The influence of a compressive stress on the nonlinear response of ferroelectric crystals

The origin of nonlinearity in a ferroelectric crystal is domain reorientation, and such a process can be affected by the presence of a compressive stress. In this article we examine how a superimposed compression affects the evolution of new domain and how it changes the shape of the hysteresis loop. We start out by considering the thermodynamic driving force for domain reorientation, and then use a dual-phase homogenization theory to calculate the overall response. To uncover the influence of a compressive stress, the theory is used to calculate the hysteresis loop between the electric displacement D and the electric field E of a BaTiO₃ crystal, first without and then with a compression, using a two-consecutive 90° switch model (i.e. 0° → 90° → 180°). It is found that, from the initial 0° position, the compressive stress will increase the thermodynamic driving force and promote an earlier onset of the 90° domain, but its presence will cause a significant delay for the reorientation process to pass through the intermediate 90° state in route to its final 180° configuration. The D vs. E loop then exhibits a more round shape and a lesser steep slope near the coercive field. The delayed passage and more rounded shape are found to be consistent with a recent experimental observation [Burcsu et al., 2004. J. Mech. Phys. Solids 52, 823–846].     

Measurements of emission spectra from hot,dense germanium plasma in short pulse laser experiments

Heating of thin foil targets by an high power laser at intensities of 10¹⁷–10¹⁹ W/cm² has been studied as a method for producing high temperature, high density samples to investigate X-ray opacity and equation of state. The targets were plastic (parylene-N) foils with a microdot made of a mixture of germanium and titanium buried at depth of 1.5 μm. The L-shell spectra from the germanium and the K-shell spectra from the titanium were taken using crystal spectrometers recording onto film and an ultra fast X-ray streak camera coupled to a conical focussing crystal with a time resolution of 1 ps. The conditions in the microdot were inferred by comparing the measured spectra to synthetic spectra produced by the time-dependent collisional–radiative (CR) models FLY and FLYCHK. The data were also compared to simulated spectra from a number of opacity codes assuming local thermodynamic equilibrium (LTE). Temperature and density gradients were taken into account in the comparisons. The sample conditions were inferred from the CR modelling using FLYCHK to be 800 ± 100 eV and 1.5 ± 0.5 g/cc. The best fit to the LTE models was at a temperature 20% lower than with the CR model. Though the sample departs from LTE significantly useful spectral comparisons can still be made. The results and comparisons are discussed along with improvements to the experimental technique to achieve conditions closer to LTE.     

Extrudate swell of linear and branched polyethylenes: ALE simulations and comparison with experiments

Extrudate swell is a common phenomenon observed in the polymer extrusion industry. Accurate prediction of the dimensions of an extrudate is important for appropriate design of dies for profile extrusion applications. Prediction of extrudate swell has been challenging due to (i) difficulties associated with accurate representation of the constitutive behavior of polymer melts, and (ii) difficulties associated with the simulation of free surfaces, which requires special techniques in the traditionally used Eulerian framework. In a previous work we had argued that an Arbitrary Lagrangian Eulerian (ALE) based finite element formulation may have advantages in simulating free surface deformations such as in extrudate swell. In the present work we reinforce this argument by comparing our ALE simulations with experimental data on the extrudate swell of commercial grades of linear polyethylene (LLDPE) and branched polyethylene (LDPE). Rheological behavior of the polymers was characterized in shear and uniaxial extensional deformations, and the data was modeled using either the Phan–Thien Tanner (PTT) model or the eXtended Pom–Pom (XPP) model. Additionally, flow birefringence and pressure drop measurements were done using a 10:1 contraction–expansion (CE) slit geometry in a MultiPass Rheometer. Simulated pressure drop and contours of the principal stress difference were compared with experimental data and were found to match well. This provided an independent test for the accuracy of the ALE code and the constitutive equations for simulating a processing-like flow. The polymers were extruded from long (L/D = 30) and short (L/D = 10) capillaries dies at 190 °C. ALE simulations were performed for the same extrusion conditions and the simulated extrudate swell showed good agreement with the experimental data.     

Numerical simulation of the fountain flow instability in injection molding

For the first time, the viscoelastic flow front instability is studied in the full non-linear regime by numerical simulation. A two-component viscoelastic numerical model is developed which can predict fountain flow behavior in a two-dimensional cavity. The eXtended Pom-Pom (XPP) viscoelastic model is used. The levelset method is used for modeling the two-component flow of polymer and gas. The difficulties arising from the three-phase contact point modeling are addressed, and solved by treating the wall as an interface and the gas as a compressible fluid with a low viscosity. The resulting set of equations is solved in a decoupled way using a finite element formulation. Since the model for the polymer does not contain a solvent viscosity, the time discretized evolution equation for the conformation tensor is substituted into the momentum balance in order to obtain a Stokes like equation for computing the velocity and pressure at the new time level. Weissenberg numbers range from 0.1 to 10. The simulations reveal a symmetric fountain flow for Wi = 0.1–5. For Wi = 10 however, an oscillating motion of the fountain flow is found with a spatial period of three times the channel height, which corresponds to experimental observations.     

