A moving dislocation in a magneto–electro-elastic solid

This work considers the generalized plane problem of a moving dislocation in an anisotropic elastic medium with piezoelectric, piezomagnetic and magnetoelectric effects. The closed-form expressions for the elastic, electric and magnetic fields are obtained using the extended Stroh formalism for steady-state motion. The radial components, E_rand H_r, of the electric and magnetic fields as well as the hoop components, D_θ and B_θ, of electric displacement and magnetic flux density are found to be independent of θ in a polar coordinate system. This interesting phenomenon is proven to be is a consequence of the electric and magnetic fields, electric displacement and magnetic flux density that exhibit the singularity r⁻¹ near the dislocation core. As an illustrative example, the more explicit results for a moving dislocation in a transversely isotropic magneto–electro-elastic medium are provided and the behavior of the coupled fields is analyzed in detail.     

Heat transfer to non-Newtonian flows over a cylinder in cross flow

Over a range of 102<Re^*<5800, 6.5<Pr^*<79, and 0.6<n<1, circumferential wall temperatures for water and aqueous polymer (purely viscous) solution flows over a smooth cylinder were measured experimentally. The cylinder was heated by passing direct electric current through it. Aqueous solutions of Carbopol 934 and EZ1 were used as power-law non-Newtonian fluids. The peripherally averaged heat transfer coefficient for purely viscous non-Newtonian fluids, at any fixed flow rate, decreases with increasing polymer concentration. A new correlation is proposed for predicting the peripherally averaged Nusselt number for power-law fluid flows over a heated cylinder in cross flow.     

The behaviour of field-responsive fluids during shear start-up

The application of an external field (magnetic or electric) to suspensions of particles in a carrier liquid often causes a dramatic increase in the flow resistance. The transient stress response of these systems during the start-up of shear flow was studied as a function of the shear rate, using a system of carbonyl iron particles dispersed in paraffinic spindle oil under magnetic flux densities up to 0.57 T. It was found that initially the stress increased in proportion to the applied strain, reaching a plateau value at a characteristic strain of 0.2. Similar strain dependence of the transient stress behaviour was observed for shear rates spanning the range 0.01 s^–1 to 10 s^–1, suggesting that strain-governed deformation and rupture of the particle aggregates in the fluid was the main contribution to the response. In addition, the steady state flow curves of these fluids were obtained over the shear rate range 0.1 to 100 s^–1.     

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a/c ≤ 1 and relative depths 0 ≤ a/t ≤ 0.8.     

The atomization of water–oil emulsions

The paper presents the results of experimental studies on atomization of the emulsions flowing through twin-fluid atomizers obtained by the use of the digital microphotography method. The main elements of the test installation were: nozzle, reservoir, pump and measurement units of liquid flow. The photographs were taken by a digital camera with automatic flash at exposure time of 1/8000 s and subsequently analyzed using Image Pro-Plus. The oils used were mineral oils 20–90, 20–70, 20–50 and 20–30. The studies were performed at flow rates of liquid phase changed from 0.0014 to 0.011 (dm³/s) and gas phase changed from 0.28 to 1.4 (dm³/s), respectively. The analysis of photos shows that the droplets being formed during the liquid atomization have very different sizes. The smallest droplets have diameters of the order of 10 μm. The experimental results showed that the changes in physical properties of a liquid phase lead to the significant changes in the spray characteristics. The analysis of the photos of water and emulsions atomization process showed that the droplet sizes are dependent on gas and liquid flow rates, construction of nozzle and properties of liquid. The differences between characteristics of atomization for water and emulsions have been observed. Analysis of photos on forming the droplets in air–water and air-emulsions systems showed that droplets are bigger in air-emulsion system (at the same value of gas to liquid mass ratio). The values of Sauter mean diameter (SMD) increased with increase of volume fraction of oil in emulsion. The droplet size increased with emulsion viscosity.     

Electric effects on the rheology of insulating oils in electrodes with flocked fabric

The rheological behavior of insulating oils is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabric. Although the oils show no electrorheological effects in uniform fields between metal electrodes with smooth surfaces, the flocked fabric leads to a striking increase of viscosity in steady shear. The viscosity enhancement increases with decreasing zero-field viscosity and decreasing conductivity of oils. In the limit of zero shear rate, the oils with low conductivity behave as solids with yield stress. When a very small quantity of fine particles is introduced into electrified oils without shear, a rapid and large-scale motion of particles is observed between the tips of fibers and the plate electrode. The local motion of fluids in high electric fields is referred to as electrohydrodynamic (EHD) convection. Periodic patterns of circulation flow are formed in static oils. The electric energy which is dissipated during the circulation motion contributes to holding the periodic flow in static oils. When the stress is very low, the periodic patterns are not broken down. The yield stress corresponds to the force required to rupture the domain structures of EHD convection. In shear fields, the additional energy may be required to change the periodic patterns of EHD convection. The striking increase of viscosity in steady shear can be attributed to the interactions between EHD convection and external shear. Received: 31 August 1998 Accepted: 17 February 1999     

