The interchain pressure effect in shear rheology

Recently, the tube diameter relaxation time in the evolution equation of the molecular stress function (MSF) model (Wagner et al., J Rheol 49: 1317–1327, 2005) with the interchain pressure effect (Marrucci and Ianniruberto, Macromolecules 37:3934–3942, 2004) included was shown to be equal to three times the Rouse time in the limit of small chain stretch. From this result, an advanced version of the MSF model was proposed, allowing modeling of the transient and steady-state elongational viscosity data of monodisperse polystyrene melts without using any nonlinear parameter, i.e., solely based on the linear viscoelastic characterization of the melts (Wagner and Rolón-Garrido 2009a, b). In this work, the same approach is extended to model experimental data in shear flow. The shear viscosity of two polybutadiene solutions (Ravindranath and Wang, J Rheol 52(3):681–695, 2008), of four styrene-butadiene random copolymer melts (Boukany et al., J Rheol 53(3):617–629, 2009), and of four polyisoprene melts (Auhl et al., J Rheol 52(3):801–835, 2008) as well as the shear viscosity and the first and second normal stress differences of a polystyrene melt (Schweizer et al., J Rheol 48(6):1345–1363, 2004), are analyzed. The capability of the MSF model with the interchain pressure effect included in the evolution equation of the chain stretch to model shear rheology on the basis of linear viscoelastic data alone is confirmed.     

A constrained theory for single crystal shape memory wires with application to restrained recovery

The theory of thin wires developed in Dret and Meunier (Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 337:143–147, 2003) is adapted to phase-transforming materials with large elastic moduli in the sense discussed in James and Rizzoni (J Elast 59:399–436, 2000). The result is a one-dimensional constitutive model for shape memory wires, characterized by a small number of material constants. The model is used to analyze self-accommodated and detwinned microstructures and to study superelasticity. It also turns out that the model successfully reproduces the behavior of shape memory wires in experiments of restrained recovery (Tsoi et al. in Mater Sci Eng A 368:299–310, 2004; Tsoi in 50:3535–3544, 2002; S̆ittner et al. in Mater Sci Eng A 286:298–311, 2000; vokoun in Smart Mater Struct 12:680–685, 2003; Zheng and Cui in Intermetallics 12:1305–1309, 2004; Zheng et al. in J Mater Sci Technol 20(4):390–394, 2004). In particular, the model is able to predict the shift to higher transformation temperatures on heating. The model also captures the effect of prestraining on the evolution of the recovery stress and of the martensite volume fraction.     

Transient rheological responses in sheared biaxial liquid crystals

We study the rheological response of monodomain ellipsoidal biaxial liquid crystal polymers (BLCP) as well as bent-core or V-shaped liquid crystal polymers (VLCP) subject to steady and time-dependent small amplitude oscillatory shear in selected regions of the model as well as flow parameter space. We adopt the two newly developed hydrodynamical kinetic theories for ellipsoidal BLCPs and VLCPs, respectively (Sircar and Wang, PRE 78:061702, 2008, J Rheol 53:819–858, 2009; Sircar et al., Comm Math Sci (in press), 2010), in which a generalized Straley’s potential is used to represent the pairwise mean-field interaction of the mesoscopic system in biaxial phases. Transient shear stresses and normal stress differences corresponding to steady and small amplitude oscillatory shear are investigated; their variations with respect to the strength of the intermolecular potential, types of biaxial interaction, and changes in the aspect ratios for ellipsoidal BLCPs and the bent angle for VLCPs are explored.     

On Entropy Flux of Transversely Isotropic Elastic Bodies

Recently (Liu in J. Elast. 90:259–270, 2008) thermodynamic theory of elastic (and viscoelastic) material bodies has been analyzed based on the general entropy inequality. It is proved that for isotropic elastic materials, the results are identical to the classical results based on the Clausius-Duhem inequality (Coleman and Noll in Arch. Ration. Mech. Anal. 13:167–178, 1963), for which one of the basic assumptions is that the entropy flux is defined as the heat flux divided by the absolute temperature. For anisotropic elastic materials in general, this classical entropy flux relation has not been proved in the new thermodynamic theory. In this note, as a supplement of the theory presented in (Liu in J. Elast. 90:259–270, 2008), it will be proved that the classical entropy flux relation need not be valid in general, by considering a transversely isotropic elastic material body.      

