A two dimensional, experimental study on the evolution of the detachment and its time-behavior in filled rubber

Summary The detachment of a rubber matrix from a rigid inclusion under monotonic loading and at subsequent relaxation is investigated within two dimensional analysis. Examined are stress–strain experimental data acquired with the help of a test bed equipped with a digital image-acquisition device. The influence of the interfacial bonding strength and the particle size on the detachment process is analyzed. The influence of the interfacial bonding strength is visible in the stress–strain diagram of loading and in the recorded images. The relaxation test reveals no influence of the bonding strength on the stress-relaxation. However, the image analysis indicates a secondary transient creep of the contour of detachment, which depends on the interfacial bonding.     

Peculiarities of rheological behavior of filled polymer melts in uniaxial stretching

The peculiarities of theological behavior of filled polymer melts in uniaxial extension in a wide range of strain rates (from 2× 10^–5 to 1 × 10^–1 s^–1) have been studied. Linear polyethylene and 1,4-polybutadiene containing up to 21.5 vol.% of carbon black, silica, calcium carbonate or glass fibers were used. It has been found that the transition from uniform to nonunion stretching due to the neck formation is typical of all specimen compositions, when they approach steady-state straining. Depending on the structure and rheological characteristics of the compositions general conditions for this transition have been established. The general regularities for varying the rheological characteristics of filled polymers in the course of their uniform stretching have been recognized. These regularities depend on the molecular characteristics of the polymer matrix and the presence in the compositions of the structural framework of high disperse filler or the network formed by the entangled fibers. Using polyethylene compositions it has been shown that the introduction of small amounts of disperse or fibrous fillers can give rise to acceleration of the relaxation process in filled polymers.     

Finite viscoelasticity of filled rubber: experiments and numerical simulation

Summary  Constitutive equations are derived for the viscoelastic behavior of particle-re-inforced elastomers at isothermal deformation with finite strain. A filled rubber is thought of as a composite medium where inclusions with high and low concentrations of junctions between chains are randomly distributed in the bulk material. The characteristic length of the inhomogeneities is assumed to be small compared to the size of the specimen and substantially exceed the radius of gyration for macromolecules. Inclusions with high concentration of junctions are associated with regions of suppressed mobility of chains that surround isolated clusters and/or the secondary network of filler. Regions with low concentration of junctions arise during the preparation process due to a heterogeneity in the spatial distribution of the cross-linker and the filler. With reference to the concept of transient networks, the time-dependent response of an elastomer is attribute d to thermally activated rearrangement of strands in the domains with low concentration of junctions. Stress–strain relations for particle-reinforced rubber are developed by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data in tensile relaxation tests for several grades of unfilled and carbon black-filled rubber. It is demonstrated that even at moderate finite deformations (with axial elongations up to 100%), the characteristic rate of relaxation is noticeably affected by strain. Unlike glassy polymers, where the rate of relaxation increases with longitudinal strain, the growth of the elongation ratio results in a decrease in the relaxation rate for natural rubber (unfilled or particle-reinforced). The latter may be explained by (partial) crystallization of chains in the regions with low concentration of junctions. Received 16 October 2001; accepted for publication 25 June 2002 Present address: A. D. Drozdov Department of Production, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg, Denmark We would like to express our gratitude to Dr. K. Fuller (TARRC, UK) for providing us with rubber specimens and to Prof. P. Haupt and Dr. S. Hartmann (University of Kassel, Germany) for sending their experimental data. We are indebted to Mr. G. Seifritz for his assistance in performing mechanical tests. ADD acknowledges stimulating discussions with Prof. N. Aksel (University of Bayreuth, Germany).     

Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model

A phenomenological uniaxial model is derived for implementation in the time domain, which captures the amplitude and frequency dependency of filled elastomers. Motivated by the experimental observation that the frequency dependency is stronger for smaller strain amplitudes than for large ones, a novel material model is presented. It utilizes a split of deformation between a generalized Maxwell chain in series with a bounding surface plasticity model with a vanishing elastic region. Many attempts to capture the behaviour of filled elastomers are found in the literature, which often utilize an additive split between an elastic and a history dependent element, in parallel. Even though some models capture the storage and loss modulus during sinusoidal excitations, they often fail to do so for more complex load histories. Simulations with the derived model are compared to measurements in simple shear on a compound of carbon black filled natural rubber used in driveline isolators in the heavy truck industry. The storage and loss modulus from simulations agree very well with measurements, using only 7 material parameters to capture 2 decades of strain (0.5–50% shear strain) and frequency (0.2–20 Hz). More importantly, with material parameters extracted from the measured storage and loss modulus, measurements of a dual sine excitation are well replicated. This enables realistic operating conditions to be simulated early in the development process, before an actual prototype is available for testing, since the loads in real life operating conditions frequently are a combination of many harmonics.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