Analysis of regular and irregular acoustic streaming patterns in a rectangular enclosure

This study reports an experimental investigation of the non-linear phenomena of regular (classical) and irregular streaming patterns generated in an air-filled rigid-walled square channel subjected to the acoustic standing waves of different frequencies and intensities. The interaction of acoustic waves and thermoviscous fluids is responsible for these phenomena. The resonator’s walls are maintained at isothermal condition. Synchronized particle image velocimetry (PIV) technique has been used to measure the streaming velocity fields. The experimental results show that at a given excitation frequency, regular streaming flow patterns are observed up to a certain value of the excitation amplitude. As the amplitude increases beyond this limit, the regular streaming is distorted to an irregular flow structure. The regular and irregular streaming are classified in terms of streaming Reynolds number . It is found that for Re_s2<50, classical streaming flow patterns are established and then deform to irregular and complex shapes as Re_s2 exceeds 50.     

Effects of electric fields and volume fraction on the rheology of hematite/silicone oil suspensions

Electrorheological (ER) fluids composed of iron(III) oxide (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. The dielectric properties of the suspensions were first studied in order to get information about the conductivity of the solid. Rheological tests under a.c. electric fields elucidated the influence of the electric field strength and volume fraction on the field-dependent yield stress. It was found that this quantity scales as a square power law in both cases. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The ER behaviour of the suspensions was analysed by considering the fundamental forces (of hydrodynamic and electrostatic origin) acting on the particles and it is found that, at a given volume fraction, all the dependencies of relative viscosity on shear rate and field strength can be described by a single function of the Mason number, Mn. Finally, two different chain models were used to explain the shear-thinning behaviour observed: rheological measurements showed a power-law dependence of relative viscosity decrease on the Mason number, _F~Mn, with –0.95.     

Stokes paradox for power-law flow around a cylinder

A simple analysis for power-law fluids shows that the Stokes paradox for creeping flow around a cylinder is removed for shear-thinning (n < 1) but not for shear-thickening (n 1) fluids. An approximate drag value is found for n < 1 and is compared with computed results.     

Rheological properties and dispersion stability of magnetorheological (MR) suspensions

In the present article, the rheological responses and dispersion stability of magnetorheological (MR) fluids were investigated experimentally. Suspensions of magnetite and carbonyl iron particles were prepared as model MR fluids. Under an external magnetic field (H ₀) and a steady shear flow, the yield stress depends upon H ₀ ^3/2. The Yield stress depended on the volume fraction of the particle (φ) linearly only at low concentration and increased faster at high fraction. Rheological behavior of MR fluids subjected to a small-strain oscillatory shear flow was investigated as a function of the strain amplitude, frequency, and the external magnetic field. In order to improve the stability of MR fluid, ferromagnetic Co-γ-Fe₂O₃ and CrO₂ particles were added as the stabilizing and thickening agent in the carbonyl iron suspension. Such needle-like particles seem to play a role in the steric repulsion between the relatively large carbonyl iron particles, resulting in improved stability against rapid sedimentation of dense iron particles. Furthermore, the additive-containing MR suspensions exhibited larger yield stress, especially at higher magnetic field strength. Received: 4 April 2000 Accepted: 6 November 2000     

Experimental investigations and numerical simulations for an open channel flow of a weak elastic polymer solution around a T-profile

The present paper is concerned with experimental and numerical investigations of planar complex flows of weak elastic polymer solutions (whose concentration are below the critical overlap concentration), characterised by small relaxation times (<0.1 s) and almost constant shear viscosities for small and medium shear rates. The main aim of the study is to detect to what extent a very small amount of elasticity present in a viscous fluid can influence its behaviour in complex flows, without introducing major modifications of classical rheological tests. The samples are polymer solutions of low PIB molecular weight dissolved in highly viscous Newtonian mineral oil. The analysed motion is steady, and takes place in an open channel around a T profile. Maximum values of the characteristic parameters for the experiments, the Reynolds and Weissenberg numbers, were 45 and 0.1, respectively. The experiments show a decrease of the wake length downstream the profile for weak elastic solutions in comparison to the Newtonian solvent. Actually, the same wake length as in the Newtonian case was obtained for tested polymer solutions, but at higher Re numbers. Numerical simulations using the Giesekus model predict the same behaviour and are consistent with experiments from both qualitative and quantitative point of views. The results of research conclude that, even in small amounts, the presence of elasticity in pure viscous liquids induces quantitative changes from Newtonian flow in complex dominant elongational flows, at elongational rates for which the sudden thickening of extensional viscosity is remarkable. The study is important, since it should enable better understanding and modelling of viscoelastic flows that involve dilute polymer solutions, or fluids with similar rheology; biofluid mechanics being one area of application of this research. Corroboration of experimental flow visualization with numerical simulation is currently a feasible method used to characterise weak elastic polymer solutions, since classical rheological techniques generally fail to obtain realistic values of relaxation time for these particular viscoelastic fluids. Corneliu Balan dedicates this paper to the anniversary of one hundred years from the birth of Academician Dumitru Dumitrescu (1904–1983), charismatic personality of the Romanian school of fluid mechanics.