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.     

Statistically Steady Incompressible DNS to Validate a New Correlation for Turbulent Burning Velocity in Turbulent Premixed Combustion

Incompressible 3-D DNS is performed in non-decaying turbulence with single step chemistry to validate a new analytical expression for turbulent burning velocity. The proposed expression is given as a sum of laminar and turbulent contributions, the latter of which is given as a product of turbulent diffusivity in unburned gas and inverse scale of wrinkling at the leading edge. The bending behavior of U _T at higher u′ was successfully reproduced by the proposed expression. It is due to decrease in the inverse scale of wrinkling at the leading edge, which is related with an asymmetric profile of FSD with increasing u′. Good agreement is achieved between the analytical expression and the turbulent burning velocities from DNS throughout the wrinkled, corrugated and thin reaction zone regimes. Results show consistent behavior with most experimental correlations in literature including those by Bradley et al. (Philos Trans R Soc Lond A 338:359–387, 1992), Peters (J Fluid Mech 384:107–132, 1999) and Lipatnikov et al. (Progr Energ Combust Sci 28:1–74, 2002).     

Asymptotic Behavior of Structures Made of Straight Rods

This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness 2δ when δ tends to 0. This analysis relies on the decomposition of the large deformation of a single rod introduced in Blanchard and Griso (Anal. Appl. 7(1):21–71, 2009) and on the extension of this technique to a multi-structure. We characterize the asymptotic behavior of the infimum of the total elastic energy as the minimum of a limit functional for an energy of order δ ^β (2<β≤4).     

Structural Optimization of Thin Elastic Plates: The Three Dimensional Approach

The natural way to find the most compliant design of an elastic plate is to consider the three-dimensional elastic structures which minimize the work of the loading term, and pass to the limit when the thickness of the design region tends to zero. In this paper, we study the asymptotics of such a compliance problem, imposing that the volume fraction remains fixed. No additional topological constraint is assumed on the admissible configurations. We determine the limit problem in different equivalent formulations, and we provide a system of necessary and sufficient optimality conditions. These results were announced in Bouchitté et al. (C. R. Acad. Sci. Paris, Ser. I. 345:713–718, 2007). Furthermore, we investigate the vanishing volume fraction limit, which turns out to be consistent with the results in Bouchitté and Fragalà (Arch. Rat. Mech. Anal. 184:257–284, 2007; SIAM J. Control Optim. 46:1664–1682, 2007). Finally, some explicit computation of optimal plates are given.     

Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size

This paper discusses the droplet imaging velocimeter and sizer (DIVAS), a two-dimensional technique to measure droplet size from very small droplets (a few microns) to very large drops (millimeters), as well as droplet velocity and concentration. DIVAS uses a particle imaging velocimetry (PIV) configuration; that is, pulsed lasers illuminate the droplets in the measurement plane and CCD cameras collect the off-axis scattered light, thus yielding a small measurement volume and correspondingly a high number density measurement capability. DIVAS is based on glare point imaging as described by van de Hulst and Wang (Appl Opt 30(33):4755–4763, 1991). By measuring the separation of cross-polarized glare points, DIVAS is capable of measuring droplet size down to a few microns with sub-pixel resolution. The measurement of large drops from the separation of glare points is straightforward. However, the paper discusses that large drops are often non-spherical and more advanced signal processing is required to retrieve their size. Both analytical studies and experiments are presented to demonstrate the feasibility of the technique.     

