A numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures

The present work is dedicated to a numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures. The main objective consists in checking out the link between percolation and mechanical response in the context of a heterogeneous medium the reinforcements of which are not homogeneously dispersed. Besides, the influence of the stiffness of inclusions is also investigated since this could impact on the percolation effects. For these purposes, large samples of volume elements are generated according to the Monte Carlo method. We consider the low cost framework of 2D random grids which enables large and in-depth investigations. Besides, the spatial distribution of heterogeneities is simulated with the help of the 2-scale Boolean scheme of disks which is a powerful tool for modelling and studying several states of dispersion. The numerical results highlight beneficial mechanical reinforcements for a heterogeneous dispersion when the percolation phenomenon is enhanced. This improvement is highly sensitive to the stiffness of heterogeneities.     

Characterisation of different types of dispersoids present in homogenised Al–4·5Zn–1Mg alloy containing Zr,Cr and Mn

Abstract

In the present paper, various types of dispersoids possibly formed during homogenisation of AA7020 alloy containing Cr, Zr and Mn are described. It shows that, in addition to the Zr containing dispersoids, three other types of dispersoids may be present in the homogenised microstructure of AA7020 aluminium alloy. These dispersoids are Cr and Mn containing ones and the one with a mixture of different elements. The Zr and Cr containing dispersoids are formed in the grain interior at all of the homogenisation conditions. However, the Mn containing ones form only in the grain boundary regions in the vicinity of Al₁₇(Fe_3·2,Mn_0·8)Si₂ particles at temperatures ?510°C and holding times longer than 4 h.     

Expression for turbulent power draw of an in-line Silverson high shear mixer

We report the validation of an expression to accurately describe the power draw of an in-line rotor–stator mixer over a range of flow rates and rotor speeds. The expression consists of a term which reflects the power required to rotate the shaft in response to the liquid resistance and a term to reflect the power convected away from the mixing chamber. A specially commissioned high speed (12,000 rpm), instrumented 150/250 MS Silverson mixer has been developed with power draw determined from both torque and calorimetric measurements. Experiments are carried out using water over a range of independently controlled flow rates and rotor speeds with losses for both techniques carefully accounted for. For the torque measurement the value of the constants for the two terms above are Po_z=0.197 and k₁=9.35, respectively. For the calorimetric technique the measured temperature rise was similar to some of the corrections and losses over a significant range of the experimental space but nevertheless with careful experimentation constants similar to those for the torque technique were obtained, Po_z=0.229 and k₁=7.46. Allowing the calibration of the temperature probes to be a fit parameter in the regression routine increased the value of k₁=8.10 but did not affect the value of Po_z. A simple graphical method is also proposed using a dimensionless form of the expression which yielded slightly higher value of Po_z but a slightly lower value of k₁. The accuracy of both measurement techniques improves with rotor speed and the differences between the constants is attributed to the better accuracy of the torque technique at higher flow rates whereas the calorimetric technique is more accurate at low flow rates where the temperature rise is larger. Several repeats of the calorimetric technique with a reduced set of experimental points show good reproducibility. Finally at low flow rates (<10% of the maximum) the power unexpectantly increases and a modification to the expression is proposed by considering the pumping efficiency.     

Effect of heat treatments and homogenisation pressure on the acid gelation properties of recombined whole milk

The homogenisation pressure and the order of heating and homogenisation were varied in the preparation of recombined whole milks. The fat globule sizes decreased from ∼2 to 0.2 μm as the homogenisation pressure increased from 50 to 850 bar for samples heated before (HEHO) or after (HOHE) homogenisation. For acid gels prepared from the milks, small increases in elastic modulus of the set gels were observed with decreasing fat globule size. The yield strain of the acid gels increased linearly with decreasing fat globule size, and HOHE gels had higher yield strains than HEHO gels. The yield stress of the set gels increased with decreasing fat globule size, and the yield stress for HOHE gels were higher than the HEHO gels. Confocal micrographs of the gels revealed an almost continuous protein network structure without pores for gels from milks treated at low homogenisation pressures, and the large fat globules did not actively interact with the strands in the gel network. In contrast, a porous protein network structure with distinct strands was observed for the samples treated at high homogenisation pressures, and the small fat globules were intimately involved in the strands in the network structure. The HOHE gels had a more porous protein network with thicker strands than the HEHO gels. The size of the fat globules and their incorporation in the protein network during acidification is proposed to affect the acid gel structure and properties.     