The Potential of MEMS for Advancing Experiments and Modeling in Cell Mechanics

Response to mechanical stimuli largely dictates cellular form and function. A host of extraordinary yet unexplained responses have been identified within the hierarchical cell structure. As experimental and model-based investigations in cell mechanics advance, the underlying structure-function mechanisms dictating these responses emerge. Here we explore the potential of microelectromechanical systems (MEMS) for advancing understanding of cell mechanics. To motivate the discussion, existing experimental techniques are summarized. Interrelated model-based approaches, which aim to interpret or predict observed results, are also outlined. We then focus on a representative set of MEMS-based devices designed for investigations in cell mechanics and point to the fact that, while these devices have yet to maximize their functionality through higher levels of sensor/actuator integration, they are highly complementary to existing techniques. In closing, novel MEMS sensor and actuator schemes that have yet to materialize in this field are discussed to motivate the next generation of MEMS for investigations in cell mechanics.     

Modeling of bubble detachment in reduced gravity under the influence of electric fields and experimental verification

A simple model for predicting bubble volume and shape at detachment in reduced gravity under the influence of electric fields is described in the paper. The model is based on relatively simple thermodynamic arguments and relies on and combines several models described in the literature. It accounts for the level of gravity and the magnitude of the electric field. For certain conditions of bubble development the properties of the bubble source are also considered. Computations were carried out for a uniform unperturbed electric field for a range of model parameters, and the significance of model assumptions and simplifications is discussed for the particular method of bubble formation. Experiments were conducted in terrestrial conditions and reduced gravity (during parabolic flights in NASAs KC-135 aircraft) by injecting air bubbles through an orifice into the electrically insulating working fluid, PF5052. Bubble shapes visualized experimentally were compared with model predictions. Measured data and model predictions show good agreement. The results suggest that the model can provide quick engineering estimates concerning bubble formation for a range of conditions (both for formation at an orifice and boiling) and such a model reduces the need for complex and expensive numerical simulations for certain applications. a Major axis of spheroid (m) - a _m Measured bubble height (m) - b Minor axis of spheroid (m) - b _m Measured bubble width (m) - A, B, C, F Parameters of the Kumar-Kuloor model - a/b Computed aspect ratio - a _m /b _m Measured aspect ratio - D Orifice diameter (m) - E Magnitude of the electric field (V/m) - g Gravitational acceleration (m/s²) - g _t Terrestrial gravity (g _t = 9.81 m/s²) - N _w Electrical Weber number - p Pressure (Pa) - Q Volume flow rate (m³/s) - r Radius of the spherical bubble (m) - R Radius of curvature at the tip of the bubble (m) - t Time (s) - t Time interval (s) - T Temperature (°C) - U Electrical potential (V) - u Velocity (m/s) - V Volume (m³) - x, y Dimensionless coordinates of the Cartesian coordinate system - x, y Scaled coordinates, Cheng-Chaddock model - X, Y Dimensional coordinates of the Cartesian coordinate system - Characteristic wave number (m^–1) - Eötvös number - Absolute dielectric permittivity (F/m) - Contact angle (deg.) - Gibbs free energy (J) - Surface tension (N/m) - Dynamic viscosity (Pa s) - Density (kg/m³) - cr Critical value - d Detachment - eq Equilibrium - g Gas - K Refers to the Kumar-Kuloor model - l Liquid - m Measured value - t Terrestrial     

Viscoelastic properties of pig kidney in shear, experimental results and modelling

