Numerical investigation of injection-induced electro-convection in a dielectric liquid between two eccentric cylinders

Numerical analysis of the 2D radial and azimuth electro-convection (EC) flow of dielectric liquid between two eccentric cylindrical electrodes driven by unipolar injection of ions is presented. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow instability is studied in various scenarios where the radius ratio Γ = R_i/R_o ranges between 0.1 and 0.7 and the eccentricity η between 0.1 and 0.5. The bifurcation of the flow patterns depends on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the two geometric parameters Γ and η. For an increasing T, the EC system develops from a weak steady convective state to chaos via different intermediate states experiencing pitchfork and Hopf bifurcations. The influence of Γ and η on the bifurcation behavior is also investigated. When Γ lies between 0.1 and 0.3, a novel periodic oscillation of the flow patterns has been observed.     

Correlation mechanism of friction behavior and topological properties of the contact network during powder compaction

The effect of friction behavior on the compacted density is significant, but the relationship between the topological properties of the contact network and friction behavior during powder compaction remains unclear. Based on the discrete element method (DEM), a DEM model for die compaction was established, and the Hertz contact model was modified into an elastoplastic contact model that was more suitable for metal-powder compaction. The evolution of the topological properties of the contact network and its mechanism during powder compaction was explored using the elastoplastic contact model. The results demonstrate that the friction behavior between the particles is closely related to the topological properties of the contact network. Side wall friction results in smaller clustering coefficient (CC) and excess contact (EC) in the lower region near the side wall. Corresponding to this phenomenon, the upper region near the side wall has more high-stress particles when the major principal stress threshold was considered, and the CC and EC are significantly higher than those in the other regions. This study provides a theoretical basis for improving powder compaction behavior.     

The role of solvent viscosity in dilute-solution polymer rheology

Capillary viscometry was performed on dilute non-Newtonian solutions of monodisperse polystyrene in theta solvents. The solvents, blends of low-molecular-weight polystyrene with styrene, had viscosities (η_s) that were varied from 0.22–27 Pa s. Data reduction of the dilute limit, [η]/[η₀] vs. β = [η₀]η_sM$\text{γ}\text{?}$/RT (where $\text{γ}\text{?}$ is shear rate) revealed a parametric dependence on η_s that has not before been reported and is not predicted by most molecular theories of polymer dynamics. It is suggested that an internal viscosity model can explain such a phenomenon.     

Youngs modulus interpreted from plane compressions of geomaterials between rough end blocks

This note derives an approximate expression of the true Youngs modulus of a rectangular solid under plane compression between two rough end blocks, provided that the Poissons ratio ν of the solid is known. The friction between the loading platens and the ends of the specimen is assumed to be large enough to restrain slippage at the contact. By using the function space concept of Prager and Synge (1947) , a correction factor λ with calculable error is obtained which can be multiplied to the apparent Youngs modulus (i.e., the one obtained by assuming uniform stress field) to yield the true Youngs modulus; it is evaluated numerically for 0 ⩽ ν ⩽ 0.49 and 0 ⩽ η ⩽ 3 (where η = b⧸h with b and h being the half width and half length of the specimen) . In general, λ increases with ν and η for both plane strain and plane stress compressions. Within this range of ν and η, λ may vary from 0.37–1.0 for the plane strain case and from 0.84–1.0 for the plane stress case. Thus, the assumption of uniform stress field may lead to erroneous interpretation of the Youngs modulus. When the special case of ν = 1⧸3 and η = 1 is considered, we obtain λ = 0.9356, which compares well with 0.9359 obtained by Greenberg and Truell, 1948 .     

Dissipative interface waves and the transient response of a three-dimensional sliding interface with Coulomb friction

We investigate the linearized response of two elastic half-spaces sliding past one another with constant Coulomb friction to small three-dimensional perturbations. Starting with the assumption that friction always opposes slip velocity, we derive a set of linearized boundary conditions relating perturbations of shear traction to slip velocity. Friction introduces an effective viscosity transverse to the direction of the original sliding, but offers no additional resistance to slip aligned with the original sliding direction. The amplitude of transverse slip depends on a nondimensional parameter η=c_sτ₀/μv₀, where τ₀ is the initial shear stress, 2v₀ is the initial slip velocity, μ is the shear modulus, and c_s is the shear wave speed. As η→0, the transverse shear traction becomes negligible, and we find an azimuthally symmetric Rayleigh wave trapped along the interface. As η→∞, the inplane and antiplane wavesystems frictionally couple into an interface wave with a velocity that is directionally dependent, increasing from the Rayleigh speed in the direction of initial sliding up to the shear wave speed in the transverse direction. Except in these frictional limits and the specialization to two-dimensional inplane geometry, the interface waves are dissipative. In addition to forward and backward propagating interface waves, we find that for η>1, a third solution to the dispersion relation appears, corresponding to a damped standing wave mode. For large-amplitude perturbations, the interface becomes isotropically dissipative. The behavior resembles the frictionless response in the extremely strong perturbation limit, except that the waves are damped. We extend the linearized analysis by presenting analytical solutions for the transient response of the medium to both line and point sources on the interface. The resulting self-similar slip pulses consist of the interface waves and head waves, and help explain the transmission of forces across fracture surfaces. Furthermore, we suggest that the η→∞ limit describes the sliding interface behind the crack edge for shear fracture problems in which the absolute level of sliding friction is much larger than any interfacial stress changes.     