Atomistic simulation of crystallization of a polyethylene melt in steady uniaxial extension

We present simulation results of flow-induced crystallization of a dense polymeric liquid subjected to a strong uniaxial elongational flow using a rigorous nonequilibrium Monte Carlo method. A distinct transition between the liquid and the crystalline phases occurred at critical values of flow strength, with an abrupt, discontinuous transition of the overall chain conformation. The flow-induced crystalline phase matched quantitatively the experimental X-ray diffraction data of the real crystals remarkably well, including the sharp Bragg peaks at small wavenumbers, k < 1.5 Å^?1, indicating the existence of a global long-range ordering. We also found that the enthalpy change (ΔH = 225 J/g) during the phase transition was quantitatively very similar to the experimental heat of fusion (276 J/g) of polyethylene crystals under quiescent conditions. Furthermore, a detailed analysis of the configuration-based temperature provided a sound microscopic physical origin for the effective enhancement of the crystallization (or melting) temperature that has been observed in experiments. Simulation results also allow for the deduction of potential nonequilibrium expressions for thermodynamic quantities, such as temperature and heat capacity.     

Fourier analysis of X-ray micro-diffraction profiles to characterize laser shock peened metals

X-ray micro-diffraction profiles using a synchrotron light source were analyzed via Fourier transformation for single crystal Aluminum and Copper samples subjected to micro-scale laser shock peening. Specifically, the asymmetric and broadened diffraction profiles registered across the shock peen region were observed and analyzed by classic Warren and Averbach (W–A) method [Warren, B.E., Averbach, B.L., 1950. The effect of cold-work distortion on X-ray patterns. Journal of Applied Physics 21, 595–599] and modified W–A method [Ungar, T., Borbely, A., 1996. The effect of dislocation contrast on X-ray line broadening: A new approach to line profile analysis. Applied Physics Letters 69, 3173–3175]. Average strain deviation, mosaic size and dislocation density were estimated for the first time with a spatial resolution of 5 μm. The results compare well with the simulation results obtained from FEM analysis and from electron backscatter diffraction (EBSD) measurements. Differences in response caused by different materials and crystalline orientations (1 1 0 and 0 0 1) were also studied.     

Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow

The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1–36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253–277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.     

Nonisothermal analysis of extrusion film casting process using molecular constitutive equations

Extrusion film casting (EFC) is a commercially important process that is used to produce several thousand tons of polymer films and coatings. In a recent work, we demonstrated the influence of polymer chain architecture on the extent of necking in an isothermal film casting operation (Pol et al., J Rheol 57:559–583, 2013). In the present research, we have explored experimentally and theoretically the effects of long-chain branching on the extent of necking during nonisothermal film casting conditions. Polyethylenes of linear and long-chain branched architectures were used for experimental studies. The EFC process was analyzed using the 1-D flow model of Silagy et al. (Polym Eng Sci 36:2614–2625, 1996) in which the energy equation was introduced to model nonisothermal effects, and two multimode constitutive equations, namely the “extended pom-pom” (XPP, for long-chain branched polymer melts) equation and the “Rolie-Poly stretch version” (RP-S, for linear polymer melts) equation, were incorporated to account for the effects of polymer chain architecture. We show that the model does a better job of capturing the qualitative features of the experimental data, thereby elucidating the role of chain architecture and nonisothermal conditions on the extent of necking.     

Energy loss at bends in the pneumatic conveying of fly ash

An accurate estimation of the total pressure drop of a pipeline is important to the reliable design of a pneumatic conveying system. The present paper presents results from an investigation into the modelling of the pressure drop at a bend in the pneumatic conveying of fly ash. Seven existing bend models were used (in conjunction with solids friction models for horizontal and vertical straight pipes, and initial acceleration losses) to predict the total pipeline pressure drop in conveying fly ash (median particle diameter: 30 μm; particle density: 2300 kg/m³; loose-poured bulk density: 700 kg/m³) in three test rigs (pipelines with dimensions of 69 mm inner diameter (I.D.) × 168 m length; 105 mm I.D. × 168 m length; 69 mm I.D. × 554 m length). A comparison of the pneumatic conveying characteristics (PCC) predicted using the seven bend models and experimental results shows that the predicted total pipeline PCC and trends depend on the choice of bend model. While some models predict trends that agree with the experimental results, other models predicted greater bend pressure drops for the dense phase of fly ash than for the dilute phase. Models of Pan, R. (1992). Improving scale-up procedures for the design of pneumatic conveying systems. Doctoral dissertation, University of Wollongong, Australia, Pan, R., & Wypych, P.W. (1998). Dilute and dense phase pneumatic conveying of fly ash. In Proceedings of the sixth International Conference on Bulk Materials Storage and Transportation (pp. 183–189), Wollongong, NSW, Australia and Chambers, A.J., & Marcus, R.D. (1986). Pneumatic conveying calculations. In Proceedings of the second International Conference on Bulk Materials Storage and Transportation (pp. 49–52), Wollongong, Australia reliably predicted the bend losses for systems conveying fly ash over a large range of air flows.     