 In this paper, the results from a series of rheological tests of fresh pig kidney have been reported. Using a standard strain-controlled rheometer, the oscillation strain sweep experiment showed a linear viscoelastic strain limit of the order of 0.2% strain. To determine the components of dynamic moduli in terms of frequency, shear oscillation tests were done at strain 0.2% using a stress-controlled rheometer. Shear stress relaxation tests were carried out with a fixed strain of 0.2% and 0.02 s rise time. The model we have developed uses a multi-mode upper convected Maxwell (UCM) model with variable viscosities and time constants, to which we have added a Mooney hyper-elastic response, both multiplied by a damping function. Different forms of damping functions that control the non-linearity of strain-stress profile have been tested. The model was fitted to our experimental data, and matched the entire test data reasonably well with a single set of parameters. Received: 5 May 2000 Accepted: 16 March 2001     

Investigation of tensile deformation behavior of PC,ABS, and PC/ABS blends from low to high strain rates

This paper experimentally studies the tensile deformation behavior of polycarbonate (PC), acrylonitrile-butadiene-styrene (ABS), and PC/ABS blends (with the blending ratios of PC to ABS being 80:20, 60:40, 50:50, and 40:60) from low to high strain rates. Using the universal MTS-810 machine and the split Hopkinson tension bar (SHTB) testing system, the quasi-static and impact tension tests are carried out at the room temperature. The curves of the true stress and the true strain are obtained. The deformation behaviors of PC, ABS, and PC/ABS blends are characterized in detail. The linear relationship between the strain rate and the yielding stress is given.     

Enhanced conduction in steady,vertical flows of water,steam and carbon dioxide in a porous medium

Transport in Porous Media - The steady, vertical transport of water, energy and carbon dioxide in a two-phase porous medium is analysed when capillarity can be ignored. Such flows are possible only...     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

Reducible properties of draw temperature,rate of strain and filler content in tensile yield stress of polymethylmethacrylate filled with ultrafine particles

The yield stress of polymethylmethacrylate (PMMA) composites filled with ultrafine SiO₂ particles was measured as a function of the draw temperature, rate of strain and filler content. The yield stress of the composites increased with increasing filler content and decreasing filler size. The tensile yield stress was found to be reducible with regard to draw temperature, rate of strain and filler content. At a given filler content, a master curve was obtained for the yield stress plotted versus the logarithm of the strain rate. The Arrhenius plot of the shift factors (a _T ) used to produce the strain rate-temperature master curve formed a single curve for all sizes and loadings of the filler. The master curves obtained for different loadings of a filler of given size could be further reduced into a master-master curve by shifting them along the axis of strain rate, with the logarithm of the second shift factors (loga _c ) proportional to the 4/5th power of the filler volume fraction (V _f ). The proportionality constant and the exponent represent the extent of the filler reinforcing effect in the polymer. These values were found to be correlated with the critical surface tension of the polymers.     

Modeling and Analysis of Seawater Intrusion in the Coastal Aquifer of Eastern Cap-Bon, Tunisia

A numerical model that treats density-dependent variably saturated flow and miscible salt transport is used to investigate the occurrence of seawater intrusion in the Korba aquifer of the eastern coast of Cap-Bon in northern Tunisia. We examine the interplay between pumping regimes and recharge scenarios and its effect on the saline water distribution. More localized simulations are used to examine, in vertical cross sections, the effects of well location and soil type and the role of the vadose zone in possible remediation actions. The exploratory simulations suggest interesting interactions between the unsaturated zone and the saltwater–freshwater interface with possible implications for groundwater exploitation from shallow unconfined coastal aquifers, involving in one case feedback between seawater intrusion and the high pressure head gradients around the pumping-induced drawdown cone and in another case threshold-like interface displacement for tight soils such as clays. The data processing steps undertaken in this GIS and modeling study are described in some detail, and a critical assessment is given of the data availability and of the requirements for successful monitoring and modeling of seawater intrusion risks in heavily exploited coastal aquifers such as those found in the semi-arid regions of the Mediterranean basin. It is shown how, with the aid of GIS, reasonably reliable information can be assembled from maps, surveys, and other sources of geospatial and hydrogeological data, an approach that is necessary in the many regions of the world with acute water resource problems but with limited means for undertaking systematic data acquisition and environmental monitoring actions. Nonetheless the need for more concerted monitoring of relevant parameters and processes and of closer coordination between monitoring and modeling is stressed. An idea of the extent of over-exploitation of the Korba aquifer is obtained by examining the pumping and rainfall/infiltration data, and the simulation results support groundwater pumping as the mechanism for and seawater intrusion as the origin of the salt contamination observed in the soils and subsurface waters of the Korba plain.     