Effects of homogenisation pressures on physicochemical changes in different layers of ultra‐high temperature whole milk during storage

The objective of this study was to investigate the effects of homogenisation pressures (10, 20, and 30 MPa) on the physicochemical changes in top, middle and bottom layers of ultra‐high temperature whole milk stored at 25 °C for 6 months. Fat separation, fat globule sizes, fat and protein contents, viscosity, free amino acids content and pH were analysed at an interval of 15 days. Results showed that higher homogenisation pressure retarded the differentiations of milk fat globule sizes, fat and protein contents and viscosity in different milk layers, but did not affect the final fat separation, proteolysis and pH.     

Investigation of sandwich structures with innovative cellular metallic cores under low velocity impact loading

Abstract

Sandwich panels are widely used for energy absorbing applications in cases of low and high velocity impacts. The core itself is capable of absorbing energy by progressive collapse, while the skins are necessary for uniformly distributing the local vertical load over the impacted area as well as for the introduction of overall panel bending resistance. In the present work, the failure response of sandwich panels with open lattice cellular cores subjected to low velocity impact is investigated. Experimental tests are performed using a mass drop testing machine. Additionally, a three-dimensional finite element model of the sandwich panels–impactor system is developed using commercial Finite Element (FE) codes. The core homogenisation is introduced in order to improve the efficiency of the FE analysis by reducing the computational time. Numerical results correlate well with experimental data, enabling detailed understanding of the parameters affecting the initiation and propagation of impact damage.     

Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations

Gas hold-up, mixing intensity of dispersion characterised by exchange flows between adjacent impellers and a volumetric mass transfer coefficient are presented for 18 impeller configurations in triple-impeller vessel of inner diameter . Rushton Turbines, six Pitched Blade impellers pumping down and hydrofoil impellers Techmix 335 (Techmix co., Czech republic) pumping up or down and their combinations were used. aqueous solution was used as a liquid phase, which represents non-coalescent batches. Gas hold-ups and volumetric mass transfer coefficients are presented for individual configurations as functions of specific power dissipated and superficial gas velocity. The regression of the mass transfer coefficients shows large standard deviation (30%). The power number included to the regression to express the impeller configuration effect did not improve the standard deviation significantly (23%). The impeller configurations with low power number (less than unity) provide higher dispersion mixing intensities, while the impeller configurations with high power number provide better mass transfer performance.     

Dynamics of diffusion with reversible binding in microscopically heterogeneous membranes: General theory and applications to dermal penetration

Essentially all biological membranes and tissues exhibit microscopic heterogeneity in the form of cellular, lamellar or other organization, and molecular diffusion in these materials is frequently slowed by binding to elements of the microstructure (“trapping”). This paper addresses situations where binding is describable as a linear reversible process at the microscale, with forward (“on”) and reverse (“off”) rate constants k_f(x) and k_r(x) that vary with position. Very commonly it is tacitly assumed that the macroscopically observable binding behavior should follow the same rate law with the substitution of appropriate effective (tissue-average) rate constants and . This assumption is probed theoretically for spatially periodic microstructures using a judicious application of numerical calculations and asymptotic analysis to prototypical one-dimensional transport problems. We find that smooth microscopic variations produce an anomalous macroscopic exchange between free and bound solute populations that is not well described by a single pair of forward and reverse rate constants, i.e., violates the usual paradigm. In contrast, discontinuous variations (as in two-phase composite media) are evidently well described by the usual paradigm. For the latter case we derive simple and general algebraic equations giving and , and generalize them to any three-dimensional unit cell representing the tissue microstructure. Validity of the formulas is demonstrated with reference to a concrete example describing molecular diffusion through the stratum corneum (barrier) layer of skin, comprising lipid (intercellular) and corneocyte (cellular) phases. Our analysis extends coarse-graining (homogenization, effective transport) theory for irreversible trapping systems to the reversible case.     

Homogenisation with application to layered materials

In this paper we are concerned with the elliptic PDEs with highly oscillating coefficients which model the behaviour of composite linear elastic materials. Analytical expressions for the effective coefficients are obtained for the case of layered materials using the theory of homogenisation. Some properties of the homogenised materials are analysed. An efficient algorithm for the numerical determination of the effective coefficients is proposed.     

Mechanical simulation of a Proton Exchange Membrane Fuel Cell stack using representative elementary volumes of stamped metallic bipolar plates

The control of the performance of a fuel cell needs the knowledge of mechanical stresses. A finite element model submitted to operational static loads is developed for pure mechanical analysis of a stack. Adapted to practical implementation in the frame of industrial projects, the tool runs on work stations. Modelling and simulations at the early stage of the stack architecture development are mandatory to lower the costs of the stack and to contribute in designing component dimensions and forms, particularly of stamped metallic bipolar plates or clamping systems. The model should also be useful for accurate local analyses and channel geometry of metallic bipolar plates must be modelled in detail. But the number of degrees of freedom is huge and some model simplification is required to compute a whole stack. The homogenisation technique was applied, replacing cell parts with composite finite elements or homogenised representative elementary volumes.