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An appraisal of rheological models as applied to polymer melt flow

Summary An attempt is made at giving an appraisal of some representative rheological models of both differential and integral type, using the standard rheological measurements of six polymer melts. Experimental data obtained were the steady shear viscosity and the first normal stress difference by means of aWeissenberg rheogoniometer over the range of shear rates: 10^–2 ~ 10 sec^–1, and by means of aHan slit/capillary rheometer over the range of shear rates: 10 ~ 10³ sec^–1. Also measured by means of theWeissenberg rheogoniometer were the dynamic viscosity and dynamic elastic modulus over the range of frequencies: 0.3 × 10^–2 ~ 3 × 10² sec^–1. Rheological models chosen for an appraisal are theSpriggs 4-constant model, theMeister model, and theBogue model.It is found that the capability of the three models considered is about the same in their prediction of the rheological behavior of polymer melts in simple shearing flow. It is pointed out however that, due to the ensuing mathematical complexities, the usefulness of these models is limited to the study of flow problems associated with simple flow situations. Therefore, in analysing the complex flow situations often encountered with various polymer processings, the authors suggest use of the empirical models of the power-law type for both the viscosity and normal stress functions.With 11 figures, 4 schemas and 1 table     

Shear flow behavior of confined magnetorheological fluids at low magnetic field strengths

The non-linear properties of iron based magneto-rheological (MR) fluids are investigated at low magnetic field strengths (0–1.7 kA/m) and different gap thickness (0–500 m) in a plate-plate configuration. Single-width chain models qualitatively predict the low-shear flow behavior when plotting the field-specific viscosity, _F, as a function of the Mason number, Mn: a slope close to –1 is observed in log-log representations. Wall depletion effects are observed when the suspensions are sheared under the presence of low external magnetic fields applied and/or large gap distances. These results are correlated to frictional yield stress measurements and chain length distribution calculations in the presence of the external magnetic field. Finally, an equivalent slip layer thickness is calculated using the method of Yoshimura and Prudhomme.     

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ^∞ and electric field E^∞ or (σ^∞,E^∞) is replaced by strain ε^∞ and electric displacement D^∞ or (ε^∞,D^∞). Mixed conditions (σ^∞,D^∞) and (ε^∞,E^∞) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E_y^∞,σ_y^∞) for negative E_y^∞ and (D_y^∞,ε_y^∞) for positive D_y^∞ while the mechanical conditions σ_y^∞ or ε_y^∞ are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions

The overall objective is to present a procedure based on a Couette analogy to quantitatively analyse torque/rotor speed data and extract viscosity/shear-rate curves using a non-conventional geometry. Diphasic flows of energetic concentrated suspensions of melt-cast insensitive explosives exhibit particular rheological properties. The characterization of these complex fluids may be a challenging task when conventional rheometers are used. Placing these dense suspensions in a classic cylindrical geometry may lead to a partial destruction of the internal fluid structure. To prevent that, a “RheoXF” a mixer-type rheometer has been developed: it consists of a mixing device with quite a complex geometry rotating in a cylindrical tank. To evaluate the rheological constants (virtual radius, virtual shear rate and stress constants) of thus mixing rheometer, we used five Newtonian fluids. After this calibration, the rheological characterizations were carried out on five formulations. The unique parameter which changes in these formulations is the batch's origin of a secondary explosive: the 3-nitro-1,2,4-triazole-5-one. These energetic particles differ by their morphology, maximum packing density and may be by their process synthesis. After having determined pseudoplastic parameters, a correlation has been made with the evolution of maximum packing density values calculated with De Larrard model.     

Steady-shear viscosity and transient stress response for elasto-thixotropic fluids

A phenomenological model for dispersed systems which exhibit complex rheological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to different kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus functionG of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic ordersn=m=2.