R410A condensation inside a commercial brazed plate heat exchanger

This paper presents the heat transfer coefficients and the pressure drop measured during HFC-410A condensation inside a commercial brazed plate heat exchanger: the effects of saturation temperature, refrigerant mass flux and vapour super-heating are investigated. The heat transfer coefficients show weak sensitivity to saturation temperature and great sensitivity to refrigerant mass flux and vapour super-heating. At low refrigerant mass flux (<20 kg/m² s) the saturated vapour condensation heat transfer coefficients are not dependent on mass flux and are well predicted by Nusselt [W. Nusselt, Die oberflachenkondensation des wasserdampfes, Energy 60 (1916) 541–546, 569–575] analysis for vertical surface: the condensation process is gravity controlled. For higher refrigerant mass flux (>20 kg/m²s) the saturated vapour condensation heat transfer coefficients depend on mass flux and are well predicted by Akers et al. [W.W. Akers, H.A. Deans, O.K. Crosser, Condensing heat transfer within horizontal tubes, Chem. Eng. Prog. Symp. Series 55 (1959) 171–176] equation: forced convection condensation occurs. In the forced convection condensation region the heat transfer coefficients show a 30% increase for a doubling of the refrigerant mass flux. The condensation heat transfer coefficients of super-heated vapour are 8–10% higher than those of saturated vapour and are well predicted by Webb [R.L. Webb, Convective condensation of superheated vapor, ASME J. Heat Transfer 120 (1998) 418–421] model. A simple linear equation based on the kinetic energy per unit volume of the refrigerant flow is proposed for the computation of the frictional pressure drop.     

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B = 10, Re = 13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B = 4, Re = 20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.     

Influence of sudden contractions on in situ volume fractions for oil–water flows in horizontal pipes

Oil–water two-phase flow experiments were conducted in horizontal ducts made of Plexiglas® to determine the in situ oil fraction (holdup) by means of the closing valves technique, using mineral oil (viscosity: 0.838 Pa s at 20 °C; density: 890 kg m⁻³) and tap water. The ducts present sudden contractions from 50 mm to 40 mm i.d. and from 50 mm to 30 mm i.d., with contraction ratios of 0.64 and 0.36, respectively. About 200–320 tests were performed by varying the flow rates of the phases. Flow patterns were investigated for both the up- and downstream pipe in order to assess whether relevant variations of the flow patterns across the sudden contraction take place. Data were then compared with predictions of a specific correlation for oil–water flow and some correlations for gas–water flow. A drift-flux model was also applied to determine the distribution parameter.     

One-dimensional interfacial area transport of vertical upward bubbly flow in narrow rectangular channel

The design and safety analysis for miniature heat exchangers, the cooling system of high performance microelectronics, research nuclear reactors, fusion reactors and the cooling system of the spallation neutron source targets requires the knowledge of the gas–liquid two-phase flow in a narrow rectangular channel. In this study, flow measurements of vertical upward air–water flows in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm were performed at seven axial locations by using the imaging processing technique. The local frictional pressure loss gradients were also measured by a differential pressure cell. In the experiment, the superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. The developing two-phase flow was characterized by the significant axial changes of the local flow parameters due to the bubble coalescence and breakup in the tested flow conditions. The existing two-phase frictional multiplier correlations such as Chisholm, 1967, Mishima et al., 1993 and Lee and Lee (2001) were verified to give a good prediction for the measured two-phase frictional multiplier. The predictions of the drift-flux model with the rectangular channel distribution parameter correlation of Ishii (1977) and several existing drift velocity correlations of Ishii, 1977, Hibiki and Ishii, 2003 and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities. The interfacial area concentration (IAC) model of Hibiki and Ishii (2002) was modified by taking the channel width as the system length scale and the modified IAC model could predict the IAC and Sauter mean diameter acceptably.     