Invariant Measures for Dissipative Systems and Generalised Banach Limits

Inspired by a theory due to Foias and coworkers (see, for example, Foias et al. Navier–Stokes equations and turbulence, Cambridge University Press, Cambridge, 2001) and recent work of Wang (Disc Cont Dyn Sys 23:521–540, 2009), we show that the generalised Banach limit can be used to construct invariant measures for continuous dynamical systems on metric spaces that have compact attracting sets, taking limits evaluated along individual trajectories. We also show that if the space is a reflexive separable Banach space, or if the dynamical system has a compact absorbing set, then rather than taking limits evaluated along individual trajectories, we can take an ensemble of initial conditions: the generalised Banach limit can be used to construct an invariant measure based on an arbitrary initial probability measure, and any invariant measure can be obtained in this way. We thus propose an alternative to the classical Krylov–Bogoliubov construction, which we show is also applicable in this situation.     

Rice Local Phase Angle Study for a Delamination Problem Between a Shape Memory Alloy and an Elastic Material

The present study is an extension of a recent paper of Freed et al. (J Mech Phys Solids 56:3003–3020, 2008). The final aim is to describe the transformation toughening behavior of a static crack along an interface between a shape memory alloy (SMA) and a linear elastic isotropic material. With an SMA as an equivalent Huber–Von Mises stress model (hypothesis of symmetric behavior between tension and compression), Freed et al. determine the initiation (ending) phase transformation yield surfaces in terms of the local phase angle introduced by Rice et al. (Metal ceramic interfaces, Pergamon Press, New York, pp 269–294, 1990). In this paper we give the general framework to determine this angle for a model integrating the asymmetry between tension and compression (experimentally measured: Vacher and Lexcellent in Proc ICM 6:231–236, 1991; Orgéas and Favier in Acta Mater 46(15):5579–5591, 2000), the Huber–Von Mises model being only a particular case. We demonstrate the local phase angle existence in an appropriate framing domain and give a sufficient hypothesis for its uniqueness and an algorithm to obtain it. Estimates are obtained in terms of physical quantities such as the Young modulus ratio, the bimaterial Poisson modulus values and also the choice of the yield loading functions. Finally, we illustrate this theoretical study by an application linking the asymmetry intensity on the width and the shape on predicted phase transformation surfaces and by a comparison with the symmetric case.     

Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Nonlinear rheological properties and stability of dibenzylidene sorbitol fiber networks in poly(propylene oxide)

Dibenzylidene sorbitol (DBS) is known to gel organic liquids and polymers such as poly(propylene oxide) (PPO) by forming long fibers and fiber networks. Potential applications of these networks depend on their ability to withstand large deformations without significant morphological changes. Therefore, we studied the nonlinear rheological properties of the DBS fiber network in PPO for different DBS concentrations. We found that the concentration dependence of critical deformation (transition from linear to nonlinear viscoelastic region) and gel strength (G′ plateau in the linear region) can be explained on the basis of a model for densely cross-linked fiber gels (MacKintosh et al., Phys Rev Lett 75:4425–4428, 1995). Performing periodic strain sweeps, we found that the decrease in gel strength during the deformation cycles can be ascribed to reversible fiber coarsening. Additionally, start-up experiments showed a strong shear thinning behavior, which is in quantitative agreement with the SGM model (Sollich, Phys Rev E 58:738–759, 1998).     

Strong-contrast expansion correlation approximations for the effective elastic moduli of multiphase composites

Following the previous approach of Pham and Torquato (J Appl Phys 94:6591–6602, 2003) and Torquato (J Mech Phys Solids 45:1421–1448, 1997; Random heterogeneous media, Springer, Berlin, 2002), we derive the strong-contrast expansions for the effective elastic moduli K _e,G _e of d-dimensional multiphase composites. The series consists of a principal reference part and a fluctuation part (perturbation about a homogeneous reference or comparison material), which contains multi-point correlation functions that characterize the microstructure of the composite. We propose a three-point correlation approximation for the fluctuation part with an objective choice of the reference phase moduli, such that the fluctuation terms vanish. That results in the approximations for the effective elastic moduli of isotropic composites, which coincide with the well-known self-consistent and Maxwell approximations for two-phase composites having respective microstructures. Applications to some two-phase materials are given.     