Transient shear flow behavior of concentrated long glass fiber suspensions in a sliding plate rheometer

In order to eventually predict the behavior of long fiber suspensions in complex flows commonly found in processing operations, it is necessary to understand their rheology and its connection to the evolution of fiber orientation and configuration in well defined flows. In this paper we report the transient behavior at the startup of shear flow of a polymer melt containing long glass fibers with a length (L) >1 mm, using a sliding plate rheometer (SPR). The operation of the SPR was confirmed by comparing the transient shear viscosity (η⁺) for a polymer melt and a melt containing short glass fibers (L < 1 mm) with measurements obtained from a cone-and-plate device, using a modified sample geometry that was designed to avoid wall effects. For the long fiber systems, measurements could only be obtained in the SPR because these systems would not stay within the gap of the rotational rheometer. Transient stress growth behavior of the long fiber systems was obtained as a function of shear rate and fiber concentration for samples prepared with three different initial orientations. Results showed that, unlike short fiber systems (with a random planar initial orientation) that usually exhibit a single overshoot peak followed by a steady state, η⁺ of the long fiber suspensions often passed through multiple transient regions, depending on the fiber concentration and applied shear rate. Additionally, η⁺ of the long fiber suspensions was found to be highly dependent on the initial orientation of the sheared samples. Finally, the initial and final fiber orientations of the long glass fiber samples were measured and used to initiate an explanation of the viscosity behavior. The results obtained in this research will be useful for future assessment of a quantitative correlation between transient rheology and the evolution of fiber orientation.     

Evaluation of particle packing models by comparing with published test results

The existing particle packing density models each with two or more parameters accounting for certain particle interactions (the loosening effect parameter, wall effect parameter, wedging effect parameter, and compaction index, denoted by a, b, c, and K, respectively) may be classified into the 2-parameter model (with a and b incorporated), the compressible model (with a, b, and K incorporated), and the 3-parameter model (with a, b, and c incorporated). This paper evaluates these models by comparing their respective packing density predictions with the test results published in the literature. It was found that their accuracy varies with both the size ratio and volumetric fractions of the binary mix. In general, when the size ratio is larger than 0.65, all the packing models are sufficiently accurate. However, when the size ratio is smaller than 0.65, some of them become inaccurate and the errors tend to be larger at around the volumetric fractions giving maximum packing density. Relatively, the 3-parameter model is the most accurate and widely applicable.     

Experimental and Theoretical Analyses on the Density and Modulus Development of Concrete Under Continued Hydration

In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson's ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly,and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C-S-H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.     

On the duration of contact for the Hertzian impact of a spherical indenter on a Maxwell solid

An expression is derived for the duration of contact for a Hertzian impact of a spherical indenter on a Maxwell solid valid for ηT₀ ? 1. The result disagrees with a previous analysis. The expression is compared with numerical predictions of the contact duration in which empirical creep and relaxation functions were used.     

Measurement of Mechanical Properties of Soft Tissues In Vitro Under Controlled Tissue Hydration

Alterations in tissue hydration that accompany inflammation or chronic remodeling of the Extracellular Matrix (ECM) have significant impact on the biomechanics of vascular tissue in health and disease. Examination of tissue behavior under controlled hydration in vitro could be helpful in better understanding the effects of tissue water content on its mechanical properties where in vivo tissue conditioning could not be possible. This study explains a multistage experimental protocol that allows both to prepare the tissue specimens with specific water content and to measure their mechanical behavior while maintaining the water content constant during the laboratory experimentation. Stress relaxation behaviors of the bovine aortic specimens–extracted from native, collagen-denatured and elastin-isolated tissues–were obtained within a water content range of 100–400 %. Using this method, distinct relaxation behaviors were obtained from tissue specimens with changing ECM treatments and hydration levels. The relaxation behavior was found to conform to a 4-parameter linear-viscoelastic macromechanical model consisting of two Maxwell components in parallel. The macromechanical model was able to distinguish between the morphological mechanisms associated with ECM elastin and collagen.