Large Eddy Simulations of turbulent particle-laden channel flow

This paper scrutinises the Large Eddy Simulation (LES) approach to simulate the behaviour of inter-acting particles in a turbulent channel flow. A series of simulations that are fully (four-way), two-way and one-way coupled are performed in order to investigate the importance of the individual physical phenomena occurring in particle-laden flows. Moreover, the soft sphere and hard sphere models, which describe the interaction between colliding particles, are compared with each other and the drawbacks and advantages of each algorithm are discussed. Different models to describe the sub-grid scale stresses with LES are compared. Finally, simulations accounting for the rough walls of the channel are compared to simulations with smooth walls. The results of the simulations are discussed with the aid of the experimental data of Kussin J. and Sommerfeld M., 2002, Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. in Fluids, 33, pp. 143–159 of Reynolds number 42,000 based on the full channel height. The simulations are carried out in a three-dimensional domain of 0.175 m × 0.035 m  × 0.035 m where the direction of gravity is perpendicular to the flow. The simulation results demonstrate that rough walls and inter-particle collisions have an important effect in redistributing the particles across the channel, even for very dilute flows. A new roughness model is proposed which takes into account the fact that a collision in the soft sphere model is fully resolved and it is shown that the new model is in very good agreement with the available experimental data.     

Effect of temperature on the effective thermal conductivity of n-tetradecane-based nanofluids containing copper nanoparticles

Nanofluids were prepared by dispersing Cu nanoparticles (∼20 nm) in n-tetradecane by a two-step method. The effective thermal conductivity was measured for various nanoparticle volume fractions (0.0001–0.02) and temperatures (306.22–452.66 K). The experimental data compares well with the Jang and Choi model. The thermal conductivity enhancement was lower above 391.06 K than for that between 306.22 and 360.77 K. The interfacial thermal resistance increased with increasing temperature. The effective thermal conductivity enhancement was greater than that obtained with a more viscous fluid as the base media at 452.66 K because of nanoconvection induced by nanoparticle Brownian motion at high temperature.     

Modeling and optimization of the parameters affecting the in-situ microencapsulation process for producing epoxy-based self-healing anti-corrosion coatings

Micro/nanocapsules of urea–formaldehyde resin loaded with linseed oil, which are a self-healing agent in glass flake epoxy anti-corrosion paint, were prepared using a combination of ultrasonic homogenization and in-situ polymerization. The main objective of this study was to model and optimize the microencapsulation process. Five-level central composite design was used to design, model, and optimize the microencapsulation process. A quadratic model was constructed to show the dependency of the percentage of encapsulated linseed oil and capsule size, as model responses, on the studied independent variables (the rotational speed of the agitator and the power and duration of sonication). Analysis of variance showed that all of the variables have significant effects on the encapsulated linseed oil percentage, while the rotational speed of the agitator and sonication time is effective variables for controlling the capsule size. Under the determined optimum conditions, a maximum encapsulated linseed oil percentage (ELO%) of 93.9% and a minimum micro/nanocapsule size of 0.574 μm were achieved at 594 rpm agitation, 350 W sonication power, and 3 min sonication time. Validation of the model was performed. The percentage relative errors between the predicted and experimental values of the ELO% and micro/nanocapsule size are 1.28% and 3.66%, respectively. The efficacy of the optimum micro/nanocapsules in healing cracks in a glass flake epoxy paint and corrosion protection was investigated by the salt spray test and Tafel polarization technique.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

Isochoric heating of reduced mass targets by ultra-intense laser produced relativistic electrons

We present measurements of the chlorine K-alpha emission from reduced mass targets, irradiated with ultra-high intensity laser pulses. Chlorinated plastic targets with diameters down to 50 μm and mass of a few 10^?8 g were irradiated with up to 7 J of laser energy focused to intensities of several 10¹⁹ W/cm². The conversion of laser energy to K-alpha radiation is measured, and high-resolution spectra that allow observation of line shifts are observed, indicating isochoric heating of the target up to 18 eV. A zero-dimensional 2-temperature equilibration model, combined with electron impact K-shell ionization and post processed spectra from collisional radiative calculations reproduces the observed K-alpha yields and line shifts, and shows the importance of target expansion due to the hot electron pressure.     

The frequency response of dynamic friction: Enhanced rate-and-state models

The prediction and control of friction-induced vibration requires a sufficiently accurate constitutive law for dynamic friction at the sliding interface: for linearised stability analysis, this requirement takes the form of a frictional frequency response function. Systematic measurements of this frictional frequency response function are presented for small samples of nylon and polycarbonate sliding against a glass disc. Previous efforts to explain such measurements from a theoretical model have failed, but an enhanced rate-and-state model is presented which is shown to match the measurements remarkably well. The tested parameter space covers a range of normal forces (10–50 N), of sliding speeds (1–10 mm/s) and frequencies (100–2000 Hz). The key new ingredient in the model is the inclusion of contact stiffness to take into account elastic deformations near the interface. A systematic methodology is presented to discriminate among possible variants of the model, and then to identify the model parameter values.