Velocity profiles and interface instability in a two-phase fluid: investigations using ultrasonic velocity profiler

In the present study the velocity profiles and the instability at the interface of a two phase water-oil fluid were investigated. The main aim of the research project was to investigate the instability mechanisms that can cause the failure of an oil spill barrier. Such mechanisms have been studied before for a vast variety of conditions (Wicks in Fluid dynamics of floating oil containment by mechanical barriers in the presence of water currents. In: Conference on prevention and control of oil spills, pp 55–106, 1969; Fannelop in Appl Ocean Res 5(2):80–92, 1983; Lee and Kang in Spill Sci Technol Bull 4(4):257–266, 1997; Fang and Johnston in J Waterway Port Coast Ocean Eng ASCE 127(4):234–239, 2001; among others). Although the velocity field in the region behind the barrier can influence the failure significantly, it had not been measured and analyzed precisely. In the present study the velocity profiles in the vicinity of different barriers were studied. To undertake the experiments, an oil layer was contained over the surface of flowing water by means of a barrier in a laboratory flume. The ultrasonic velocity profiler method was used to measure velocity profiles in each phase and to detect the oil–water interface. The effect of the barrier geometry on velocity profiles was studied. It was determined that the contained oil slick, although similar to a gravity current, can not be considered as a gravity current. The oil–water interface, derived from ultrasonic echo, was used to find the velocity profile in each fluid. Finally it was shown that the fluctuations at the rearward side of the oil slick head are due to Kelvin–Helmholtz instabilities.     

Elastic Constants Determination and Deformation Observation Using Brazilian Disk Geometry

Brazilian disk compression has been proposed as an alternative for measuring elastic constants of brittle solids with very low tensile strength (Hondros, Aust J Appl Sci 10:243–268, 1959). Subsequently however, the Brazilian disk geometry was mainly used for measuring fracture toughness and tensile strength of brittle materials, like rocks and concretes. In this study, we revisit the Brazilian disk specimen as a tool for determining elastic constants and for observing the deformation process up to failure. We used the optical digital image correlation (DIC) technique to obtain the displacement field on the specimen surface and proposed a scheme for determining the elastic constants from the measured displacement field and the applied load. Details of the elastic constant determination of a homogeneous material, epoxy resin, were presented. Comparison of the elastic constant measured using Brazilian disk with those obtained through more conventional means was carried out. We also present observations of the deformation evolution of the epoxy resin disk subjected to large nonlinear deformation up to failure and subjected to compressive loading and unloading.     

Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows

Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Re _λ between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)³. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation ε in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other. The high Reynolds number version of the k-ε-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does. In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles of the kinetic energy k and the dissipation ε. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138, 2008), is used to examine the Menter–Egorov ε model equation. An expression for the evolution of ε is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which with increasing Reynolds number approach the empirical values.     

Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application

This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435–457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249–275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler–Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375–413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647–667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001–1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima–Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.     

A numerical simulation of external heat transfer around turbine blades

External heat transfer prediction is performed in two-dimensional turbine blade cascades using the Reynolds-averaged Navier–Stokes equations. For this purpose, six different turbulence models including the algebraic Baldwin–Lomax (AIAA paper 78-257, 1978), three low-Re k−ɛ models (Chien in AIAA J 20:33–38, 1982; Launder and Sharma in Lett Heat Mass Transf 1(2):131–138, 1974; Biswas and Fukuyama in J Turbomach 116:765–773, 1994), and two k−ω models (Wilcox in AIAA J 32(2):247–255, 1994) are taken into account. The computer code developed employs a finite volume method to solve governing equations based on an explicit time marching approach with capability to simulate subsonic, transonic and supersonic flows. The Roe method is used to decompose the inviscid fluxes and the gradient theorem to decompose viscous fluxes. The performance of different turbulence models in prediction of heat transfer is examined. To do so, the effect of Reynolds and Mach numbers along with the turbulent intensity are taken into account, and the numerical results obtained are compared with the experimental data available.