Investigation of the band texture occurring in hydroxypropylcellulose solutions using rheo-optical, rheological and small angle light scattering techniques

The band texture occurs in lyotropic and thermotropic main-chain polymers after cessation of flow. This paper begins with a review of work concerned with band texture formation following shear and is followed by the presentation of original results obtained during a recent investigation. The evolution of band texture formation in a Klucel EF, 50% hydroxypropylcellulose (HPC) water solution, has been observed using polarized optical microscopy. The relationship determined between the primary shear rate and the rate of evolution of the band texture is complex and three different behaviours have been observed corresponding to three shear rate regions. Both steady flow and dynamic rheological investigations have been conducted on the HPC solution, the results of which have been related to the optical behaviour of the band texture. Data from steady flow investigations suggest that the viscosity of the solution when the band texture is present, decreases following increasing primary shear rates, is shear thinning and increases linearly with the time following its formation. Dynamic investigations suggest a definite link between the band texture evolution and the evolution of both G′ and G′′. In addition, the perfection of the band texture versus the primary shear rate has been quantified by studying the evolution of tan(δ) following the cessation of the primary shear. Dynamic experiments show that the structure of the band texture remains longer than suggested by the optical aspect of the texture. Small angle light scattering patterns have been correlated with the development of the band texture and confirm the continuing presence of the band texture structure following its optical disappearance. Received: 2 March 1999/Accepted: 26 July 1999     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

Investigation of the band texture occurring in acetoxypropylcellulose thermotropic liquid crystalline polymer using rheo-optical, rheological and light scattering techniques

The optical evolution of the band texture occurring in acetoxypropylcellulose thermotropic polymer has been investigated as a function of temperature and primary shear rate. Two distinct kinds of band texture were observed which are referred to here as the `fast' and `slow' band textures with regard to their rate of evolution. The fast band texture appears very quickly following the cessation of shear and then disappears. The slow band texture is much finer than the fast band texture and appears to exist both during and after the appearance of the fast band texture. The evolution behaviour of the fast band texture is interpreted in terms of the shifting of a three-region evolution curve. Particular attention has been paid to investigating the influence of temperature on the formation of the fast band texture. Rheo-optical experiments show that the minimum shear rate required to form the fast band texture increases as a power-law function of the temperature. By subsequently performing steady flow measurements over a range of temperatures, the minimum shear stress required to form the fast band texture has been found to be independent of temperature and to increase linearly with the molecular weight of the sample. Results obtained from dynamic tests are compared with similar tests conducted previously on a lyotropic hydroxypropylcellulose water solution (Harrison and Navard 1999). The results of the comparison provide evidence in support of a connection between the behaviour of the dynamic functions and the optical evolution of the slow band texture. These results suggest that nematic and cholesteric fluids can relax through several different possible mechanisms, each of which results in a periodic band texture following the cessation of shear. Received: 2 March 1999/Accepted: 26 July 1999     

Existence, uniqueness and stability of steady flows of second and third grade fluids in an unbounded “pipe-like” domain

We study steady motions of viscous incompressible third-grade fluids in unbounded channels with arbitrary shape. Such flows exist for small fluxes, due to a pressure drop. We prove that they are asymptotically stable in time, provided the viscosity is sufficiently large, and the initial condition on the perturbation sufficiently small.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 2. Flows with heat transfer and combustion

The objective of this part of the paper is to summarize the information concerning the authors' works in the field of simulation of two-phase gas-particle turbulent flows with heat transfer and combustion. A kinetic equation had been derived for the probability density function (PDF) of the particle velocity, temperature, and mass distributions in turbulent flows. This PDF equation is used for the construction of the governing conservation equations of mass, momentum, and heat transfer in the dispersed particle phase.The numerical scheme incorporates two-phase fluid dynamics, convective and radiative heat transfer, and combustion. The proposed models have been applied to the calculation of various particle-laden turbulent flows in jets, combustion and gasification chambers, and furnaces.     

Modeling of Liquid Fuel Injection, Evaporation and Mixing in a Gas Turbine Burner Using Large Eddy Simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described. This revised version was published online in July 2006 with corrections to the Cover Date.