the frequency of traveling waves are in reasonable accord with a stability analysis that predicts a tricritical condition [ital all] [ital along] the instability boundary. Visualization of the pattern from the side reveals that the asymptotic state immediately above the onset of instability consists of packets of traveling finite amplitude plumes.

The redistribution of carbon interstitials during the ageing of martensite through the clustering and coarsening of carbon multiplets

The Mossbauer spectra of 9.5 at.% C as-quenched and aged martensite are analyzed in terms of seven Fe environments according to the the carbon multiplet model; in particular, one distinguishes the Fe atoms first nearest neighbours of an interstitial along or perpendicularly to the c axis. Recent13C NMR results are consistent with the model which leads to a B2 monoclinic iron carbide with parallelepiped cell of 5.73, 6.74 and 8.60 A.

The clustering and coarsening of carbon multiplets during the aging of martensite from mössbauer spectroscopy: The preprecipitation stage of epsilon carbide

Mossbauer spectra of as-quenched and aged martensite (9.5 at. pct C) are analyzed in terms of seven Fe environments, the abundances of which evolve with aging time. Besides the atoms of the matrix (A), Fe atoms which are first nearest neighbors of an isolated interstitial can only be distinguished by their quadrupole shift depending upon whether they lie in a direction perpendicular (Ba) or parallel to thec axis (Bc); classC atoms have two carbon neighbors whileD orE belong to an ordered phase; classF atoms have three carbon neighbors. The carbon multiplet model, based on interstitials residing exclusively in octahedral sites, an elastic stability of theC-C 1/2«111” doublet and a diffusion path for carbon in (001)α' can explain all the features observed: a first step attributed to the clustering of isolated multiplets, and a second step to the coarsening into extended multiplets which leads to the emergence of a new ordered iron carbide (B2 monoclinic with parallelepiped cell of 5.73, 6.74, and 8.60 A) which transformsin situ into e-carbide (~Fe9C4) (η carbide as long as it is coherent with the matrix). The positions of carbon atoms in Fe9C4 are specified and a synopsis with related phenomena is drawn.

Variational Methods for Dispersion Relations and Elastic Properties of Composite Materials

The propagation of harmonic elastic waves through composite media with a periodic structure is analyzed. Methods utilizing the Floquet or Bloch theory common in the study of the quantum mechanics of crystal lattices are applied. Variational principles in the form of integrals over a single cell of the composite are developed, and applied in some simple illustrative cases. This approach covers waves moving in any direction relative to the lattice structure, and applies to structures of the Bravais lattice groups which include, for example, parallel rods in a square or hexagonal pattern, and an arbitrary parallelepiped cell. More than one type of inclusion can be considered, and the elastic properties and density of the inclusion and matrix can vary with position, as long as they are periodic from cell to cell. The Rayleigh-Ritz procedure can be applied to the solution of the variational equations, which provides a means of calculating dispersion relations and elastic properties of specific composite materials. Detailed calculations carried out on layered composites confirm the effectiveness of the method.